**Light Transmission via Subwavelength Apertures in Metallic Thin Films**

V. A. G. Rivera, F. A. Ferri, O. B. Silva, F. W. A. Sobreira and E. Marega Jr.

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/50807

### **1. Introduction**

22 Will-be-set-by-IN-TECH

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The optical properties of subwavelength apertures in metallic films have been the focus of much research activity around the world since the extraordinary optical transmission (EOT) phenomenon was reported over a decade ago (Ebbesen et al., 1998).

EOT is an optical phenomenon in which a structure containing subwavelength apertures in an opaque screen transmits more light than might naively be expected on the basis of either ray optics or even knowledge of the transmission through individual apertures. The phenomenon was discovered serendipitously for two-dimensional (2D) periodic arrays of subwavelength holes in metals (Garcia-Vidal et al., 2010). Surprisingly, such arrays may, for certain wavelengths, exhibit transmission efficiencies normalized to the total area of the holes that exceed unity. In other words, for these wavelengths a periodic array of subwavelength holes transmits more light than a large macroscopic hole with the same area as the sum of all the small holes. The surprise is compounded by the fact that a single subwavelength aperture generally transmits light with an efficiency that is substantially below unity.

This remarkable transmission enhancement has potential applications in photolithography, near-field microscopy, and photonic devices (Lal et al., 2007). Although the detailed picture of the transmission enhancement is still being investigated, the excitation of surface plasmon-polaritons (SPPs) is proposed to be involved in the process (Weiner, 2009). Ever since the first experimental report on EOT through subwavelength apertures, considerable theoretical effort has been devoted to interpreting the essential physics of the process in slit arrays (Porto et al., 1999; Takahura, 2001; Xie et al., 2005). Experimental studies subsequent to the initial report were also performed, which demonstrated a number of surprising features. For instance, spectral transmission measurements (Lezec et al., 2004) revealed that suppression, as well as enhancement, was a characteristic property of slit arrays. Additionally, interferometric studies (Gay et al., 2006a, 2006b; Kalkum et al., 2007) showed

© 2012 Rivera et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### 158 Plasmonics – Principles and Applications

that the contribution of transient diffracted surface modes is as important as the SPP guided mode in the immediate vicinity of the subwavelength object. A more recent investigation (Pacifici et al., 2008) with the aim to confront the question of how transmission minima and maxima depend on array periodicity showed a minimum in transmission at slit separations equal to the wavelength of the SPP mode, and maxima occurring approximately at halfinteger multiples.

Light Transmission via Subwavelength Apertures in Metallic Thin Films 159

θ / krsinθ , where the

Kirchhoff scalar theory of light diffraction (Jackson, 1999). This theory is based on a scalar wave theory, and, thus, it does not take into account effects due to the polarization of light. In the case of normal incidence of light through a circular aperture, it is easy to show that the transmitted intensity (dI) per unit solid angle (dΩ) in the far-field region, also known as

incident intensity I0 is equally distributed on the aperture area πr2. The wavenumber of the incident light is k=2π/λ0, θ is the angle between the normal to the aperture and the direction of the emitted radiation, and J1(krsinθ) is the Bessel function of the first kind. The pattern described by this formula is the well known Airy pattern, composed by a central bright spot surrounded by concentric bright rings of decreasing intensity, caused by the interference of light rays originated inside the aperture (see Fig. 1). The ratio of the total transmitted intensity to I0, given by ( ) <sup>0</sup> T = I <sup>θ</sup> <sup>d</sup><sup>Ω</sup> / I , is called the transmission coeficient. For large

0 1 I θ ≅ I k r / 4 2J krsin π

Fraunhofer diffraction limit, is given by ( ) ( ) ( ) <sup>2</sup> 2 2

apertures, with r λ0, in which case the treatment is outlined here is valid, T ≈ 1.

**Figure 1.** Transmission of light through a circular aperture or radius r in an infinitely thin opaque screen

It has been proposed (Weiner, 2009) that the existence of surface waves such as SPPs are involved in the transmission process. For this reason, the regime of subwavelength apertures r λ0 is much more interesting, because near-field effects are expected to contribute dominantly in the transmission process. The problem arising here is that even in an approximate analysis of a perfectly conducting screen in the limit of zero width, we must use a vector description via Maxwell's equations. In Kirchhoff's method, the basic assumption is that the electromagnetic field in the aperture is the same as if the opaque screen is not present, a case which does not fulfil the boundary condition of zero tangential electric filed on the screen. For large holes, in which r λ0, this basic failure is less severe, because the diffracted fields are small when compared to the directly transmitted ones. Nevertheless, for subwavelength apertures this approximation is inadequate even in a first order treatment of the problem.

Assuming that the incident light intensity I0 is constant over the area of the aperture, Bethe and Bouwkamp arrived at an exact analytical solution for light transmission through a subwavelength circular hole in an ideal perfectly conducting and infinitely thin screen (Bethe, 1944; Bouwkamp, 1950a; Bouwkamp, 1950b). For normal incidence, the aperture can be described as a magnetic dipole located in the plane of the hole. The transmission coefficient

for an incident plane wave is then given by (Maier, 2007)

These previous studies focused attention on the properties of arrays fabricated in metallic films. It was already shown that a single slit is an interesting structure, since it combines the compactness of a single defect with the directionality of an array launcher. The extended dimension of the long axis imposes directionality on the transmitted light beam, the divergence of which can easily be controlled (Laluet et al., 2008). In a very recent investigation dealing with single subwavelength slits, it was possible to observe that the slit transmission is notably affected by the film thickness, and increases linearly with increasing slit width for a fixed film thickness (Ferri et al., 2011).

In this chapter, we selected some fundamental subjects of high and general interest involved in the phenomenon of light transmission via subwavelength apertures in metallic thin films. The manuscript will cover issues on both theory and experiment, such as (1) fabrication and measurement setup characteristics, (2) different materials and metallic structures, and (3) phenomena from the metallic film/dielectric interface. In addition, numerical simulations were performed in order to investigate the optical transmission through subwavelength apertures.

The paper is organized as follows. In Section 2, we comment on the classical theories of diffraction by subwavelength apertures. In Section 3, a rapid discussion about preceding experiments and interpretations are presented. In Section 4, we give a simple introduction to the plasmon-polariton. In Section 5, some characteristics of focused-ion beam (FIB) nanofabrication are presented. In this manner, the topics covered by the above mentioned sections are basically a compilation of information found in literature. In Section 6, we in fact demonstrate some applications made by our research group investigating the (1) influence of the metallic film thickness, as well as the (2) use of multilayered metallic thin films on the optical transmission through subwavelength slits. A short summary is provided in Section 7.

### **2. Diffraction by subwavelength apertures**

The wave nature of light implies modifications in the transmission through apertures like the phenomenon of diffraction. This common process, that even in simple geometries is very complex, have been extensively studied and many different models and approximations were developed based on the classical theory of diffraction (Jackson, 1999; Bouwkamp, 1954). Probably the simplest geometry, and maybe for this reason one that received the most attention, is that of a circular aperture with radius r in an infinitely thin and perfect conducting screen (Fig. 1).

If the radius r of the aperture is some orders of magnitude larger than the wavelength λ0 of the impinging radiation, i.e., r λ0, the problem can be treated with the Huygens-Fresnel principle and its mathematical formulation can be given as a good approaching by the Kirchhoff scalar theory of light diffraction (Jackson, 1999). This theory is based on a scalar wave theory, and, thus, it does not take into account effects due to the polarization of light. In the case of normal incidence of light through a circular aperture, it is easy to show that the transmitted intensity (dI) per unit solid angle (dΩ) in the far-field region, also known as Fraunhofer diffraction limit, is given by ( ) ( ) ( ) <sup>2</sup> 2 2 0 1 I θ ≅ I k r / 4 2J krsin π θ / krsinθ , where the incident intensity I0 is equally distributed on the aperture area πr2. The wavenumber of the incident light is k=2π/λ0, θ is the angle between the normal to the aperture and the direction of the emitted radiation, and J1(krsinθ) is the Bessel function of the first kind. The pattern described by this formula is the well known Airy pattern, composed by a central bright spot surrounded by concentric bright rings of decreasing intensity, caused by the interference of light rays originated inside the aperture (see Fig. 1). The ratio of the total transmitted intensity to I0, given by ( ) <sup>0</sup> T = I <sup>θ</sup> <sup>d</sup><sup>Ω</sup> / I , is called the transmission coeficient. For large apertures, with r λ0, in which case the treatment is outlined here is valid, T ≈ 1.

158 Plasmonics – Principles and Applications

slit width for a fixed film thickness (Ferri et al., 2011).

**2. Diffraction by subwavelength apertures** 

conducting screen (Fig. 1).

integer multiples.

that the contribution of transient diffracted surface modes is as important as the SPP guided mode in the immediate vicinity of the subwavelength object. A more recent investigation (Pacifici et al., 2008) with the aim to confront the question of how transmission minima and maxima depend on array periodicity showed a minimum in transmission at slit separations equal to the wavelength of the SPP mode, and maxima occurring approximately at half-

These previous studies focused attention on the properties of arrays fabricated in metallic films. It was already shown that a single slit is an interesting structure, since it combines the compactness of a single defect with the directionality of an array launcher. The extended dimension of the long axis imposes directionality on the transmitted light beam, the divergence of which can easily be controlled (Laluet et al., 2008). In a very recent investigation dealing with single subwavelength slits, it was possible to observe that the slit transmission is notably affected by the film thickness, and increases linearly with increasing

In this chapter, we selected some fundamental subjects of high and general interest involved in the phenomenon of light transmission via subwavelength apertures in metallic thin films. The manuscript will cover issues on both theory and experiment, such as (1) fabrication and measurement setup characteristics, (2) different materials and metallic structures, and (3) phenomena from the metallic film/dielectric interface. In addition, numerical simulations were performed in order to investigate the optical transmission through subwavelength apertures. The paper is organized as follows. In Section 2, we comment on the classical theories of diffraction by subwavelength apertures. In Section 3, a rapid discussion about preceding experiments and interpretations are presented. In Section 4, we give a simple introduction to the plasmon-polariton. In Section 5, some characteristics of focused-ion beam (FIB) nanofabrication are presented. In this manner, the topics covered by the above mentioned sections are basically a compilation of information found in literature. In Section 6, we in fact demonstrate some applications made by our research group investigating the (1) influence of the metallic film thickness, as well as the (2) use of multilayered metallic thin films on the optical transmission through subwavelength slits. A short summary is provided in Section 7.

The wave nature of light implies modifications in the transmission through apertures like the phenomenon of diffraction. This common process, that even in simple geometries is very complex, have been extensively studied and many different models and approximations were developed based on the classical theory of diffraction (Jackson, 1999; Bouwkamp, 1954). Probably the simplest geometry, and maybe for this reason one that received the most attention, is that of a circular aperture with radius r in an infinitely thin and perfect

If the radius r of the aperture is some orders of magnitude larger than the wavelength λ0 of the impinging radiation, i.e., r λ0, the problem can be treated with the Huygens-Fresnel principle and its mathematical formulation can be given as a good approaching by the

**Figure 1.** Transmission of light through a circular aperture or radius r in an infinitely thin opaque screen

It has been proposed (Weiner, 2009) that the existence of surface waves such as SPPs are involved in the transmission process. For this reason, the regime of subwavelength apertures r λ0 is much more interesting, because near-field effects are expected to contribute dominantly in the transmission process. The problem arising here is that even in an approximate analysis of a perfectly conducting screen in the limit of zero width, we must use a vector description via Maxwell's equations. In Kirchhoff's method, the basic assumption is that the electromagnetic field in the aperture is the same as if the opaque screen is not present, a case which does not fulfil the boundary condition of zero tangential electric filed on the screen. For large holes, in which r λ0, this basic failure is less severe, because the diffracted fields are small when compared to the directly transmitted ones. Nevertheless, for subwavelength apertures this approximation is inadequate even in a first order treatment of the problem.

Assuming that the incident light intensity I0 is constant over the area of the aperture, Bethe and Bouwkamp arrived at an exact analytical solution for light transmission through a subwavelength circular hole in an ideal perfectly conducting and infinitely thin screen (Bethe, 1944; Bouwkamp, 1950a; Bouwkamp, 1950b). For normal incidence, the aperture can be described as a magnetic dipole located in the plane of the hole. The transmission coefficient for an incident plane wave is then given by (Maier, 2007)

$$\text{T} = \frac{64}{27\,\text{m}^2} \text{(kr)}^4 \approx \left(\frac{\text{r}}{\lambda\_0}\right)^4 \tag{1}$$

Light Transmission via Subwavelength Apertures in Metallic Thin Films 161

(SP) waves supported by the periodic array structure in the metal film. The physics of SP waves shall be discussed in the next Section. About a year later Treacy suggested (Treacy, 1999) "dynamic diffraction" as another model to investigate the problem of light transmission through a periodic array of holes or slits. It was pointed out that the oscillation at frequency ω of the optical field would induce currents within the skin depth of the metal. The periodic structuring of holes in the metal gives rise to Bloch modes of the E-M field induced in the metal within the skin depth and consistent with its periodicity. There will be an oscillating current associated to each of these Bloch modes. Then, Treacy invoked "interband scattering" as a way to distribute these energy among these Bloch modes and from there to the propagating modes and surface waves at the aperture exit. It was not exactly clarified how does this redistribution occurs, but Treacy suspected that the success of "dynamic diffraction" for interpreting X-ray scattering in crystals might be useful for the

understanding of light transmission through these new structures as well.

**Figure 2.** Left panel: schematic of the original spectral transmission experiments. A broadband, incoherent light source is spectrally filtered by a scanning spectrophotometer and focused onto an array of subwavelength structures (holes or slits). A charge-coupled device (CCD) camera records the transmission intensity through the structure as a function of wavelength of the input light (adapted from Weiner, 2009). Right panel: transmission spectrum from an array of holes in an Ag metal film evaporated onto a transparent substrate as reported by Ebbesen et al. Array periodicity: 900 nm, hole diameter: 150 nm, metal film thickness: 200 nm. The point indicated a0 marks the array periodicity

A much more complete presentation of dynamic diffraction was published two years later by Treacy (Treacy, 2002). In this work it was clarified the relation between this approach and earlier interpretations of transmission in terms of "resonant" excitation of SP waves. This pioneering paper pointed out the way forward by emphasizing critical factors in the proper analysis of the problem. The most important thing to observe is that Bloch modes are determined by the E-M field present on and below the metal surface where are placed the periodic structures. These modes obey the periodic boundary conditions of the structure independently of the wavelength of the incident light. The simplest case is that of a one dimensional (1D) structure, with arrays and/or grooves placed periodically. In this case the modes are parallel to the surface in the metal and in the dielectric media, and evanescently

There is a weak total transmission for a subwavelength aperture due to the scaling with (r/λ0)4, smaller by an amount of (r/λ0)2 compared to Kirchhoff's scalar theory. This scaling of T ∝ λ0<sup>−</sup>4 is in agreement with the theory of light scattering by small objects due to Rayleigh. The case described in Eq. (1) is that of normal light incidence with both transverse electric (TE) and transverse magnetic (TM) polarization. This is not the case when radiation is incident in the screen at another angle, in this case an additional electric dipole in the normal direction is needed to describe the different behaviour of the process. More radiation is transmitted for TM than for TE polarization in this case (Bethe, 1944).

There are two major approximations in the Bethe-Bouwkamp theory of light transmission through a circular aperture in a screen. The screen is said to be made of an ideal perfectly conducting screen, and so perfectly opaque to the transmission of radiation, and its thickness is taken to be infinitely small. One of these assumptions could be omitted by taking numerical simulations for the problem of screens with finite thickness (Maier, 2007). However, when discussing the transmission properties through real apertures, i.e., in real metals, the finite conductivity, and so the transmission, should be taken into account. The thin films used in optical experiments cannot be taken as perfectly opaque screens, and we could not employ the Bethe-Bouwkamp theory. On the other hand, if the film thickness is higher than some skin depths, that is, if we are dealing with a "thick" film, it could be taken as an opaque screen. It has been shown that for apertures fulfilling these conditions, localized surface plasmons have a significant influence in the transmission process (Degiron et al., 2004).

### **3. Early experiments and implications**

In the paper published by Ebbesen et al., it was affirmed the measurement of "transmission efficiency...orders of magnitude greater than predicted by standard aperture theory". A typical result obtained in the original experiments is shown in the right panel of Fig. 2. The figure shows the transmitted power as a function of the incident light wavelength λ through a circular aperture of radius r. The transmission intensity is normalized to the cross-sectional area of the hole A=πr2. Using the experimental parameters of the caption of Fig. 2, the efficiency predicted by Bethe theory, given by Eq. (1), is 0.34%, while the results obtained by Ebbesen et al. reported peak efficiencies of a factor more than two. In this case, the enhancement of light transmission over that expected by Bethe theory is about 600 times. In a following paper (Ghaemi et al., 1998) the same group reported peak transmission efficiencies "that are about 1000 times higher than that expected for subwavelength holes". To obtain an EOT it is plausible to say that would be necessary at least a three-order of magnitude increase over the predictions of Bethe formula.

It was proposed in these early reports that transmission enhancements were caused by a new phenomenon not taken into account in electromagnetic (E-M) vector field Bethe theory nor in the scalar diffraction Kirchhoff model: the resonant excitation of surface plasmons (SP) waves supported by the periodic array structure in the metal film. The physics of SP waves shall be discussed in the next Section. About a year later Treacy suggested (Treacy, 1999) "dynamic diffraction" as another model to investigate the problem of light transmission through a periodic array of holes or slits. It was pointed out that the oscillation at frequency ω of the optical field would induce currents within the skin depth of the metal. The periodic structuring of holes in the metal gives rise to Bloch modes of the E-M field induced in the metal within the skin depth and consistent with its periodicity. There will be an oscillating current associated to each of these Bloch modes. Then, Treacy invoked "interband scattering" as a way to distribute these energy among these Bloch modes and from there to the propagating modes and surface waves at the aperture exit. It was not exactly clarified how does this redistribution occurs, but Treacy suspected that the success of "dynamic diffraction" for interpreting X-ray scattering in crystals might be useful for the understanding of light transmission through these new structures as well.

160 Plasmonics – Principles and Applications

( )

There is a weak total transmission for a subwavelength aperture due to the scaling with (r/λ0)4, smaller by an amount of (r/λ0)2 compared to Kirchhoff's scalar theory. This scaling of T ∝ λ0<sup>−</sup>4 is in agreement with the theory of light scattering by small objects due to Rayleigh. The case described in Eq. (1) is that of normal light incidence with both transverse electric (TE) and transverse magnetic (TM) polarization. This is not the case when radiation is incident in the screen at another angle, in this case an additional electric dipole in the normal direction is needed to describe the different behaviour of the process. More radiation

There are two major approximations in the Bethe-Bouwkamp theory of light transmission through a circular aperture in a screen. The screen is said to be made of an ideal perfectly conducting screen, and so perfectly opaque to the transmission of radiation, and its thickness is taken to be infinitely small. One of these assumptions could be omitted by taking numerical simulations for the problem of screens with finite thickness (Maier, 2007). However, when discussing the transmission properties through real apertures, i.e., in real metals, the finite conductivity, and so the transmission, should be taken into account. The thin films used in optical experiments cannot be taken as perfectly opaque screens, and we could not employ the Bethe-Bouwkamp theory. On the other hand, if the film thickness is higher than some skin depths, that is, if we are dealing with a "thick" film, it could be taken as an opaque screen. It has been shown that for apertures fulfilling these conditions, localized surface plasmons have

In the paper published by Ebbesen et al., it was affirmed the measurement of "transmission efficiency...orders of magnitude greater than predicted by standard aperture theory". A typical result obtained in the original experiments is shown in the right panel of Fig. 2. The figure shows the transmitted power as a function of the incident light wavelength λ through a circular aperture of radius r. The transmission intensity is normalized to the cross-sectional

efficiency predicted by Bethe theory, given by Eq. (1), is 0.34%, while the results obtained by Ebbesen et al. reported peak efficiencies of a factor more than two. In this case, the enhancement of light transmission over that expected by Bethe theory is about 600 times. In a following paper (Ghaemi et al., 1998) the same group reported peak transmission efficiencies "that are about 1000 times higher than that expected for subwavelength holes". To obtain an EOT it is plausible to say that would be necessary at least a three-order of

It was proposed in these early reports that transmission enhancements were caused by a new phenomenon not taken into account in electromagnetic (E-M) vector field Bethe theory nor in the scalar diffraction Kirchhoff model: the resonant excitation of surface plasmons

r2. Using the experimental parameters of the caption of Fig. 2, the

<sup>64</sup> <sup>r</sup> T = kr

2

27π

is transmitted for TM than for TE polarization in this case (Bethe, 1944).

a significant influence in the transmission process (Degiron et al., 2004).

**3. Early experiments and implications** 

π

magnitude increase over the predictions of Bethe formula.

area of the hole A=

4

λ

4

(1)

0

 <sup>∝</sup> 

**Figure 2.** Left panel: schematic of the original spectral transmission experiments. A broadband, incoherent light source is spectrally filtered by a scanning spectrophotometer and focused onto an array of subwavelength structures (holes or slits). A charge-coupled device (CCD) camera records the transmission intensity through the structure as a function of wavelength of the input light (adapted from Weiner, 2009). Right panel: transmission spectrum from an array of holes in an Ag metal film evaporated onto a transparent substrate as reported by Ebbesen et al. Array periodicity: 900 nm, hole diameter: 150 nm, metal film thickness: 200 nm. The point indicated a0 marks the array periodicity

A much more complete presentation of dynamic diffraction was published two years later by Treacy (Treacy, 2002). In this work it was clarified the relation between this approach and earlier interpretations of transmission in terms of "resonant" excitation of SP waves. This pioneering paper pointed out the way forward by emphasizing critical factors in the proper analysis of the problem. The most important thing to observe is that Bloch modes are determined by the E-M field present on and below the metal surface where are placed the periodic structures. These modes obey the periodic boundary conditions of the structure independently of the wavelength of the incident light. The simplest case is that of a one dimensional (1D) structure, with arrays and/or grooves placed periodically. In this case the modes are parallel to the surface in the metal and in the dielectric media, and evanescently vanishing in the normal direction. In parallel to this there are propagating modes. These propagating modes are responsible for the transmission of light through the structures. The transmission of the E-M filed is defined by both, propagating and evanescent fields, as a result of linear combinations of Bloch modes.

### **4. Plasmon-polaritons**

It is important to stress here that metals play a more important role in plasmonics than dielectric media (Huang et al., 2007). In a metal, the optical as well as the electric properties are very different from dielectrics because of the existence of huge free electrons. These electrons have a fast response to varying fields leading to a different response than that in a dielectric media.

In the Drude model for free electrons, the dielectric constant is given by

$$\varepsilon\_{\rm m} = 1 - \frac{\omega\_{\rm p}^{\prime 2}}{\omega(\omega + i\gamma)}\tag{2}$$

Light Transmission via Subwavelength Apertures in Metallic Thin Films 163

Some features of the SPP propagation along these flat interfaces between a metal and a

It was discussed that SPP modes are the result of a coupling between the free electrons in the metal side and light (E-M field). The modes given by the dispersion relation in Eq. (3) are called TM modes. These are the only allowed modes, in the case of an interface between two non-magnetic media, and are characterized by a magnetic field normal to the propagation direction (in the left panel of Fig. 3 it is normal to the plane of the paper) and an electric filed that has components parallel (E//) and normal (E⊥) to the direction of propagation (the plane of the paper in Fig. 3). The ratio of the normal and parallel components of electric field inside the dielectric (E⊥/E//)d = m d ε /ε and inside the metal (E⊥/E//)m = d m - ε /ε shows that, inside the metal, as the electric field is almost completely concentrated in the direction of propagation, the free electrons present a movement of back and forth in the direction of

**Figure 3.** Plasmon-polariton modes associated with the metals. Left panel: SPP mode in a schematic view of infinite metal/dielectric interface. Right panel: dispersion relation of BPP and SPP modes. The dashed lines I and II denote the light dispersion ω = ck and ω d = ck/ ε , respectively. The frequency range between ωSP and ωP corresponds to a gap where the electromagnetic wave cannot propagate via

The SPP modes propagate along the interface between media with a larger propagation constant ( SPP 0 d k > k ε ), so the wavelength and propagation velocity are smaller than in vacuum. Taking into account that the metal permittivity still has a negative part, that is responsible for losses, the propagation of SPP is reduced to a finite value given by the

parts of metal permittivity, respectively. In visible and near-infrared region, LSPP can take values of several micrometers, as can be seen in Fig. 4, that shows the real and imaginary parts of permittivity for Au and Ag [Fig. 4(a)], and the propagation length for each of these

The confinement of SPP modes along the surface is characterized by its evanescent behaviour in either side of the interface, which happens because of the larger propagation constant. On the dielectric side there is a higher penetration of the E-M field, given by the

mε and "

<sup>m</sup>ε are the real and imaginary

SPP m 0 m d <sup>L</sup> <sup>≈</sup> <sup>ε</sup> /k ε ε , where '

dielectric, as summarized by Huang et al., are addressed in the following.

propagation. These are the electron density waves shown in Fig. 3.

either bulk or surface modes (Huang et al., 2007)

propagation length ' 2 " 3/2

media with an interface with air [Fig. 4(b)].

The constant ωP is called the bulk plasma frequency and is a constant that depends on the metal. The constant γ is associated to the scattering of electrons in the Drude model. In "good" metals, where the scattering process is reduced we can neglect the damping (γ = 0). For high frequencies the dielectric constant is positive and there are modes whose dispersion relation is given by 2 2 22 <sup>ω</sup> P = ω + c k . In this expression, c is the light velocity in vacuum. These modes are known as bulk plasmon-polaritons (BPPs) and are a result of the coupling between light and the free electrons in metals. For light at low frequencies, which is the case of visible light for metals, then ω < ωp, and light propagation is forbidden by the negative permittivity.

For the case of a metal, whose real part of permittivity is negative, light incident normally to the surface gives rise to evanescent modes. But even in metals, there are propagating modes in the surface of the metal, provided that the surface of the metal is interfaced with a dielectric (or vacuum). These modes are the so-called SPP waves mentioned before. A typical geometry for this kind of problem is a metal and a dielectric separated by an infinite plane surface, as shown in the left panel of Fig. 3. This surface wave is based on the coupling between the surface free charges along the metal and light. In this case, the dispersion relation is given by (Zayats et al., 2005):

$$\mathbf{k}\_{\rm SPP} = \frac{\alpha}{\mathbf{c}} \sqrt{\frac{\varepsilon\_{\rm m} \varepsilon\_{\rm d}}{\varepsilon\_{\rm m} + \varepsilon\_{\rm d}}} \tag{3}$$

Here, εd is the permittivity of dielectric. The condition for the propagation of the SPP is that kSPP is real. As the permittivity of metal is negative it is necessary that εm + εd < 0, in this case ω SP P d < ω ω≡ / 1 + ε , where ωSP is the surface plasmon frequency. The dispersion relation for the SPPs and BPPs are plotted schematically in the right panel of Fig. 3. The left panel of Fig. 3 shows the mechanism of how the surface plasmon propagates along the metal/dielectric surface.

Some features of the SPP propagation along these flat interfaces between a metal and a dielectric, as summarized by Huang et al., are addressed in the following.

162 Plasmonics – Principles and Applications

**4. Plasmon-polaritons** 

dielectric media.

result of linear combinations of Bloch modes.

relation is given by (Zayats et al., 2005):

metal/dielectric surface.

vanishing in the normal direction. In parallel to this there are propagating modes. These propagating modes are responsible for the transmission of light through the structures. The transmission of the E-M filed is defined by both, propagating and evanescent fields, as a

It is important to stress here that metals play a more important role in plasmonics than dielectric media (Huang et al., 2007). In a metal, the optical as well as the electric properties are very different from dielectrics because of the existence of huge free electrons. These electrons have a fast response to varying fields leading to a different response than that in a

> ( ) 2 P

> > m d

m d

c ε + ε

SPP

<sup>ω</sup> ε ε k =

Here, εd is the permittivity of dielectric. The condition for the propagation of the SPP is that kSPP is real. As the permittivity of metal is negative it is necessary that εm + εd < 0, in this case ω SP P d < ω ω≡ / 1 + ε , where ωSP is the surface plasmon frequency. The dispersion relation for the SPPs and BPPs are plotted schematically in the right panel of Fig. 3. The left panel of Fig. 3 shows the mechanism of how the surface plasmon propagates along the

(2)

(3)

ω

ω ω + iγ

The constant ωP is called the bulk plasma frequency and is a constant that depends on the metal. The constant γ is associated to the scattering of electrons in the Drude model. In "good" metals, where the scattering process is reduced we can neglect the damping (γ = 0). For high frequencies the dielectric constant is positive and there are modes whose dispersion relation is given by 2 2 22 <sup>ω</sup> P = ω + c k . In this expression, c is the light velocity in vacuum. These modes are known as bulk plasmon-polaritons (BPPs) and are a result of the coupling between light and the free electrons in metals. For light at low frequencies, which is the case of visible light for metals, then ω < ωp, and light propagation is forbidden by the negative permittivity. For the case of a metal, whose real part of permittivity is negative, light incident normally to the surface gives rise to evanescent modes. But even in metals, there are propagating modes in the surface of the metal, provided that the surface of the metal is interfaced with a dielectric (or vacuum). These modes are the so-called SPP waves mentioned before. A typical geometry for this kind of problem is a metal and a dielectric separated by an infinite plane surface, as shown in the left panel of Fig. 3. This surface wave is based on the coupling between the surface free charges along the metal and light. In this case, the dispersion

In the Drude model for free electrons, the dielectric constant is given by

m

ε = 1 -

It was discussed that SPP modes are the result of a coupling between the free electrons in the metal side and light (E-M field). The modes given by the dispersion relation in Eq. (3) are called TM modes. These are the only allowed modes, in the case of an interface between two non-magnetic media, and are characterized by a magnetic field normal to the propagation direction (in the left panel of Fig. 3 it is normal to the plane of the paper) and an electric filed that has components parallel (E//) and normal (E⊥) to the direction of propagation (the plane of the paper in Fig. 3). The ratio of the normal and parallel components of electric field inside the dielectric (E⊥/E//)d = m d ε /ε and inside the metal (E⊥/E//)m = d m - ε /ε shows that, inside the metal, as the electric field is almost completely concentrated in the direction of propagation, the free electrons present a movement of back and forth in the direction of propagation. These are the electron density waves shown in Fig. 3.

**Figure 3.** Plasmon-polariton modes associated with the metals. Left panel: SPP mode in a schematic view of infinite metal/dielectric interface. Right panel: dispersion relation of BPP and SPP modes. The dashed lines I and II denote the light dispersion ω = ck and ω d = ck/ ε , respectively. The frequency range between ωSP and ωP corresponds to a gap where the electromagnetic wave cannot propagate via either bulk or surface modes (Huang et al., 2007)

The SPP modes propagate along the interface between media with a larger propagation constant ( SPP 0 d k > k ε ), so the wavelength and propagation velocity are smaller than in vacuum. Taking into account that the metal permittivity still has a negative part, that is responsible for losses, the propagation of SPP is reduced to a finite value given by the propagation length ' 2 " 3/2 SPP m 0 m d <sup>L</sup> <sup>≈</sup> <sup>ε</sup> /k ε ε , where ' mε and " <sup>m</sup>ε are the real and imaginary parts of metal permittivity, respectively. In visible and near-infrared region, LSPP can take values of several micrometers, as can be seen in Fig. 4, that shows the real and imaginary parts of permittivity for Au and Ag [Fig. 4(a)], and the propagation length for each of these media with an interface with air [Fig. 4(b)].

The confinement of SPP modes along the surface is characterized by its evanescent behaviour in either side of the interface, which happens because of the larger propagation constant. On the dielectric side there is a higher penetration of the E-M field, given by the decaying length ' d m 0d δ ε ≈ /k ε . On the metal side, where the decaying length is ' m 0m δ ≈ 1/k ε , there is a higher confinement than in the dielectric side. The relation between these lengths δd/δm is about some tens. This is what is desired in practice. Moreover, there is a strong enhancement of the fields near the interface of the media.

Light Transmission via Subwavelength Apertures in Metallic Thin Films 165

polariton modes that are excited in particles with have dimensions much smaller than the E-M wavelength. A detailed discussion on this topic can be found in (Hutter et al., 2004).

Plasmonic structures can be obtained by many standard techniques, some of them are: optical lithography, electron-beam lithography, focused-ion beam (FIB) lithography, atomic layer deposition, soft lithography and template stripping (Lindquist et al., 2012). Taking into account that in the present work FIB lithography was extensively used, we will briefly discuss here only this fabrication technique. A comprehensive discussion of the other mentioned techniques (as well as FIB lithography) is very well presented in the work by Lindquist et al.

FIB lithography has been extensively used for direct fabrication of metallic nanostructures, by making patterns on substrates (Melngailis, 1987; Orloff et al., 1993; Langford et al., 2007). It can also be used for the deposition of various metals by using ion-beam induced deposition (Tao et al., 1990), for doping semiconductors (Melngailis, 1987; Moberlychan et al. 2007), and for preparing transmission electron microscope (TEM) samples (Reyntjens et al., 2001; Mayer, 2007). These methods proved to be very useful to make tests of device designs and geometries, fix masks or electrical traces, or to produce high-resolution ionbeam images, and have been an essential tool for the development of the field of plasmonics. FIBs impinging on a surface offer a very different form of nanopatterning compared with other conventional methods that use resist, exposure and development. In general, the accelerating potential of the ions is of tens of kilovolts, the current beams range from many orders of magnitude, from picoamps to several nanoamps. Depending on the column optics, ion source and beam current, the beam spot sizes can range from ~ 5 nm up to a micrometer. Numerous ion species can be used in the setup, such as Al, Au, B, Be, Cu, Ga, Ge, Fe, In, Li, P, Pb and Si, the most commonly used being the semiconductor dopants (Melngailis, 1987; Orloff et al., 1993). In particular, Ga is widely used due to its low melting temperature

The FIB system is based on a liquid-metal ion source which is used to produce a smaller and brighter ion beam (Volkert et al., 2007). A metal source is heated up, such that it flows down and wets a sharp tungsten needle. An extraction voltage applied between the metal source and an extraction aperture forces the liquid metal to be pulled into an extremely sharp "Taylor–Gilbert" cone (Volkert et al., 2007; Forbes et al., 1996). The balance between the electrostatic force produced by the extraction voltage and the surface tension forces in the liquid (Orloff et al., 1993), the liquid source can have a tip size on the order of several nanometers (Melngailis, 1987). Then, the ions are extracted from the tip of this cone by field emission. As opposed to e-beam imaging systems, the "lenses" used in FIB are electrostatic and not magnetic, this happens because the Lorentz force in heavy ions, as those used, is much smaller than in electrons with the same kinetic energy (Volkert et al., 2007). Some other similarities and differences in these two kind of systems is presented in Fig. 5(a). To make the patterns a fast beam blanker is used. In commercial systems many patterns can be drawn by using pre-fabricated CAD proprietary files or using options within the control

(30 °C), low volatility and low vapour pressure (Volkert et al., 2007).

**5. Focused-ion beam nanofabrication** 

**Figure 4.** (a) Real ' mε and imaginary " <sup>m</sup>ε parts of permittivity for Au and Ag as obtained using data from Palik, and the corresponding (b) Propagation length LSPP as a function of the wavelength. In this case it is considered an interface between metal and air, whose permittivity is taken to be unity

SPP modes cannot be excited directly by the incident light because of its larger propagation constant. Special techniques have been used (Zayats et al., 2005) to compensate the phase mismatch as well as the difference in the wavevectors. Some of these techniques employ, for example, prism coupling by attenuated total reflection and diffraction gratings. It is also possible to couple plasmons by near-field excitation with a near-field optical microscope. An efficient mode to excite SPP is a subwavelength hole or slit (Zayats et al., 2005; Yin et al., 2004; Lalanne et al., 2005), where the diffraction components can ensure momentum conservation. Because of its localized feature, a direct observation of SPP is very difficult. Some methods, like the observation by using near-field microscopy (Hecht et al., 1996) can be used for this purpose. It is also possible to map SPP modes by recording the scattered light from a metal surface (Bouhelier et al., 2001) prepared with structured nanoscale corrugations. Another method, called fluorescence imaging (Ditlbacher et al., 2002a), has been proposed and consists in a metal surface covered with fluorescent molecules which emit radiation with intensity proportional to the electric field. This method was successfully used to observe interference, beam splitting and reflection of SPP modes (Ditlbacher et al., 2002b).

It is also important to note that even in more complex cases of metal/dielectric interfaces, SPP modes can exist with some parallel characteristics. A good example is that of a thin metal film where the thickness is of the same order of the skin depth. In this case, the SPP modes excited in each of its surfaces couple together and give rise to the so-called longrange SPP modes (Sarid, 1981). There is also a current research interest in particle plasmonpolariton modes that are excited in particles with have dimensions much smaller than the E-M wavelength. A detailed discussion on this topic can be found in (Hutter et al., 2004).

### **5. Focused-ion beam nanofabrication**

164 Plasmonics – Principles and Applications

decaying length '

'

**Figure 4.** (a) Real '

**-360 -270 -180 -90 0** ε' **m**

ε''**<sup>m</sup>**

**Permittivity (**ε**)**

mε and imaginary "

λ **(**μ**m)**

**0.0 0.5 1.0 1.5 2.0 2.5 3.0**

beam splitting and reflection of SPP modes (Ditlbacher et al., 2002b).

d m 0d δ ε ≈ /k ε . On the metal side, where the decaying length is

 **Ag Au**

<sup>m</sup>ε parts of permittivity for Au and Ag as obtained using data

**0.0 0.5 1.0 1.5 2.0 2.5 3.0**

λ **(**μ**m)**

**(b)**

m 0m δ ≈ 1/k ε , there is a higher confinement than in the dielectric side. The relation between these lengths δd/δm is about some tens. This is what is desired in practice. Moreover,

from Palik, and the corresponding (b) Propagation length LSPP as a function of the wavelength. In this case it is considered an interface between metal and air, whose permittivity is taken to be unity

**0**

**200**

**400**

**LSPP (**μ**m)**

**600**

**800**

**1000**

SPP modes cannot be excited directly by the incident light because of its larger propagation constant. Special techniques have been used (Zayats et al., 2005) to compensate the phase mismatch as well as the difference in the wavevectors. Some of these techniques employ, for example, prism coupling by attenuated total reflection and diffraction gratings. It is also possible to couple plasmons by near-field excitation with a near-field optical microscope. An efficient mode to excite SPP is a subwavelength hole or slit (Zayats et al., 2005; Yin et al., 2004; Lalanne et al., 2005), where the diffraction components can ensure momentum conservation. Because of its localized feature, a direct observation of SPP is very difficult. Some methods, like the observation by using near-field microscopy (Hecht et al., 1996) can be used for this purpose. It is also possible to map SPP modes by recording the scattered light from a metal surface (Bouhelier et al., 2001) prepared with structured nanoscale corrugations. Another method, called fluorescence imaging (Ditlbacher et al., 2002a), has been proposed and consists in a metal surface covered with fluorescent molecules which emit radiation with intensity proportional to the electric field. This method was successfully used to observe interference,

It is also important to note that even in more complex cases of metal/dielectric interfaces, SPP modes can exist with some parallel characteristics. A good example is that of a thin metal film where the thickness is of the same order of the skin depth. In this case, the SPP modes excited in each of its surfaces couple together and give rise to the so-called longrange SPP modes (Sarid, 1981). There is also a current research interest in particle plasmon-

there is a strong enhancement of the fields near the interface of the media.

 **Ag Au**

**(a)**

Plasmonic structures can be obtained by many standard techniques, some of them are: optical lithography, electron-beam lithography, focused-ion beam (FIB) lithography, atomic layer deposition, soft lithography and template stripping (Lindquist et al., 2012). Taking into account that in the present work FIB lithography was extensively used, we will briefly discuss here only this fabrication technique. A comprehensive discussion of the other mentioned techniques (as well as FIB lithography) is very well presented in the work by Lindquist et al.

FIB lithography has been extensively used for direct fabrication of metallic nanostructures, by making patterns on substrates (Melngailis, 1987; Orloff et al., 1993; Langford et al., 2007). It can also be used for the deposition of various metals by using ion-beam induced deposition (Tao et al., 1990), for doping semiconductors (Melngailis, 1987; Moberlychan et al. 2007), and for preparing transmission electron microscope (TEM) samples (Reyntjens et al., 2001; Mayer, 2007). These methods proved to be very useful to make tests of device designs and geometries, fix masks or electrical traces, or to produce high-resolution ionbeam images, and have been an essential tool for the development of the field of plasmonics.

FIBs impinging on a surface offer a very different form of nanopatterning compared with other conventional methods that use resist, exposure and development. In general, the accelerating potential of the ions is of tens of kilovolts, the current beams range from many orders of magnitude, from picoamps to several nanoamps. Depending on the column optics, ion source and beam current, the beam spot sizes can range from ~ 5 nm up to a micrometer. Numerous ion species can be used in the setup, such as Al, Au, B, Be, Cu, Ga, Ge, Fe, In, Li, P, Pb and Si, the most commonly used being the semiconductor dopants (Melngailis, 1987; Orloff et al., 1993). In particular, Ga is widely used due to its low melting temperature (30 °C), low volatility and low vapour pressure (Volkert et al., 2007).

The FIB system is based on a liquid-metal ion source which is used to produce a smaller and brighter ion beam (Volkert et al., 2007). A metal source is heated up, such that it flows down and wets a sharp tungsten needle. An extraction voltage applied between the metal source and an extraction aperture forces the liquid metal to be pulled into an extremely sharp "Taylor–Gilbert" cone (Volkert et al., 2007; Forbes et al., 1996). The balance between the electrostatic force produced by the extraction voltage and the surface tension forces in the liquid (Orloff et al., 1993), the liquid source can have a tip size on the order of several nanometers (Melngailis, 1987). Then, the ions are extracted from the tip of this cone by field emission. As opposed to e-beam imaging systems, the "lenses" used in FIB are electrostatic and not magnetic, this happens because the Lorentz force in heavy ions, as those used, is much smaller than in electrons with the same kinetic energy (Volkert et al., 2007). Some other similarities and differences in these two kind of systems is presented in Fig. 5(a). To make the patterns a fast beam blanker is used. In commercial systems many patterns can be drawn by using pre-fabricated CAD proprietary files or using options within the control software. The final size and the resolution of the focused beam can, in general, be affected by chromatic aberration, i.e., the energy dispersion of ions in the beam, but with a good approximation it can be regarded as a Gaussian profile. The minimum beam size is on the order of ~ 5 nm. A schematic view of the ion source is shown in Fig. 5(b).

Light Transmission via Subwavelength Apertures in Metallic Thin Films 167

whether the patterns designed were done in single of multiple steps, even with the same overall dose. Also, milling a trench with large total ion doses deviates from the Gaussian profile, giving an unexpectedly deep, V-shaped groove (Melngailis, 1987). The FIB milling process depends on many aspects such as the material to be patterned, ion-beam incident angle, redeposition of sputtered materials and even the crystal orientation, as outlined in Fig. 6. Grain orientation-dependent FIB sputtering can also lead to severe surface roughness on polycrystalline samples, however, care can be taken to produce well-defined structures

FIB can also be used for the deposition of various metals (such as W, Pt, C and Au) via sitespecific chemical vapour deposition (CVD), this can be done by using a gas injection system (GIS) (Volkert et al., 2007). A high-efficiency deposition can be achieved, with about 1 μm per minute accumulation rates, by adjusting the gas precursor flow rates and the ion-beam current density. The reaction of the ion beams with the precursor materials offers the ability to weld micromanipulators to specific parts of a substrate in situ. With subsequent FIB milling and thinning, those parts are cut free, and are often mounted to a TEM imaging grid (Mayer, 2007). A deficiency of this kind of system is that metals deposited via FIB have a high contamination by carbon. It can also be used other GIS systems, instead of depositing

FIB instruments offer many significant advantages, like a direct write, maskless, highresolution nanofabrication with the ability to sputter, image, analyse and deposit. It is possible to design 2D and 3D patterns (Langford et al., 2007). However, it has some limitations as a patterning tool, particularly for metals. FIB milling is a serial lithography technique, such as ebeam lithography, patterning only one spot or device at a time, unlike optical lithography that patterns the whole wafer with one short exposure. Large area patterning is not feasible. For high-resolution (< 100 nm) features, FIB milling can also be slow since very low currents (~ pA) must be used. Along with FIB-induced sample damage (Mayer, 2007), Ga ions are implanted at atomic fractions of 1–50% near the sample surface (Volkert et al., 2007). The plasmonic properties of the patterned metal films can be degraded is this process. For high surface roughness of metals the SPP propagation length can be strongly reduced (Lindquist et al., 2012). As such, the advantages and disadvantages of FIB milling need to be taken into account when fabricating new optical or electronic devices. When combined with a template stripping technique, many of these roughness and contamination issues are minimized, since FIB is then used to only pattern a reusable template, leaving the resulting metal films smooth and

**6. Applications: Optical transmission through subwavelength single slits** 

By focusing attention on the properties of arrays fabricated in metallic films with fixed thickness, some previous studies mentioned in Section 1 apparently missed the important

(Lindquist et al., 2012).

metals, to enhance the inherent FIB milling etch rate.

contamination-free (Lindquist et al., 2012).

**6.1. Influence of metallic film thickness** 

*6.1.1. Motivation* 

**Figure 5.** (a) Schematic view showing the similarities and differences between typical e-beam and FIB systems. (b) Scheme of the gallium liquid-metal source (Lindquist et al., 2012)

**Figure 6.** The crystal orientation of a sample can affect the FIB sputtering rates, shown in (a) and (b). (c) The sputtering rate is also affected by the mass of the atoms (orange atoms are more massive) and (d) by the local geometry of the sample (Lindquist et al., 2012). Original figure from Volkert et al.

In the process of milling a substrate by using FIB, many effects can be produced, with approximately one to five atoms removed per incident ion depending on the ion energy or substrate. It is even possible to displace atoms from their equilibrium positions, to induce chemical reactions and use the emerging electrons for imaging. The Gaussian profile of the beam is not the only factor that the shape of the milled groove depends (Melngailis, 1987). Redeposition and self-focusing effects can lead to large geometric differences depending on whether the patterns designed were done in single of multiple steps, even with the same overall dose. Also, milling a trench with large total ion doses deviates from the Gaussian profile, giving an unexpectedly deep, V-shaped groove (Melngailis, 1987). The FIB milling process depends on many aspects such as the material to be patterned, ion-beam incident angle, redeposition of sputtered materials and even the crystal orientation, as outlined in Fig. 6. Grain orientation-dependent FIB sputtering can also lead to severe surface roughness on polycrystalline samples, however, care can be taken to produce well-defined structures (Lindquist et al., 2012).

FIB can also be used for the deposition of various metals (such as W, Pt, C and Au) via sitespecific chemical vapour deposition (CVD), this can be done by using a gas injection system (GIS) (Volkert et al., 2007). A high-efficiency deposition can be achieved, with about 1 μm per minute accumulation rates, by adjusting the gas precursor flow rates and the ion-beam current density. The reaction of the ion beams with the precursor materials offers the ability to weld micromanipulators to specific parts of a substrate in situ. With subsequent FIB milling and thinning, those parts are cut free, and are often mounted to a TEM imaging grid (Mayer, 2007). A deficiency of this kind of system is that metals deposited via FIB have a high contamination by carbon. It can also be used other GIS systems, instead of depositing metals, to enhance the inherent FIB milling etch rate.

FIB instruments offer many significant advantages, like a direct write, maskless, highresolution nanofabrication with the ability to sputter, image, analyse and deposit. It is possible to design 2D and 3D patterns (Langford et al., 2007). However, it has some limitations as a patterning tool, particularly for metals. FIB milling is a serial lithography technique, such as ebeam lithography, patterning only one spot or device at a time, unlike optical lithography that patterns the whole wafer with one short exposure. Large area patterning is not feasible. For high-resolution (< 100 nm) features, FIB milling can also be slow since very low currents (~ pA) must be used. Along with FIB-induced sample damage (Mayer, 2007), Ga ions are implanted at atomic fractions of 1–50% near the sample surface (Volkert et al., 2007). The plasmonic properties of the patterned metal films can be degraded is this process. For high surface roughness of metals the SPP propagation length can be strongly reduced (Lindquist et al., 2012). As such, the advantages and disadvantages of FIB milling need to be taken into account when fabricating new optical or electronic devices. When combined with a template stripping technique, many of these roughness and contamination issues are minimized, since FIB is then used to only pattern a reusable template, leaving the resulting metal films smooth and contamination-free (Lindquist et al., 2012).

### **6. Applications: Optical transmission through subwavelength single slits**

#### **6.1. Influence of metallic film thickness**

#### *6.1.1. Motivation*

166 Plasmonics – Principles and Applications

software. The final size and the resolution of the focused beam can, in general, be affected by chromatic aberration, i.e., the energy dispersion of ions in the beam, but with a good approximation it can be regarded as a Gaussian profile. The minimum beam size is on the

**Figure 5.** (a) Schematic view showing the similarities and differences between typical e-beam and FIB

**Figure 6.** The crystal orientation of a sample can affect the FIB sputtering rates, shown in (a) and (b). (c) The sputtering rate is also affected by the mass of the atoms (orange atoms are more massive) and (d) by the local geometry of the sample (Lindquist et al., 2012). Original figure from Volkert et al.

In the process of milling a substrate by using FIB, many effects can be produced, with approximately one to five atoms removed per incident ion depending on the ion energy or substrate. It is even possible to displace atoms from their equilibrium positions, to induce chemical reactions and use the emerging electrons for imaging. The Gaussian profile of the beam is not the only factor that the shape of the milled groove depends (Melngailis, 1987). Redeposition and self-focusing effects can lead to large geometric differences depending on

order of ~ 5 nm. A schematic view of the ion source is shown in Fig. 5(b).

systems. (b) Scheme of the gallium liquid-metal source (Lindquist et al., 2012)

By focusing attention on the properties of arrays fabricated in metallic films with fixed thickness, some previous studies mentioned in Section 1 apparently missed the important

#### 168 Plasmonics – Principles and Applications

role played by the film thickness. For example, in the designing of surface-plasmon-based sensors, a proper choice of the thickness of the metallic film for the optimization of the device sensitivity is very important (Fontana, 2006). There are only a few theoretical (Xie et al., 2005; Fontana, 2006; Janssen et al., 2006) and experimental (Shou et al., 2005; Kim et al., 2006; Pang et al., 2007) investigations taking into account the influence of film thickness on the considered process. Therefore, the present studies are motivated by the necessity to understand the physics of this phenomenon and to develop optimum designs practices for subwavelength structure fabrication. We present here a systematic study of the optical transmission through subwavelength slits fabricated in Ag and Au film samples possessing different thicknesses. The influence of slit width was also considered. The present work deals with single slits. The extended dimension of the long axis imposes directionality on the transmitted light beam, the divergence of which can easily be controlled (Laluet et al., 2008). A slit is thus an interesting structure since it combines the compactness of a single defect with the directionality of an array launcher. Moreover, in order to remove measurement ambiguities existing in setups employing an incoherent and broadband light source dispersed through a scanning spectrophotometer, as shown in the left panel of Fig. 2, we have measured the transmission intensity through the slits using coherent and monochromatic spectral sources (Pacifici et al., 2008; Ferri et al., 2011).

Light Transmission via Subwavelength Apertures in Metallic Thin Films 169

**Figure 7.** Left panel shows a schematic of the optical transmission experiment. 488.0 nm (for Ag) and 632.8nm (for Au) Ar ion and HeNe laser light sources, respectively, are normally focused onto the sample surface by a 20× microscope objective lens. A CCD camera records the transmission intensity through the slits as the sample surface was stepped. Right panel shows a scanning electron micrograph (taken with 40000× magnification) of a typical structure. The considered slit has approximately 150 nm of width and was focused-ion-beam milled through a 200 nm thick Ag layer. In the experiments, the thicknesses of the Ag and Au films were varied in the range of 100–450 nm. The width is varied from 70

Fig. 8 shows the physical picture adopted in this work to investigate the light transmission through the subwavelength slits. The essential elements of the model, which describes a plasmonic damped wave with amplitude decreasing as the inverse of the film thickness (Gay et al., 2006b), are represented in the sketch of Fig. 8. Basically, an incident monochromatic light beam with wave vector k0 in air is linearly polarized perpendicular to the slit of subwavelength width w, milled in a metallic film with thickness t, and deposited

The far-field intensity enhancement for the single slits involves multiple coupling processes (see Fig. 8). Initially, the incident laser light generates SPs on the metal film. Because of vertical plasmon coupling, which depends on the film depth (t), surface charges are induced on the top metal film and simultaneously a strong electric field is generated inside the slit. Subsequently, an SPP mode (Maier, 2007), i.e., an electromagnetic excitation propagating at the interface between the dielectric and the metallic conductor, evanescently confined in the perpendicular direction, is generated on the metal film/BK7 interface. The SPP evanescent mode travels along the interface toward the slit, where it reconverts to a propagating wave and interferes with the travelling field directly transmitted through the slit. Additionally, penetration of the incident field inside the film enables the excitation of localized SP resonances (Maier, 2007) on the rim of the aperture, which contribute to the superposed

to 270 nm (Ferri et al., 2011)

*6.1.3. Results and discussion* 

on a dielectric substrate (BK7 glass).

#### *6.1.2. Experimental considerations*

A series of Ag films with thicknesses of 120, 160, 200, 270, and 330 nm and a set of Au samples with thicknesses of 120, 180, 260, 360, and 450 nm, as measured by a Talystep profilometer, were thermally evaporated onto BK7 glass substrates. Slits with widths in the range of approximately 70–150 nm in the Ag films, and 120–270 nm in the Au films, were milled with an FEI focused ion beam QUANTA 3D 200i (Ga+ ions, 30 keV). In order to verify the depth of the slits, the gallium ions' source was calibrated using atomic force microscopy. For example, the right panel of Fig. 7 shows a scanning electron micrograph of a slit with 150 nm of width fabricated in the 200 nm thick Ag film.

We have undertaken a series of high-resolution measurements of the optical transmission through the slits. The transmission measurement setup consists of 488.0 nm (for Ag) and 632.8 nm (for Au) wavelength light beams from Ar ion and HeNe lasers, respectively, with a power of about 1 µW, aligned to the optical axis of a microscope. The beam is focused at normal incidence onto the sample surface by a 20× microscope objective (with an NA of 0.4) in TM polarization (magnetic field component parallel to the long axis of the slits). Light intensity transmitted through each slit is then gathered by an optical fibre and detected with a CCD array detector. It was used on a multimode fibre with an NA of 0.22 and a core diameter of 200 µm. Light intensity is obtained by integrating the signal over the entire region of interest in the CCD image and subtracting the background originating from electronic noise. The transmitted intensity of every slit was recorded in the far-field by the CCD as the sample was stepped using an x-y translation stage. The left panel of Fig. 7 shows the schematic of the measurement setup.

**Figure 7.** Left panel shows a schematic of the optical transmission experiment. 488.0 nm (for Ag) and 632.8nm (for Au) Ar ion and HeNe laser light sources, respectively, are normally focused onto the sample surface by a 20× microscope objective lens. A CCD camera records the transmission intensity through the slits as the sample surface was stepped. Right panel shows a scanning electron micrograph (taken with 40000× magnification) of a typical structure. The considered slit has approximately 150 nm of width and was focused-ion-beam milled through a 200 nm thick Ag layer. In the experiments, the thicknesses of the Ag and Au films were varied in the range of 100–450 nm. The width is varied from 70 to 270 nm (Ferri et al., 2011)

#### *6.1.3. Results and discussion*

168 Plasmonics – Principles and Applications

*6.1.2. Experimental considerations* 

role played by the film thickness. For example, in the designing of surface-plasmon-based sensors, a proper choice of the thickness of the metallic film for the optimization of the device sensitivity is very important (Fontana, 2006). There are only a few theoretical (Xie et al., 2005; Fontana, 2006; Janssen et al., 2006) and experimental (Shou et al., 2005; Kim et al., 2006; Pang et al., 2007) investigations taking into account the influence of film thickness on the considered process. Therefore, the present studies are motivated by the necessity to understand the physics of this phenomenon and to develop optimum designs practices for subwavelength structure fabrication. We present here a systematic study of the optical transmission through subwavelength slits fabricated in Ag and Au film samples possessing different thicknesses. The influence of slit width was also considered. The present work deals with single slits. The extended dimension of the long axis imposes directionality on the transmitted light beam, the divergence of which can easily be controlled (Laluet et al., 2008). A slit is thus an interesting structure since it combines the compactness of a single defect with the directionality of an array launcher. Moreover, in order to remove measurement ambiguities existing in setups employing an incoherent and broadband light source dispersed through a scanning spectrophotometer, as shown in the left panel of Fig. 2, we have measured the transmission intensity through the slits using coherent and

A series of Ag films with thicknesses of 120, 160, 200, 270, and 330 nm and a set of Au samples with thicknesses of 120, 180, 260, 360, and 450 nm, as measured by a Talystep profilometer, were thermally evaporated onto BK7 glass substrates. Slits with widths in the range of approximately 70–150 nm in the Ag films, and 120–270 nm in the Au films, were milled with an FEI focused ion beam QUANTA 3D 200i (Ga+ ions, 30 keV). In order to verify the depth of the slits, the gallium ions' source was calibrated using atomic force microscopy. For example, the right panel of Fig. 7 shows a scanning electron micrograph of a slit with

We have undertaken a series of high-resolution measurements of the optical transmission through the slits. The transmission measurement setup consists of 488.0 nm (for Ag) and 632.8 nm (for Au) wavelength light beams from Ar ion and HeNe lasers, respectively, with a power of about 1 µW, aligned to the optical axis of a microscope. The beam is focused at normal incidence onto the sample surface by a 20× microscope objective (with an NA of 0.4) in TM polarization (magnetic field component parallel to the long axis of the slits). Light intensity transmitted through each slit is then gathered by an optical fibre and detected with a CCD array detector. It was used on a multimode fibre with an NA of 0.22 and a core diameter of 200 µm. Light intensity is obtained by integrating the signal over the entire region of interest in the CCD image and subtracting the background originating from electronic noise. The transmitted intensity of every slit was recorded in the far-field by the CCD as the sample was stepped using an x-y translation stage. The left panel of Fig. 7 shows

monochromatic spectral sources (Pacifici et al., 2008; Ferri et al., 2011).

150 nm of width fabricated in the 200 nm thick Ag film.

the schematic of the measurement setup.

Fig. 8 shows the physical picture adopted in this work to investigate the light transmission through the subwavelength slits. The essential elements of the model, which describes a plasmonic damped wave with amplitude decreasing as the inverse of the film thickness (Gay et al., 2006b), are represented in the sketch of Fig. 8. Basically, an incident monochromatic light beam with wave vector k0 in air is linearly polarized perpendicular to the slit of subwavelength width w, milled in a metallic film with thickness t, and deposited on a dielectric substrate (BK7 glass).

The far-field intensity enhancement for the single slits involves multiple coupling processes (see Fig. 8). Initially, the incident laser light generates SPs on the metal film. Because of vertical plasmon coupling, which depends on the film depth (t), surface charges are induced on the top metal film and simultaneously a strong electric field is generated inside the slit. Subsequently, an SPP mode (Maier, 2007), i.e., an electromagnetic excitation propagating at the interface between the dielectric and the metallic conductor, evanescently confined in the perpendicular direction, is generated on the metal film/BK7 interface. The SPP evanescent mode travels along the interface toward the slit, where it reconverts to a propagating wave and interferes with the travelling field directly transmitted through the slit. Additionally, penetration of the incident field inside the film enables the excitation of localized SP resonances (Maier, 2007) on the rim of the aperture, which contribute to the superposed output field. In this way, induced dipole moments at each rim form an "antenna coupling", which radiatively generate strong field enhancement (top and bottom). Then, the intensity of the resulting field can be written as

**Figure 8.** Illustration of the adopted model. A single frequency incoming plane wave with wave vector k0 in air is linearly polarized perpendicular to a slit of subwavelength width w, milled in a metallic film with thickness t deposited on a BK7 glass substrate. Here, kSPP is the wavevector of the SPP mode. (Ferri et al., 2011)

$$\mathbf{E} = \frac{\mathbf{E}\_0}{\pi} \frac{\mathbf{w}}{\mathbf{t}} \cos \left( \mathbf{k}\_{\rm SPP} \mathbf{t} + \frac{\pi}{2} \right) \tag{4}$$

Light Transmission via Subwavelength Apertures in Metallic Thin Films 171

amplitude of the magnetic H field (along the z direction). Figs. 9(b) and 9(c) shows the amplitude of the electric E field (in the y direction), with its vector representation in the x-y plane. Fig. 9(a) shows how the incident plane wave is modified by the existing subwavelength slit. It is possible to see that the considered wave is almost completely reflected from the unstructured part of the film. Around the slit entrance, the amplitude of the standing wave is markedly attenuated, where some lightwave transmission to the exit facet is apparent. On the dielectric/metal interface, a train of surface waves (SPPs) is evident together with waves propagating into space. In the rims, different charge configurations can be obtained, which can be symmetric or antisymmetrically coupled (Prodan et al., 2003). This coupling leads to determined charge configurations in each rim of the slit (top and bottom). From Figs. 9(b) and 9(c), these surface modes are clearly seen. It is possible to notice from the figures these resonances [antisymmetrically and symmetrically coupled in Figs. 9(b) and 9(c), respectively] on the facets of the slit. These modes are associated with localized SPs, which are nonpropagating excitations due to direct light illumination of the conduction electrons of the metallic nanostructure coupled to the electromagnetic field (Maier, 2007). A similar behaviour was observed in the simulations for Au films when

**Figure 9.** 2D numerical simulations of a 150 nm slit fabricated in an Ag film when illuminated by the line at 488.0 nm of an Ar ion laser. (a) Amplitude of the magnetic H field (along the z direction). (b) and (c) Amplitude of the electric E field (in the y direction), and its vector representation in the x-y plane. The value of the Ag film thickness in (a) and (b) is 120 nm, and in (c) is 270 nm. Length spans: (a) x = 4

µm and y = 2 µm, (b) and (c) x = 600 nm and y = 400 nm

where SPP SPP k = 2 / π λ , SPP λ = 2 /Re π β , 0 SPP <sup>β</sup> = k n , ( )1/2 SPP metal glass metal glass n = ε ε /ε + ε , and 0 0 k = 2 / π λ (Gay et al., 2006b; Pacifici et al., 2008; Maier, 2007). Here, E0 represents the electrical field of the incoming plane wave, where λ0 is its wavelength. Also, kSPP and λSPP are the wavevector and wavelength of the SPP, β is the propagation constant of the superposed travelling wave, and nSPP is the effective index of the SPP, which is for the interface between the metal and dielectric. In addition, εmetal and εglass are the dielectric permittivities of metal and glass, respectively, and are functions of the excitation wavelength. In this sense, εAg = - 7.89 + 0.74i and εglass = 2.31 are the tabulated dielectric constants of Ag and BK7 glass in the wavelength of 488.0 nm. In the same way, εAu = - 9.49 + 1.23i and εglass = 2.29 are the corresponding dielectric constants of Au and BK7 in 632.8 nm (Palik, 1985). Here it is important to point out that the wavelength values of 488.0 and 632.8 nm are known to be close to the plasmon excitation wavelength of Ag and Au, respectively. Increasing the metallic film thickness leads to decoupling of the top and bottom antenna.

For illustration purposes, Fig. 9 shows corresponding 2D numerical simulations carried out with Comsol Multiphysics® for TM-polarized waves for a 150 nm slit fabricated in an Ag film when illuminated by the line at 488.0 nm of an Ar ion laser. Fig. 9(a) shows the amplitude of the magnetic H field (along the z direction). Figs. 9(b) and 9(c) shows the amplitude of the electric E field (in the y direction), with its vector representation in the x-y plane. Fig. 9(a) shows how the incident plane wave is modified by the existing subwavelength slit. It is possible to see that the considered wave is almost completely reflected from the unstructured part of the film. Around the slit entrance, the amplitude of the standing wave is markedly attenuated, where some lightwave transmission to the exit facet is apparent. On the dielectric/metal interface, a train of surface waves (SPPs) is evident together with waves propagating into space. In the rims, different charge configurations can be obtained, which can be symmetric or antisymmetrically coupled (Prodan et al., 2003). This coupling leads to determined charge configurations in each rim of the slit (top and bottom). From Figs. 9(b) and 9(c), these surface modes are clearly seen. It is possible to notice from the figures these resonances [antisymmetrically and symmetrically coupled in Figs. 9(b) and 9(c), respectively] on the facets of the slit. These modes are associated with localized SPs, which are nonpropagating excitations due to direct light illumination of the conduction electrons of the metallic nanostructure coupled to the electromagnetic field (Maier, 2007). A similar behaviour was observed in the simulations for Au films when

170 Plasmonics – Principles and Applications

et al., 2011)

0 0 k = 2 / π

where SPP SPP k = 2 /

π

λ , SPP λ = 2 /Re

π

of the resulting field can be written as

output field. In this way, induced dipole moments at each rim form an "antenna coupling", which radiatively generate strong field enhancement (top and bottom). Then, the intensity

**Figure 8.** Illustration of the adopted model. A single frequency incoming plane wave with wave vector k0 in air is linearly polarized perpendicular to a slit of subwavelength width w, milled in a metallic film with thickness t deposited on a BK7 glass substrate. Here, kSPP is the wavevector of the SPP mode. (Ferri

<sup>E</sup> <sup>w</sup> E cos k t +

SPP

π

β , 0 SPP <sup>β</sup> = k n , ( )1/2

(4)

SPP metal glass metal glass n = ε ε /ε + ε , and

t 2

λ (Gay et al., 2006b; Pacifici et al., 2008; Maier, 2007). Here, E0 represents the

electrical field of the incoming plane wave, where λ0 is its wavelength. Also, kSPP and λSPP are the wavevector and wavelength of the SPP, β is the propagation constant of the superposed travelling wave, and nSPP is the effective index of the SPP, which is for the interface between the metal and dielectric. In addition, εmetal and εglass are the dielectric permittivities of metal and glass, respectively, and are functions of the excitation wavelength. In this sense, εAg = - 7.89 + 0.74i and εglass = 2.31 are the tabulated dielectric constants of Ag and BK7 glass in the wavelength of 488.0 nm. In the same way, εAu = - 9.49 + 1.23i and εglass = 2.29 are the corresponding dielectric constants of Au and BK7 in 632.8 nm (Palik, 1985). Here it is important to point out that the wavelength values of 488.0 and 632.8 nm are known to be close to the plasmon excitation wavelength of Ag and Au, respectively. Increasing the metallic film thickness leads to decoupling of the top and bottom antenna.

For illustration purposes, Fig. 9 shows corresponding 2D numerical simulations carried out with Comsol Multiphysics® for TM-polarized waves for a 150 nm slit fabricated in an Ag film when illuminated by the line at 488.0 nm of an Ar ion laser. Fig. 9(a) shows the

<sup>≈</sup>

0

π

**Figure 9.** 2D numerical simulations of a 150 nm slit fabricated in an Ag film when illuminated by the line at 488.0 nm of an Ar ion laser. (a) Amplitude of the magnetic H field (along the z direction). (b) and (c) Amplitude of the electric E field (in the y direction), and its vector representation in the x-y plane. The value of the Ag film thickness in (a) and (b) is 120 nm, and in (c) is 270 nm. Length spans: (a) x = 4 µm and y = 2 µm, (b) and (c) x = 600 nm and y = 400 nm

excited by the line at 632.8 nm of an HeNe laser. The main apparent difference is the lower transmitted intensity due to a higher absorption loss attributable to the particular characteristics of Au (Palik, 1985), i.e., Re[εAu] = - 9.49 in contrast to Re[εAg] = - 7.89. This is verified in Fig. 10, where it can be seen that the normalized transmission intensity for the Ag films is improved more than for the Au samples.

Light Transmission via Subwavelength Apertures in Metallic Thin Films 173

be simply explained for the present Ag and Au films. Therefore, when the film thickness is near half- or full-integer wavelengths of the guided mode within the slit "cavity", optimal

**Figure 10.** Theoretically estimated (lines) and experimental (symbols) normalized slit transmission intensities versus film thickness for the slits of the (a) 120, 160, 200, 270, and 330 nm thick Ag films, and the (b) 120, 180, 260, 360, and 450 nm thick Au samples. The dotted straight lines point out the thickness of the considered samples. The insets show the measured transmission versus slit width for some film thicknesses. Here, the dashed straight lines are linear fittings of the experimental points (Ferri et al.,

( ) -1

(6)

2sin 1/ f π

where ( )-2 f = 4R 1 - R is the finesse factor. Here, R is the reflectivity, given by R = 1 - T, where T is the transmission (Born et al., 1993). We determine from Fig. 10(a) for the Ag samples with 100 nm of slit width and thicknesses of 120, 160, 200, 270, and 330 nm, the reflectivities R = 0.73, 0.67, 0.46, 0.99, and 0.73, and the corresponding finesses F = 9.98, 7.74, 3.84, 312.58, and 9.89, respectively. From Fig. 10(b) for the Au samples with 120nm of slit width and thicknesses of 120, 180, 260, 360, and 450 nm, we determine the reflectivities R = 0.66, 0.99, 0.79, 0.98, and 0.91, and the resultant finesses F = 7.45, 312.58, 13.27, 155.49, and 33.29, respectively. Here it is important to point out that for an FP cavity, the definition of quality factor (Q factor) is equivalent to the finesse (Shyu et al., 2011). Therefore, we can clearly see that both the R and Q factor values are significantly affected by the film thickness for a fixed slit width. Also, it is interesting to notice that near-zero transmission is a sign of high reflectivity values and high Q

Finally, the fact that the transmission increases linearly with increasing slit width is in accordance with literature (Kihm et al., 2008), where it was observed that the far-field

We can apply an FP analysis to obtain the finesse F from Fig. 10, given by

F =

factors. For the maximum transmission points, a backward reasoning applies.

2011)

transmission is achieved, which implies a field enhancement inside the slit.

In general, the present numerical simulations qualitatively show appreciable light transmission through the slits. Actually, it was experimentally observed that the transmission sensitively depends on the metallic film thickness and slit width. As a first approximation, the theoretical slit transmission intensity can be given simply by the square modulus of Eq. (4). In this way, Fig. 10 plots as predicted [from Eq. (4)] and measured (using the setup shown in Fig. 7) transmission intensities as a function of the film thickness for the various slit widths milled in the Ag and Au samples. Also, the insets of Fig. 10 show the measured transmission versus slit width for certain film thicknesses. The relative slit transmission intensities are obtained by subtracting the background originating from the metal film and normalizing to the intensity from the wider slit structures. It is valuable to notice from Fig. 10 the very good correspondence between the theoretical estimate and the experiment. Therefore, taking into account the errors associated with the experimental determination of film thickness, slit width, and optical transmission intensities, it is possible to affirm that (1) the slits' transmission varies with metallic film thickness and presents a damped oscillatory behaviour as the film thickness increases, and (2) the transmission increases linearly with increasing slit width for a fixed metallic film thickness. Although the general behaviour is similar, distinct optical properties [see Fig. 4(a)] lead to perceptible differences in the transmitted intensity and the position of maxima and minima between the Ag and Au films.

To help in elucidating the first observation, it is valuable to note that Fabry–Perot (FP) resonances are expected to contribute to the enhanced transmission of subwavelength slit arrays (Porto et al., 1999; Takahura, 2001; Pang et al., 2007; Garcia-Vidal et al., 2002). In this way, FP modes related to the finite depth of the slits in the present films should give rise to transmission maxima at certain wavelengths (Garcia-Vidal et al., 2002). Actually, an accurate analysis recently published shows that the two maxima observed in Figs. 10(a) and 10(b) correspond to FP-like resonances within the slit volume for the first half-wave and full wave of the light within the slit (Weiner, 2011). In this sense, the FP multiple reflection effect within the slits leads to significant modulation of the transmission as a function of metal film thickness. These transmission maxima occur if the FP resonance condition is fulfilled (Li et al., 2009):

$$2\mathbf{k}\_0 \text{Re}\left[\frac{\lambda\_0}{\lambda\_{\text{SPP}}}\right]\mathbf{t} + \arg\left(\phi\_1 \phi\_2\right) = 2\mathbf{m}\_\chi \pi \tag{5}$$

where my (the FP mode) is an integer and φ1 and φ2 denote the phase of the reflection coefficients of the slit at the incident and output interfaces, respectively. Thus, the effect of slit depth on the transmission enhancement can be easily understood. When the incident wavelength and slit depth are satisfied by Eq. (5), a transmission maximum will occur. Furthermore, from Eq. (5), it is expected that the transmission under a certain incident wavelength has a period of λSPP/2 as a function of slit depth. The results of Fig. 10 can now be simply explained for the present Ag and Au films. Therefore, when the film thickness is near half- or full-integer wavelengths of the guided mode within the slit "cavity", optimal transmission is achieved, which implies a field enhancement inside the slit.

172 Plasmonics – Principles and Applications

films is improved more than for the Au samples.

maxima and minima between the Ag and Au films.

excited by the line at 632.8 nm of an HeNe laser. The main apparent difference is the lower transmitted intensity due to a higher absorption loss attributable to the particular characteristics of Au (Palik, 1985), i.e., Re[εAu] = - 9.49 in contrast to Re[εAg] = - 7.89. This is verified in Fig. 10, where it can be seen that the normalized transmission intensity for the Ag

In general, the present numerical simulations qualitatively show appreciable light transmission through the slits. Actually, it was experimentally observed that the transmission sensitively depends on the metallic film thickness and slit width. As a first approximation, the theoretical slit transmission intensity can be given simply by the square modulus of Eq. (4). In this way, Fig. 10 plots as predicted [from Eq. (4)] and measured (using the setup shown in Fig. 7) transmission intensities as a function of the film thickness for the various slit widths milled in the Ag and Au samples. Also, the insets of Fig. 10 show the measured transmission versus slit width for certain film thicknesses. The relative slit transmission intensities are obtained by subtracting the background originating from the metal film and normalizing to the intensity from the wider slit structures. It is valuable to notice from Fig. 10 the very good correspondence between the theoretical estimate and the experiment. Therefore, taking into account the errors associated with the experimental determination of film thickness, slit width, and optical transmission intensities, it is possible to affirm that (1) the slits' transmission varies with metallic film thickness and presents a damped oscillatory behaviour as the film thickness increases, and (2) the transmission increases linearly with increasing slit width for a fixed metallic film thickness. Although the general behaviour is similar, distinct optical properties [see Fig. 4(a)] lead to perceptible differences in the transmitted intensity and the position of

To help in elucidating the first observation, it is valuable to note that Fabry–Perot (FP) resonances are expected to contribute to the enhanced transmission of subwavelength slit arrays (Porto et al., 1999; Takahura, 2001; Pang et al., 2007; Garcia-Vidal et al., 2002). In this way, FP modes related to the finite depth of the slits in the present films should give rise to transmission maxima at certain wavelengths (Garcia-Vidal et al., 2002). Actually, an accurate analysis recently published shows that the two maxima observed in Figs. 10(a) and 10(b) correspond to FP-like resonances within the slit volume for the first half-wave and full wave of the light within the slit (Weiner, 2011). In this sense, the FP multiple reflection effect within the slits leads to significant modulation of the transmission as a function of metal film thickness. These transmission maxima occur if the FP resonance condition is fulfilled (Li et al., 2009):

> ( ) <sup>0</sup> 0 12 y

where my (the FP mode) is an integer and φ1 and φ2 denote the phase of the reflection coefficients of the slit at the incident and output interfaces, respectively. Thus, the effect of slit depth on the transmission enhancement can be easily understood. When the incident wavelength and slit depth are satisfied by Eq. (5), a transmission maximum will occur. Furthermore, from Eq. (5), it is expected that the transmission under a certain incident wavelength has a period of λSPP/2 as a function of slit depth. The results of Fig. 10 can now

π

(5)

<sup>λ</sup> 2k Re t + arg φ φ = 2m

SPP

 

λ

**Figure 10.** Theoretically estimated (lines) and experimental (symbols) normalized slit transmission intensities versus film thickness for the slits of the (a) 120, 160, 200, 270, and 330 nm thick Ag films, and the (b) 120, 180, 260, 360, and 450 nm thick Au samples. The dotted straight lines point out the thickness of the considered samples. The insets show the measured transmission versus slit width for some film thicknesses. Here, the dashed straight lines are linear fittings of the experimental points (Ferri et al., 2011)

We can apply an FP analysis to obtain the finesse F from Fig. 10, given by

$$\mathbf{F} = \frac{\pi}{2\sin^{-1}\left(1/\sqrt{\mathbf{f}}\right)}\tag{6}$$

where ( )-2 f = 4R 1 - R is the finesse factor. Here, R is the reflectivity, given by R = 1 - T, where T is the transmission (Born et al., 1993). We determine from Fig. 10(a) for the Ag samples with 100 nm of slit width and thicknesses of 120, 160, 200, 270, and 330 nm, the reflectivities R = 0.73, 0.67, 0.46, 0.99, and 0.73, and the corresponding finesses F = 9.98, 7.74, 3.84, 312.58, and 9.89, respectively. From Fig. 10(b) for the Au samples with 120nm of slit width and thicknesses of 120, 180, 260, 360, and 450 nm, we determine the reflectivities R = 0.66, 0.99, 0.79, 0.98, and 0.91, and the resultant finesses F = 7.45, 312.58, 13.27, 155.49, and 33.29, respectively. Here it is important to point out that for an FP cavity, the definition of quality factor (Q factor) is equivalent to the finesse (Shyu et al., 2011). Therefore, we can clearly see that both the R and Q factor values are significantly affected by the film thickness for a fixed slit width. Also, it is interesting to notice that near-zero transmission is a sign of high reflectivity values and high Q factors. For the maximum transmission points, a backward reasoning applies.

Finally, the fact that the transmission increases linearly with increasing slit width is in accordance with literature (Kihm et al., 2008), where it was observed that the far-field

#### 174 Plasmonics – Principles and Applications

transmitted intensity from a single slit shows a monotonic increase with the width, as expected from macroscopic intuition. In other words, the physical cavity length Lz and the optical cavity length Lc(λ) are related, such that () ()() <sup>2</sup> c z L λ = L + 2δ λ r λ , where r() () λ = r λ exp i( ) φ is the Fresnel coefficient, describes the shift of resonance wavelength from a perfect metal reflector due to field penetration δ(λ) into the metal mirror. But Lz is constant for all studied samples (20 µm), resulting in φz constant for a determined depth of metallic film. Nevertheless, the monotonic increase with the width w (= Lx) can also be explained considering FP resonances, for which we will use a simple analytical model to investigate the experimental results based on geometric arguments. Considering the standing wave mode in the cavity, when the penetration depth is ignored, the resonant condition of the slits can be written as

$$\frac{1}{\left(\lambda\_{\rm SPP}\right)^{2}} = \left(\frac{\mathbf{m}\_{\rm x} + \boldsymbol{\phi}\_{\rm x}}{2\mathbf{L}\_{\rm x}}\right)^{2} + \left(\frac{\mathbf{m}\_{\rm x} + \boldsymbol{\phi}\_{\rm x}}{2\mathbf{L}\_{\rm x}}\right)^{2} \tag{7}$$

Light Transmission via Subwavelength Apertures in Metallic Thin Films 175

The experimental procedure adopted here is similar to that shown in Section 6.1.2. Multilayered Ag/Au/Ag/Au and Au/Ag/Au/Ag films with total thickness t = 200 nm (d = 50 nm for each layer) were thermally evaporated onto BK7 glass substrates. Slits with widths in the range of approximately 60−600 nm were milled in the films using FIB lithography with the same already mentioned conditions. The slit length was fixed at 5 µm. For example, the right panel of Fig. 11 shows a scanning electron micrograph of a slit with width w about 180

The transmission measurement setup is identical to that shown in the left panel of Fig. 7. Here, the 488.0 nm wavelength light beam from the Ar ion laser was used for the Ag/Au/Ag/Au film, and the 632.8 nm wavelength light beam from the HeNe laser was used for the Au/Ag/Au/Ag

**Figure 11.** Left panel shows a simplified schematic of the optical transmission experiment. Similarly to the left panel of Fig. 7, a 488.0 nm (for the Ag/Au/Ag/Au film) and a 632.8 nm (for the Au/Ag/Au/Ag sample) Ar ion and HeNe laser light sources, respectively, are normally focused onto the sample surface by a 20× microscope objective lens. Right panel shows a scanning electron micrograph (taken with 60000× magnification) of a typical structure. The considered slit has approximately 180 nm of width and was focused-ion beam milled through the Ag/Au/Ag/Au sample. In the experiments, the total thickness t of the Ag/Au/Ag/Au and Au/Ag/Au/Ag films was fixed at 200 nm. The width w is varied from 60 nm

Fig. 12(a) shows the physical picture adopted in this work to investigate the light transmission through the subwavelength slits fabricated in the multilayered metallic films. The essential elements of the model are represented (Gay et al., 2006b). Basically, an incident monochromatic light beam in air is linearly polarized perpendicular to the slit of subwavelength width w, milled in a multilayered metallic film with thickness t, deposited

on a dielectric substrate (BK7 glass). Each metallic layer has a thickness d (= 50 nm).

sample. The left panel of Fig. 11 shows the basic schematic of the experimental setup.

*6.2.2. Experimental considerations* 

nm fabricated in the Ag/Au/Ag/Au film.

to 600 nm (Ferri et al., 2012)

*6.2.3. Results and discussion* 

We have applied Eq. (7) using the data of 200 nm of depth with widths Lx = 70, 100, and 150 nm for an Ag film, and 260 nm of depth with widths Lx = 120, 180, and 270 nm for an Au film. Lz = 20 µm for both samples. Also, we considered in our calculations that φz and φx are practically constant, since we did not observe any peak shift in the transmission spectra of the samples in analysis. In the interface, values of λSPP-Ag = 269.9 nm and λSPP-Au = 361.6 nm were used. It was obtained for the Ag film mz = 78 and mx = 1, 1.4, and 2, and for the Au film mz = 145 and mx = 1, 1.5, and 2, i.e., an increase in Lx allows an increase in the transmission intensity spectra for a fixed depth [see insets of Figs. 10(a) and 10(b)].

#### **6.2. Multilayered metallic thin films**

#### *6.2.1. Motivation*

Although the detailed picture of the transmission enhancement is still being investigated, the excitation of SPPs on the two surfaces of the metal film has been proposed to be involved in the process (Moreno et al., 2004; Lezec et al., 2004). In fact, it was already shown that when two perforated metal films are spaced by a dielectric layer (cascaded metallic structure), the transmission is further increased compared to a single perforated metal film (Ye et al., 2005). Additionally, bimetallic structures, such as films and nanoparticles, have attracted considerable attention for plasmon resonance excitation (Zynio et al., 2002; Gupta et al., 2005; Tan et al., 2007; Chen et al., 2010). These works are focused on improving sensitivity and evanescent field enhancement by optimization of the thickness of Ag/Au layers. Recently, optimization in terms of spectral characteristics was also theoretically demonstrated (Dyankov et al., 2011).

Here, we propose novel structures providing a unique opportunity to generate plasmonic modes. The structures are based on subwavelength slits fabricated in multilayered metallic thin films. The main feature of the novel structure is that the metal film consists of alternating layers of Ag and Au. In this Section, we demonstrate that the slits transmission can be augmented by increasing their widths, with the advantage to offer minor losses in comparison with a single perforated metal film.

### *6.2.2. Experimental considerations*

174 Plasmonics – Principles and Applications

length Lc(λ) are related, such that () ()() <sup>2</sup>

depth is ignored, the resonant condition of the slits can be written as

2

intensity spectra for a fixed depth [see insets of Figs. 10(a) and 10(b)].

**6.2. Multilayered metallic thin films** 

comparison with a single perforated metal film.

*6.2.1. Motivation* 

transmitted intensity from a single slit shows a monotonic increase with the width, as expected from macroscopic intuition. In other words, the physical cavity length Lz and the optical cavity

Fresnel coefficient, describes the shift of resonance wavelength from a perfect metal reflector due to field penetration δ(λ) into the metal mirror. But Lz is constant for all studied samples (20 µm), resulting in φz constant for a determined depth of metallic film. Nevertheless, the monotonic increase with the width w (= Lx) can also be explained considering FP resonances, for which we will use a simple analytical model to investigate the experimental results based on geometric arguments. Considering the standing wave mode in the cavity, when the penetration

c z L λ = L + 2δ λ r λ , where r() () λ = r λ exp i( ) φ is the

(7)

2 2

zz xx

 

SPP z x <sup>1</sup> m + <sup>φ</sup> m + φ = + λ 2L 2L

We have applied Eq. (7) using the data of 200 nm of depth with widths Lx = 70, 100, and 150 nm for an Ag film, and 260 nm of depth with widths Lx = 120, 180, and 270 nm for an Au film. Lz = 20 µm for both samples. Also, we considered in our calculations that φz and φx are practically constant, since we did not observe any peak shift in the transmission spectra of the samples in analysis. In the interface, values of λSPP-Ag = 269.9 nm and λSPP-Au = 361.6 nm were used. It was obtained for the Ag film mz = 78 and mx = 1, 1.4, and 2, and for the Au film mz = 145 and mx = 1, 1.5, and 2, i.e., an increase in Lx allows an increase in the transmission

Although the detailed picture of the transmission enhancement is still being investigated, the excitation of SPPs on the two surfaces of the metal film has been proposed to be involved in the process (Moreno et al., 2004; Lezec et al., 2004). In fact, it was already shown that when two perforated metal films are spaced by a dielectric layer (cascaded metallic structure), the transmission is further increased compared to a single perforated metal film (Ye et al., 2005). Additionally, bimetallic structures, such as films and nanoparticles, have attracted considerable attention for plasmon resonance excitation (Zynio et al., 2002; Gupta et al., 2005; Tan et al., 2007; Chen et al., 2010). These works are focused on improving sensitivity and evanescent field enhancement by optimization of the thickness of Ag/Au layers. Recently, optimization in terms

Here, we propose novel structures providing a unique opportunity to generate plasmonic modes. The structures are based on subwavelength slits fabricated in multilayered metallic thin films. The main feature of the novel structure is that the metal film consists of alternating layers of Ag and Au. In this Section, we demonstrate that the slits transmission can be augmented by increasing their widths, with the advantage to offer minor losses in

of spectral characteristics was also theoretically demonstrated (Dyankov et al., 2011).

The experimental procedure adopted here is similar to that shown in Section 6.1.2. Multilayered Ag/Au/Ag/Au and Au/Ag/Au/Ag films with total thickness t = 200 nm (d = 50 nm for each layer) were thermally evaporated onto BK7 glass substrates. Slits with widths in the range of approximately 60−600 nm were milled in the films using FIB lithography with the same already mentioned conditions. The slit length was fixed at 5 µm. For example, the right panel of Fig. 11 shows a scanning electron micrograph of a slit with width w about 180 nm fabricated in the Ag/Au/Ag/Au film.

The transmission measurement setup is identical to that shown in the left panel of Fig. 7. Here, the 488.0 nm wavelength light beam from the Ar ion laser was used for the Ag/Au/Ag/Au film, and the 632.8 nm wavelength light beam from the HeNe laser was used for the Au/Ag/Au/Ag sample. The left panel of Fig. 11 shows the basic schematic of the experimental setup.

**Figure 11.** Left panel shows a simplified schematic of the optical transmission experiment. Similarly to the left panel of Fig. 7, a 488.0 nm (for the Ag/Au/Ag/Au film) and a 632.8 nm (for the Au/Ag/Au/Ag sample) Ar ion and HeNe laser light sources, respectively, are normally focused onto the sample surface by a 20× microscope objective lens. Right panel shows a scanning electron micrograph (taken with 60000× magnification) of a typical structure. The considered slit has approximately 180 nm of width and was focused-ion beam milled through the Ag/Au/Ag/Au sample. In the experiments, the total thickness t of the Ag/Au/Ag/Au and Au/Ag/Au/Ag films was fixed at 200 nm. The width w is varied from 60 nm to 600 nm (Ferri et al., 2012)

#### *6.2.3. Results and discussion*

Fig. 12(a) shows the physical picture adopted in this work to investigate the light transmission through the subwavelength slits fabricated in the multilayered metallic films. The essential elements of the model are represented (Gay et al., 2006b). Basically, an incident monochromatic light beam in air is linearly polarized perpendicular to the slit of subwavelength width w, milled in a multilayered metallic film with thickness t, deposited on a dielectric substrate (BK7 glass). Each metallic layer has a thickness d (= 50 nm).

The physical processes involved in the far-field intensity enhancement for the present subwavelength slits are similar to those discussed in Section 6.1.3, in the sense that the first metallic layer is responsible to start the generation of plasmonic excitations. Form our simulation results we can see that at the interface between the adjacent metallic layers the condition for generation of SPPs is not fulfilled, Fig. 12(b). Nevertheless, there is an induced charge current due to the plasmonic surface excitations from the first to the last metallic layer, see Fig. 12(c), resulting in an asymmetric distribution [similar to Fig. 9(b)]. Additionally, the transmission over each layer is given by the Beer-Lambert law, i.e., i i-1 I = I exp(- d) α (Born et al., 1993), where α is the absorption coefficient of the corresponding metal layer, d is the thickness of the layers, and i is the layer number. Then, the resulting transmitted intensity can be written as (Gay et al., 2006b; Maier, 2007; Pacifici et al., 2008; Ferri et al., 2011),

$$\mathbf{I}\_{\rm out} = \mathbf{I}\_{\rm i} + \left| \frac{\mathbf{E}\_0}{\pi} \frac{\mathbf{w}}{\mathbf{t}} \cos \left( \mathbf{k}\_{\rm SPP} \mathbf{t} + \frac{\pi}{2} \right) \right|^2, \mathbf{i} = 1, \ldots, 4 \tag{8}$$

Light Transmission via Subwavelength Apertures in Metallic Thin Films 177

**Figure 12.** (a) Illustration of the adopted model. A single frequency incoming plane wave with intensity I0 in air is linearly polarized perpendicular to a slit of subwavelength width w, milled in a multilayered metallic film with thickness t deposited on a BK7 glass substrate. Each metallic layer has a thickness d. The overall transmitted intensity Iout is a sum of the transmission of each layer Ii with the contribution due to the SPPs created in the air/metallic film interface ISPP. (b) and (c) 2D simulations of a slit fabricated in the Au/Ag/Au/Ag film. (b) Amplitude of the magnetic H field (along the z direction). (c) Amplitude of the electric E field (in the y direction), and its vector representation in the x-y plane. Length spans: (b) x =

4 µm and y = 2 µm, and (c) x = 600 nm and y = 400 nm (adapted from Ferri et al., 2012)

**Figure 13.** Theoretically estimated (dashed straight lines) and experimentally obtained (squares) normalized slit transmission intensities versus slit width for the various subwavelength structures milled in the (a) Ag/Au/Ag/Au and (b) Au/Ag/Au/Ag samples. The insets show details of the simulated slit optical transmission versus slit width for the considered metallic multilayered films and single

perforated Ag and Au films with 200 nm of thickness (Ferri et al., 2012)

Here, the physical quantities of the second term are identical with those in Eq. (4). The only difference is that the considered dielectric medium is the air, which tabulated dielectric constant is εair = 1.00 (Palik, 1985). In this sense, the first layer is assumed to govern the extraordinary transmission (ISPP) of the subwavelength slits fabricated in the present multilayered metallic films.

Numerical simulations carried out with Comsol Multiphysics® were also performed for the multilayered metallic samples. A similar behaviour was observed in comparison to that shown in Section 6.1.3. For illustration purposes, Figs. 12(b) and 12(c) show simulations for a 50 nm slit fabricated in the Au/Ag/Au/Ag film when illuminated by the line at 632.8 nm typical of an HeNe laser. Fig. 12(b) shows the amplitude of the magnetic H field (along the z direction). Fig. 12(c) shows the amplitude of the electric E field (in the y direction), with its vector representation in the x-y plane.

The theoretical slit transmission intensity can be given by Eq. (8). In this way, Fig. 13 plots as predicted and measured transmission intensities as a function of the slit width for the various subwavelength structures milled in the Ag/Au/Ag/Au and Au/Ag/Au/Ag samples. For comparison purposes, the insets of Fig. 13 also show the simulated slit optical transmission obtained from Comsol Multiphysics® versus slit width for the considered multilayered metallic films and single perforated Ag and Au films with 200 nm of thickness. The relative slit transmission intensities are obtained by subtracting the background originating from the metal film and normalizing to the intensity from the wider slit structures. It is valuable to notice from Fig. 13 the very good correspondence between the theoretical estimative and experiment. Therefore, it is possible to affirm that: (1) the transmission increases linearly with increasing slit width, and (2) for a fixed width, the transmission of the multilayered structures is augmented in comparison with a single perforated metal film of the same thickness. It is evident that this last observation is more apparent for the Au/Ag/Au/Ag film.

176 Plasmonics – Principles and Applications

i i-1 I = I exp(- d)

α

et al., 2008; Ferri et al., 2011),

multilayered metallic films.

vector representation in the x-y plane.

apparent for the Au/Ag/Au/Ag film.

(Born et al., 1993), where

0 out i SPP

π

The physical processes involved in the far-field intensity enhancement for the present subwavelength slits are similar to those discussed in Section 6.1.3, in the sense that the first metallic layer is responsible to start the generation of plasmonic excitations. Form our simulation results we can see that at the interface between the adjacent metallic layers the condition for generation of SPPs is not fulfilled, Fig. 12(b). Nevertheless, there is an induced charge current due to the plasmonic surface excitations from the first to the last metallic layer, see Fig. 12(c), resulting in an asymmetric distribution [similar to Fig. 9(b)]. Additionally, the transmission over each layer is given by the Beer-Lambert law, i.e.,

α

  2

π

corresponding metal layer, d is the thickness of the layers, and i is the layer number. Then, the resulting transmitted intensity can be written as (Gay et al., 2006b; Maier, 2007; Pacifici

<sup>E</sup> <sup>w</sup> I = I + cos k t + , i = 1,...,4 t 2

Here, the physical quantities of the second term are identical with those in Eq. (4). The only difference is that the considered dielectric medium is the air, which tabulated dielectric constant is εair = 1.00 (Palik, 1985). In this sense, the first layer is assumed to govern the extraordinary transmission (ISPP) of the subwavelength slits fabricated in the present

Numerical simulations carried out with Comsol Multiphysics® were also performed for the multilayered metallic samples. A similar behaviour was observed in comparison to that shown in Section 6.1.3. For illustration purposes, Figs. 12(b) and 12(c) show simulations for a 50 nm slit fabricated in the Au/Ag/Au/Ag film when illuminated by the line at 632.8 nm typical of an HeNe laser. Fig. 12(b) shows the amplitude of the magnetic H field (along the z direction). Fig. 12(c) shows the amplitude of the electric E field (in the y direction), with its

The theoretical slit transmission intensity can be given by Eq. (8). In this way, Fig. 13 plots as predicted and measured transmission intensities as a function of the slit width for the various subwavelength structures milled in the Ag/Au/Ag/Au and Au/Ag/Au/Ag samples. For comparison purposes, the insets of Fig. 13 also show the simulated slit optical transmission obtained from Comsol Multiphysics® versus slit width for the considered multilayered metallic films and single perforated Ag and Au films with 200 nm of thickness. The relative slit transmission intensities are obtained by subtracting the background originating from the metal film and normalizing to the intensity from the wider slit structures. It is valuable to notice from Fig. 13 the very good correspondence between the theoretical estimative and experiment. Therefore, it is possible to affirm that: (1) the transmission increases linearly with increasing slit width, and (2) for a fixed width, the transmission of the multilayered structures is augmented in comparison with a single perforated metal film of the same thickness. It is evident that this last observation is more

is the absorption coefficient of the

(8)

**Figure 12.** (a) Illustration of the adopted model. A single frequency incoming plane wave with intensity I0 in air is linearly polarized perpendicular to a slit of subwavelength width w, milled in a multilayered metallic film with thickness t deposited on a BK7 glass substrate. Each metallic layer has a thickness d. The overall transmitted intensity Iout is a sum of the transmission of each layer Ii with the contribution due to the SPPs created in the air/metallic film interface ISPP. (b) and (c) 2D simulations of a slit fabricated in the Au/Ag/Au/Ag film. (b) Amplitude of the magnetic H field (along the z direction). (c) Amplitude of the electric E field (in the y direction), and its vector representation in the x-y plane. Length spans: (b) x = 4 µm and y = 2 µm, and (c) x = 600 nm and y = 400 nm (adapted from Ferri et al., 2012)

**Figure 13.** Theoretically estimated (dashed straight lines) and experimentally obtained (squares) normalized slit transmission intensities versus slit width for the various subwavelength structures milled in the (a) Ag/Au/Ag/Au and (b) Au/Ag/Au/Ag samples. The insets show details of the simulated slit optical transmission versus slit width for the considered metallic multilayered films and single perforated Ag and Au films with 200 nm of thickness (Ferri et al., 2012)

#### 178 Plasmonics – Principles and Applications

The fact that the far-field transmitted intensity from the present slits shows a monotonic increase with their widths is in the same trend of that previously observed in single perforated metal films (Ferri et al., 2011; Kihm et al., 2008), as expected from macroscopic intuition. In that case, the dependence could be explained considering Fabry-Perot resonances of the standing wave mode in the slit "cavity", in conjunction with the generation of SPPs. However, in the present case, such a resonant condition (Ferri et al., 2011; Kihm et al., 2008; Li et al., 2009) cannot be applied, since we have distinct reflection coefficients due to the existence of different materials in the slits. Nevertheless, the monotonic increase with the width is expected simply by considering the dependence of the transmitted intensity with the w parameter in Eq. (8).

Light Transmission via Subwavelength Apertures in Metallic Thin Films 179

the slits lead to significant modulation of the transmission as a function of metal film thickness. As well, it was shown that the transmission of multilayered structures is augmented in comparison with a single perforated metal film with a similar thickness. In this sense, we have demonstrated that metallic multilayered structures have the advantage

The authors are indebted to Prof. J. Weiner, Prof. A. R. Zanatta and Dr. M. A. Pereira-da-Silva (all at the Instituto de Física de São Carlos, USP, Brazil) for the helpful discussions, optical transmission experiments and atomic force microscopy measurements, respectively. We also would like to thanks Prof. B.-H. V. Borges (Departamento de Engenharia Elétrica, EESC, USP, Brazil) for the support with Comsol Multiphysics®. This work was financially

Avrutsky, I. (2004). Surface Plasmons at Nanoscale Relief Gratings between a Metal and a Dielectric medium with Optical Gain. *Physical Review B*, Vol.70, No.15, pp. 155416-1 –

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Bouwkamp, C.J. (1950). On Bethe's Theory of Diffraction by Small Holes. *Philips Research*

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Bouwkamp, C.J. (1954). Diffraction theory. *Reports on Progress in Physics*, Vol.17, No.1 pp. 35–100. Chen, X. & Jiang, K. (2010). Effect of aging on optical properties of bimetallic sensor chips.

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to offer minor losses in comparison with a single perforated metal film.

V. A. G. Rivera, F. A. Ferri, O. B. Silva, F. W. A. Sobreira and E. Marega Jr. *Instituto de Física de São Carlos, Universidade de São Paulo, São Carlos, Brazil* 

supported by the Brazilian agencies FAPESP and CNPq under CEPOF/INOF.

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**Author details** 

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**8. References** 

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Finally, the observation that the transmission of the metallic multilayered structures is augmented in comparison with a metal film of the same thickness when perforated with subwavelength slits, can be elucidated considering that, for the present multilayered films, the optical transmission profile is assumed to be mainly governed by the first metallic layer,

given that it is responsible to start the generation of plasmonic excitations. Subsequently, we just have electronic conduction to the underlying metallic layers, as already pointed out. Furthermore, each metallic layer (with 50 nm of thickness) additionally contribute to the overall transmission according to the Beer-Lambert law, in contrast to a single perforated metal film with the same total thickness of 200 nm of the proposed multilayered films.

Independently of the preceding discussion about multilayered metallic thin films, it is valuable to mention that gain-assisted propagation of SPPs at the interface between a metal and a dielectric with optical gain have been the focus of much research activity (Avrutsky, 2004; Nezhad et al., 2004). In this context, Er3+-doped tellurite glasses as the dielectric medium is very attractive (Wang et al., 1994). Very recently, our research group have gave significant contributions regarding the excitation and/or improvement of the luminescence of Er3+ ions embedded in these glassy matrices through plasmonic nanostructures (Rivera et al., 2012a; Rivera et al., 2012b).

### **7. Conclusion**

The physics of the transmission of light through subwavelength apertures in metallic films has been a topic of intense research in recent times. In this chapter, we have presented a review of this field, showing some essential subjects involved in this phenomenon. Although the current understanding of this phenomenon is not complete or even not substantially correct, the materials presented in many literatures are useful and clue us on how to go ahead. In particular, we presented in this chapter some contributions of our research group regarding the optical transmission through subwavelength single slits in metallic thin films. The simulations qualitatively reveal that the transmission profile is controlled by interference between the incident standing wave and plasmonic surface excitations. It was possible to observe that the slits' transmission is significantly affected by the metallic film thickness, presenting a damped oscillatory behavior as the film thickness is augmented. In addition, for a fixed metallic film thickness, the transmission increases linearly with increasing slit width. For a fixed wavelength and slit width, FP modes within the slits lead to significant modulation of the transmission as a function of metal film thickness. As well, it was shown that the transmission of multilayered structures is augmented in comparison with a single perforated metal film with a similar thickness. In this sense, we have demonstrated that metallic multilayered structures have the advantage to offer minor losses in comparison with a single perforated metal film.

### **Author details**

178 Plasmonics – Principles and Applications

al., 2012a; Rivera et al., 2012b).

**7. Conclusion** 

The fact that the far-field transmitted intensity from the present slits shows a monotonic increase with their widths is in the same trend of that previously observed in single perforated metal films (Ferri et al., 2011; Kihm et al., 2008), as expected from macroscopic intuition. In that case, the dependence could be explained considering Fabry-Perot resonances of the standing wave mode in the slit "cavity", in conjunction with the generation of SPPs. However, in the present case, such a resonant condition (Ferri et al., 2011; Kihm et al., 2008; Li et al., 2009) cannot be applied, since we have distinct reflection coefficients due to the existence of different materials in the slits. Nevertheless, the monotonic increase with the width is expected simply by considering the dependence of the transmitted intensity with the w parameter in Eq. (8).

Finally, the observation that the transmission of the metallic multilayered structures is augmented in comparison with a metal film of the same thickness when perforated with subwavelength slits, can be elucidated considering that, for the present multilayered films, the optical transmission profile is assumed to be mainly governed by the first metallic layer, given that it is responsible to start the generation of plasmonic excitations. Subsequently, we just have electronic conduction to the underlying metallic layers, as already pointed out. Furthermore, each metallic layer (with 50 nm of thickness) additionally contribute to the overall transmission according to the Beer-Lambert law, in contrast to a single perforated metal film with the same total thickness of 200 nm of the proposed multilayered films.

Independently of the preceding discussion about multilayered metallic thin films, it is valuable to mention that gain-assisted propagation of SPPs at the interface between a metal and a dielectric with optical gain have been the focus of much research activity (Avrutsky, 2004; Nezhad et al., 2004). In this context, Er3+-doped tellurite glasses as the dielectric medium is very attractive (Wang et al., 1994). Very recently, our research group have gave significant contributions regarding the excitation and/or improvement of the luminescence of Er3+ ions embedded in these glassy matrices through plasmonic nanostructures (Rivera et

The physics of the transmission of light through subwavelength apertures in metallic films has been a topic of intense research in recent times. In this chapter, we have presented a review of this field, showing some essential subjects involved in this phenomenon. Although the current understanding of this phenomenon is not complete or even not substantially correct, the materials presented in many literatures are useful and clue us on how to go ahead. In particular, we presented in this chapter some contributions of our research group regarding the optical transmission through subwavelength single slits in metallic thin films. The simulations qualitatively reveal that the transmission profile is controlled by interference between the incident standing wave and plasmonic surface excitations. It was possible to observe that the slits' transmission is significantly affected by the metallic film thickness, presenting a damped oscillatory behavior as the film thickness is augmented. In addition, for a fixed metallic film thickness, the transmission increases linearly with increasing slit width. For a fixed wavelength and slit width, FP modes within V. A. G. Rivera, F. A. Ferri, O. B. Silva, F. W. A. Sobreira and E. Marega Jr. *Instituto de Física de São Carlos, Universidade de São Paulo, São Carlos, Brazil* 

### **Acknowledgement**

The authors are indebted to Prof. J. Weiner, Prof. A. R. Zanatta and Dr. M. A. Pereira-da-Silva (all at the Instituto de Física de São Carlos, USP, Brazil) for the helpful discussions, optical transmission experiments and atomic force microscopy measurements, respectively. We also would like to thanks Prof. B.-H. V. Borges (Departamento de Engenharia Elétrica, EESC, USP, Brazil) for the support with Comsol Multiphysics®. This work was financially supported by the Brazilian agencies FAPESP and CNPq under CEPOF/INOF.

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**Chapter 8** 

© 2012 Fu et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

**Plasmonic Lenses** 

http://dx.doi.org/10.5772/50029

**1. Introduction** 

**2.1. Superlens** 

Yongqi Fu, Jun Wang and Daohua Zhang

Additional information is available at the end of the chapter

focusing, imaging, and beam shaping and so on.

typical concepts of the plasmonic lens reported so far.

The resolution of almost all conventional optical system is indispensably governed by the diffraction limit. This resolution limit can be overcome by use of focusing the evanescent waves in the near field region. The concept of "superlens" was proposed firstly by Pendry in 2000 [1]. When ε= -1and μ= -1, the negative refractive index material plate can be a perfect lens [2-4]. Because of the dispersion and absorption in the materials, the conditions of ε= - 1and μ= -1 is hard to satisfy for the natural materials. Although the perfect lens may not exist, the superlens which can provide higher resolution beyond the diffraction limit have been proved. And focusing by means of surface plasmon polarisons (SPPs) by plasmonic lens is attracting much interest recently due to its unique feature of extraordinary enhanced transmission [5-8]. It means that we can focus the evanescent components of an illuminated object in the near-field region with subdiffraction-limit resolution [9]. This allows them to break the conventional barrier of diffraction limit, and leads to the formation of concentrated sub-wavelength light spots on the order of nanometers. Plasmonic lens is always consisted by metal and dielectric and can excite SPPs and always can be used for

In this paper, a literature review is given for the purpose of displaying a physical picture of plasmonic lenses for the relevant reader. Firstly, the basic theory about the plasmonic lens is presented. Then several examples of plasmonic lens are given. Here we mainly focus on the

Although perfect lens proposed by Pendry may not exist, superlens is realized and proved by Zhang's group in 2003 [10-13] and other research groups [14-21]. Here we mainly introduce the typical works which were done by Zhang's group. They showed that optical

and reproduction in any medium, provided the original work is properly cited.

**2. Plasmonic lens on the basis of negative refractive index materials** 


## **Plasmonic Lenses**

182 Plasmonics – Principles and Applications

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surface plasmon resonance. *Sensors*, Vol.2, No.2, pp. 62-70.

Yongqi Fu, Jun Wang and Daohua Zhang

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/50029

### **1. Introduction**

The resolution of almost all conventional optical system is indispensably governed by the diffraction limit. This resolution limit can be overcome by use of focusing the evanescent waves in the near field region. The concept of "superlens" was proposed firstly by Pendry in 2000 [1]. When ε= -1and μ= -1, the negative refractive index material plate can be a perfect lens [2-4]. Because of the dispersion and absorption in the materials, the conditions of ε= - 1and μ= -1 is hard to satisfy for the natural materials. Although the perfect lens may not exist, the superlens which can provide higher resolution beyond the diffraction limit have been proved. And focusing by means of surface plasmon polarisons (SPPs) by plasmonic lens is attracting much interest recently due to its unique feature of extraordinary enhanced transmission [5-8]. It means that we can focus the evanescent components of an illuminated object in the near-field region with subdiffraction-limit resolution [9]. This allows them to break the conventional barrier of diffraction limit, and leads to the formation of concentrated sub-wavelength light spots on the order of nanometers. Plasmonic lens is always consisted by metal and dielectric and can excite SPPs and always can be used for focusing, imaging, and beam shaping and so on.

In this paper, a literature review is given for the purpose of displaying a physical picture of plasmonic lenses for the relevant reader. Firstly, the basic theory about the plasmonic lens is presented. Then several examples of plasmonic lens are given. Here we mainly focus on the typical concepts of the plasmonic lens reported so far.

## **2. Plasmonic lens on the basis of negative refractive index materials**

### **2.1. Superlens**

Although perfect lens proposed by Pendry may not exist, superlens is realized and proved by Zhang's group in 2003 [10-13] and other research groups [14-21]. Here we mainly introduce the typical works which were done by Zhang's group. They showed that optical

© 2012 Fu et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

evanescent waves could indeed be enhanced as they passed through a sliver superlens. Figure 1 below shows configuration of the superlens they designed.

Plasmonic Lenses 185

ε

 ε+ = ) has

that of the adjacent medium are equal and of opposite sign. Such a delicate resance is essential to ensure the evanescent enhancement across the slab. For enhanced transmission of evanescent waves, it is found that an asymptotic impedance match ( / / 0 *zi i zj j k k*

to be met at the surface of the silver, known as the surface plasmon excitation condition (*k*zi, cross-plane, wave vector in silver; εi, permittivity of silver; *k*zj, cross-plane wave vector in dielectric; and εj, permittivity of dielectric). It is widely known in metal optics that when the two media take the opposite sign in permittivity and |εi| >>εj, only surface plasmons at the narrow range of in-plane wave vector (*k*x) that are close to ko can be resonantly coupled. However, less well known is that when |εi| ~εj and we are of opposite sign, the excitable surface plasmon band of *k*x is significantly broadened, resulting in the superlensing effect.

**Figure 2.** (A) AFM of the developed image (scale bar, 1 μm; color scale from dark red to bright yellow, 0 to 150 nm). (B) Control experiments were carried out, in which the silver superlens layer was replaced by a 35 nm thick PMMA layer, for a total PMMA thickness of 75nm. (C) The blue solid curve shows the clearly demonstrating the 63 ± 4 nm half-pitch resolved with a 35 nm silver superlens. X direction is relative displacement along the cross-section direction. (D) The blue solid curve shows the average cross section of Fig. 2B (control sample). Reprinted with permission from "N. Fang, H. Lee, C. Sun and X.

Zhang, Science 308, 534-537 (2005)." of copyright ©2005 American Institute of Physics.

The intensity of evanescent waves decays with a characteristic length *Z*, and

**Figure 1.** Optical superlensing designed by Zhang's group. Reprinted with permission from "N. Fang, H. Lee, C. Sun and X. Zhang, Science 308, 534-537 (2005)." of copyright ©2005 American Institute of Physics.

As can be seen, a set of objects were inscribed onto a chrome screen. The objects were designed to be placed about 40 nm away from the silver film which is 35 nm in thickness. And the chrome objects were patterned on quartz by using focused ion beam (FIB) technique, a 40 nm thick layer of polymethyl methacrylate (PMMA) was used to planarized them. The objects are imaged onto the photoresist on the other side of the silver film under ultraviolet (UV) illumination (at a wavelength of 365 nm). The negative photoresist which is 120 nm thick is used to record the near-field image. The substrate is food-exposed under an I-line (365 nm) mercury lamp. The exposure flux is 8 mW/cm2, and an optimal exposure time of 60 s is applied to reduce the surface root mean square modulation below 1 nm for both the silver and PMMA surfaced; otherwise, the dispersion characteristics of the superlens would be modified and would in turn smear the details of the recorded image. The optical image is converted into topographic modulations by developing the negative photoresist and is mapped using atomic force microscopy (AFM).

Because the electric and magnetic responses of materials were decoupled in the near field, only the permittivity needs to be considered for transverse magnetic (TM) waves. This makes noble metals such as silver natural candidates for optical superlensing. Silver is chosen here. As surface charges accumulate at the interface between the silver and the imaging medium, the normal component of an electric of silver is selected and the permittivity of the silver and that of the adjacent medium are equal and of opposite sign. Such a delicate resance is essential to ensure the evanescent enhancement across the slab. For enhanced transmission of evanescent waves, it is found that an asymptotic impedance match ( / / 0 *zi i zj j k k* ε ε + = ) has to be met at the surface of the silver, known as the surface plasmon excitation condition (*k*zi, cross-plane, wave vector in silver; εi, permittivity of silver; *k*zj, cross-plane wave vector in dielectric; and εj, permittivity of dielectric). It is widely known in metal optics that when the two media take the opposite sign in permittivity and |εi| >>εj, only surface plasmons at the narrow range of in-plane wave vector (*k*x) that are close to ko can be resonantly coupled. However, less well known is that when |εi| ~εj and we are of opposite sign, the excitable surface plasmon band of *k*x is significantly broadened, resulting in the superlensing effect.

184 Plasmonics – Principles and Applications

evanescent waves could indeed be enhanced as they passed through a sliver superlens.

**Figure 1.** Optical superlensing designed by Zhang's group. Reprinted with permission from "N. Fang, H. Lee, C. Sun and X. Zhang, Science 308, 534-537 (2005)." of copyright ©2005 American Institute of Physics.

As can be seen, a set of objects were inscribed onto a chrome screen. The objects were designed to be placed about 40 nm away from the silver film which is 35 nm in thickness. And the chrome objects were patterned on quartz by using focused ion beam (FIB) technique, a 40 nm thick layer of polymethyl methacrylate (PMMA) was used to planarized them. The objects are imaged onto the photoresist on the other side of the silver film under ultraviolet (UV) illumination (at a wavelength of 365 nm). The negative photoresist which is 120 nm thick is used to record the near-field image. The substrate is food-exposed under an I-line (365 nm) mercury lamp. The exposure flux is 8 mW/cm2, and an optimal exposure time of 60 s is applied to reduce the surface root mean square modulation below 1 nm for both the silver and PMMA surfaced; otherwise, the dispersion characteristics of the superlens would be modified and would in turn smear the details of the recorded image. The optical image is converted into topographic modulations by developing the negative

Because the electric and magnetic responses of materials were decoupled in the near field, only the permittivity needs to be considered for transverse magnetic (TM) waves. This makes noble metals such as silver natural candidates for optical superlensing. Silver is chosen here. As surface charges accumulate at the interface between the silver and the imaging medium, the normal component of an electric of silver is selected and the permittivity of the silver and

photoresist and is mapped using atomic force microscopy (AFM).

Figure 1 below shows configuration of the superlens they designed.

**Figure 2.** (A) AFM of the developed image (scale bar, 1 μm; color scale from dark red to bright yellow, 0 to 150 nm). (B) Control experiments were carried out, in which the silver superlens layer was replaced by a 35 nm thick PMMA layer, for a total PMMA thickness of 75nm. (C) The blue solid curve shows the clearly demonstrating the 63 ± 4 nm half-pitch resolved with a 35 nm silver superlens. X direction is relative displacement along the cross-section direction. (D) The blue solid curve shows the average cross section of Fig. 2B (control sample). Reprinted with permission from "N. Fang, H. Lee, C. Sun and X. Zhang, Science 308, 534-537 (2005)." of copyright ©2005 American Institute of Physics.

The intensity of evanescent waves decays with a characteristic length *Z*, and

#### 186 Plasmonics – Principles and Applications

$$
\omega Z^{-1} = 4\pi \sqrt{a^{-2} - \varepsilon \mathcal{X}^{-2}} \,, \tag{1}
$$

Plasmonic Lenses 187

**Figure 4.** Optical hyperlens. (A) Schematic of heperlens and nymerical simulation of imaging of subdiffraction-limited objects. (B) Hyperlens imaging of line pair object with line width of 35 nm and spacing of 150 nm. From left to right, scanning electron microscope image of the line pair object fabricated near the inner side of the hyperlens, magnified hyperlens image showing that the 150-nmspaced line pair object can be clearly resolved, and the resulting diffraction-limited image from a control experiment without the hyperlens. (C) The averaged cross section of hyperlens image of the line pair object with 150-nm spacing (red), whereas a diffraction-limited image obtained in the control experiment (green). A.U.: arbitrary units. (D) An arbitrary object "ON" imaged with subdiffraction resolution. Line width of the object is about 40 nm. The hyperlens is made of 16 layers of Ag/Al2O3. Reprinted with permission from "Zhaowei Liu, Hyesog Lee, Yi Xiong, Cheng Sun, Xiang Zhang,

Science 315. 1686 (2007)" of copyright ©2007 of AAAS.

where a is the period of a line array, and *ε* is the permittivity of the surrounding media. In Zhang's experiment, for the 60 nm half-pitch and ε = 2.4, the decay length is estimated to be 11 nm. Thus it is obviously difficult to resolve a 60 nm half-pitch object from a distance of 75 nm away if there isn't a superlens to enhance and transmit the evanescent waves. So we could find the photoresist images with typical average height modulations of 5 nm to 10 nm from Fig. 2 C. And this is assisted by careful control of the surface morphology of the PMMA and silver surface. In addition, Zhang also proved that the silver superlens can also image arbitrary nanostructures with sub-diffraction-limited resolution. The recorded image "NANO" in Fig. 3 B shows that the fine features from the mask showed in Fig. 3 A in all directions with good fidelity can be faithfully produced.

**Figure 3.** An arbitrary object "NANO" was imaged by silver superlens. (A) FIB image of the object. The linewidth of the "NANO" object was 40 nm. Scale bar in (A) to (C), 2 μm. (B) AFM of the developed image on photoresist with a silver superlens. (C) AFM of the developed image on photoresist when the 35 nm thick layer of silver was replaced by PMMA spacer as a control experiment. (D) The average cross section of letter "A" shows an exposed line width of 89 nm (blue line), whereas in the control experiment, we measured a diffraction-limited full width at half-maximum ling width of 321 ± 10 nm (red line). Reprinted with permission from "N. Fang, H. Lee, C. Sun and X. Zhang, Science 308, 534-537 (2005)." of copyright ©2005 American Institute of Physics.

#### **2.2. Hyperlens**

The images imaged by the superlens we talked about above are the same size as the objects. And there is no working distance. The hyperlens here was also proposed by Zhang's group [22]. It can magnify a sub-diffraction-limited image and projects it into the far field. Figure 4 A is the schematic of the hyperlens. It consists of a curved periodic stack of Ag (35 nm) and Al2O3 (35 nm) deposited on a half-cylindrical cavity fabricated on a quartz substrate. Subdiffracion-limited objects were inscribed into a 50-nm-thick chrome layer located at the inner surface (air side). The anisotropic metamaterial was designed so that the radial and tangential permittivities have different signs.

186 Plasmonics – Principles and Applications

directions with good fidelity can be faithfully produced.

(2005)." of copyright ©2005 American Institute of Physics.

tangential permittivities have different signs.

**2.2. Hyperlens** 

1 22 *Z a* 4π

where a is the period of a line array, and *ε* is the permittivity of the surrounding media. In Zhang's experiment, for the 60 nm half-pitch and ε = 2.4, the decay length is estimated to be 11 nm. Thus it is obviously difficult to resolve a 60 nm half-pitch object from a distance of 75 nm away if there isn't a superlens to enhance and transmit the evanescent waves. So we could find the photoresist images with typical average height modulations of 5 nm to 10 nm from Fig. 2 C. And this is assisted by careful control of the surface morphology of the PMMA and silver surface. In addition, Zhang also proved that the silver superlens can also image arbitrary nanostructures with sub-diffraction-limited resolution. The recorded image "NANO" in Fig. 3 B shows that the fine features from the mask showed in Fig. 3 A in all

**Figure 3.** An arbitrary object "NANO" was imaged by silver superlens. (A) FIB image of the object. The linewidth of the "NANO" object was 40 nm. Scale bar in (A) to (C), 2 μm. (B) AFM of the developed image on photoresist with a silver superlens. (C) AFM of the developed image on photoresist when the 35 nm thick layer of silver was replaced by PMMA spacer as a control experiment. (D) The average cross section of letter "A" shows an exposed line width of 89 nm (blue line), whereas in the control experiment, we measured a diffraction-limited full width at half-maximum ling width of 321 ± 10 nm (red line). Reprinted with permission from "N. Fang, H. Lee, C. Sun and X. Zhang, Science 308, 534-537

The images imaged by the superlens we talked about above are the same size as the objects. And there is no working distance. The hyperlens here was also proposed by Zhang's group [22]. It can magnify a sub-diffraction-limited image and projects it into the far field. Figure 4 A is the schematic of the hyperlens. It consists of a curved periodic stack of Ag (35 nm) and Al2O3 (35 nm) deposited on a half-cylindrical cavity fabricated on a quartz substrate. Subdiffracion-limited objects were inscribed into a 50-nm-thick chrome layer located at the inner surface (air side). The anisotropic metamaterial was designed so that the radial and

 ελ

− −− = − , (1)

**Figure 4.** Optical hyperlens. (A) Schematic of heperlens and nymerical simulation of imaging of subdiffraction-limited objects. (B) Hyperlens imaging of line pair object with line width of 35 nm and spacing of 150 nm. From left to right, scanning electron microscope image of the line pair object fabricated near the inner side of the hyperlens, magnified hyperlens image showing that the 150-nmspaced line pair object can be clearly resolved, and the resulting diffraction-limited image from a control experiment without the hyperlens. (C) The averaged cross section of hyperlens image of the line pair object with 150-nm spacing (red), whereas a diffraction-limited image obtained in the control experiment (green). A.U.: arbitrary units. (D) An arbitrary object "ON" imaged with subdiffraction resolution. Line width of the object is about 40 nm. The hyperlens is made of 16 layers of Ag/Al2O3. Reprinted with permission from "Zhaowei Liu, Hyesog Lee, Yi Xiong, Cheng Sun, Xiang Zhang, Science 315. 1686 (2007)" of copyright ©2007 of AAAS.

The object imaged with hyperlens was a pair of 35-nm-wide lines spaced 150 nm apart. Upon illumination, the scattered evanescent field from the object enters the anisotropic medium and propagates along the radial direction. Because of the conservation of angular momentum, the tangential wave vectors are progressively compressed as the waves travel outward, resulting in a magnified image at the outer boundary of the hyperlens. Hence the magnified image (350-nm spacing) can be clearly resolved with an optical microscopy.

Plasmonic Lenses 189

**Figure 5.** FIB image of the fabricated depth-tuned nanostructure (type of concave) on the Ag thin film

**Figure 6.** Schematic drawing of the nanoplasmonic slits with (a) convex, (b) concave and (c) flat shaped profiles. (d) Schematic drawing of near-field measurement setup. (e) Measured topographic image of the slit with concave corrugations. The marked area 'A' shows a larger overall depth than that of the area 'B'. (f) Cross section of the concave groove-slit at the position indicated by the dashed line in (e).

with thickness of 200 nm.

### **3. Plasmonic lens on the basis of subwavelength metallic structures**

### **3.1. Subwavelength metallic structure for superfocusing**

### *3.1.1. One-dimensional structures for focusing*

In this section, we presented two types of tuning methods for the purpose of phase modulation: depth tuning [23] and width tuning [24-26] approaches.

#### *3.1.1.1. Depth-tuned. strctures*

Three types of plasmonic slits (convex, concave, and flat/constant groove depth) with different stepped grooves have been designed and fabricated to achieve efficient plasmonic focusing and focal depth modulation of the transmitted beam. Figure 5 shows the fabricated depthtuned plasmonic lens using focused ion beam milling [27]. The general design of the plasmonic slit is shown in Fig. 6 (a) [28]. When a TM polarized (magnetic field parallel to the ydirection) monochromatic plane wave impinges on the slit, it excites collective oscillations of the electrons at the surface, which is known as SPPs. The SPPs propagate along the surface of the metal film and are diffracted to the far-field by the periodic grooves, which are designed with a width smaller than half of the incident wavelength to allow a high diffraction efficiency [29]. Constructing interference of such diffracted beams leads to the focusing effect at a certain point on the beam axis [30]. Since the diffracted beams are modulated by the nanometric grooves, through adjusting the parameters of the grooves (such as our width, depth, period and number), the diffracted beams can be fully manipulated resulting in a tailored ultracompact lens with subwavelength resolution and nanometer accuracy [31]. Most interestingly, it has been numerically found [32] that the relative phase at the exit end of the slit increases steadily with the increasing groove depth, making it possible to achieve continuous phase retardation by simply designing surrounding grooves with stepped depths as shown in Figs. 6 (b) and 6 (c). This has led to a great simplification of the plasmonic lens design without increasing the groove number or generating a bump on the metal film [33].

Figure 7 (a) presents a detailed comparison of the measured intensity distribution with simulation using FDTD at the slit cross section (along x-direction, as indicated by the white dot line in Fig. 2 (a) [23]). A good agreement has been found between the experiment and the theoretical prediction except that the measured full-width at a half-maximum (FWHM) of the central lobe (approximately 281 nm) is slightly larger than the calculated value of about 230 nm. This is because the measured intensity distribution approximately equals to the convolution of the finite probe size (30-80nm) and the actual intensity distribution of the transmitted light.

188 Plasmonics – Principles and Applications

*3.1.1.1. Depth-tuned. strctures* 

transmitted light.

The object imaged with hyperlens was a pair of 35-nm-wide lines spaced 150 nm apart. Upon illumination, the scattered evanescent field from the object enters the anisotropic medium and propagates along the radial direction. Because of the conservation of angular momentum, the tangential wave vectors are progressively compressed as the waves travel outward, resulting in a magnified image at the outer boundary of the hyperlens. Hence the magnified image (350-nm spacing) can be clearly resolved with an optical microscopy.

**3. Plasmonic lens on the basis of subwavelength metallic structures** 

In this section, we presented two types of tuning methods for the purpose of phase

Three types of plasmonic slits (convex, concave, and flat/constant groove depth) with different stepped grooves have been designed and fabricated to achieve efficient plasmonic focusing and focal depth modulation of the transmitted beam. Figure 5 shows the fabricated depthtuned plasmonic lens using focused ion beam milling [27]. The general design of the plasmonic slit is shown in Fig. 6 (a) [28]. When a TM polarized (magnetic field parallel to the ydirection) monochromatic plane wave impinges on the slit, it excites collective oscillations of the electrons at the surface, which is known as SPPs. The SPPs propagate along the surface of the metal film and are diffracted to the far-field by the periodic grooves, which are designed with a width smaller than half of the incident wavelength to allow a high diffraction efficiency [29]. Constructing interference of such diffracted beams leads to the focusing effect at a certain point on the beam axis [30]. Since the diffracted beams are modulated by the nanometric grooves, through adjusting the parameters of the grooves (such as our width, depth, period and number), the diffracted beams can be fully manipulated resulting in a tailored ultracompact lens with subwavelength resolution and nanometer accuracy [31]. Most interestingly, it has been numerically found [32] that the relative phase at the exit end of the slit increases steadily with the increasing groove depth, making it possible to achieve continuous phase retardation by simply designing surrounding grooves with stepped depths as shown in Figs. 6 (b) and 6 (c). This has led to a great simplification of the plasmonic lens design without

**3.1. Subwavelength metallic structure for superfocusing** 

modulation: depth tuning [23] and width tuning [24-26] approaches.

increasing the groove number or generating a bump on the metal film [33].

Figure 7 (a) presents a detailed comparison of the measured intensity distribution with simulation using FDTD at the slit cross section (along x-direction, as indicated by the white dot line in Fig. 2 (a) [23]). A good agreement has been found between the experiment and the theoretical prediction except that the measured full-width at a half-maximum (FWHM) of the central lobe (approximately 281 nm) is slightly larger than the calculated value of about 230 nm. This is because the measured intensity distribution approximately equals to the convolution of the finite probe size (30-80nm) and the actual intensity distribution of the

*3.1.1. One-dimensional structures for focusing* 

**Figure 5.** FIB image of the fabricated depth-tuned nanostructure (type of concave) on the Ag thin film with thickness of 200 nm.

**Figure 6.** Schematic drawing of the nanoplasmonic slits with (a) convex, (b) concave and (c) flat shaped profiles. (d) Schematic drawing of near-field measurement setup. (e) Measured topographic image of the slit with concave corrugations. The marked area 'A' shows a larger overall depth than that of the area 'B'. (f) Cross section of the concave groove-slit at the position indicated by the dashed line in (e).

Plasmonic Lenses 191

**Figure 8.** AFM probe for tapping mode. (a) the commercial probe with half cone angle of 17° and

Influence of polarization states on focusing properties of the depth-tuned metallic structures was reported [31]. The structure was designed with geometrical parameteres shown as Fig. 9. Figure 10 shows the total electric-field intensity |E|2=|Ex|2+|Ey|2+|Ez|2 at x-y plane along the longitudinal direction at z = 1.35 μm at λ=420 nm for the (a) elliptical polarization (EP), (b) circular polarization (CP), and (c) radial polarization (RP) cases. The intensity of transverse electric field, |Ex|2+|Ey|2, is significantly tuned. In the figure, the intensity along the horizontal (x) is equal to that along the vertical (y), while the intensity along the

**Figure 9.** An annular plasmonic lens having a depth-tuned structure (groove depths, t1= 130 nm, t2= 80 nm and t3=30 nm) milled in the output side of a Ag thin film (thickness, h = 200nm). Other structure parameters are: central hole diameter=200 nm, groove width=200 nm, and groove period=420 nm. The structure is incident with TM-polarized light having electric vector along the x direction. Reprinted with permission from "Jun Wang, Wei Zhou and Anand K. Asundi, Opt. Express 17, 8137-8143 (2009)." of

material of Si3N4. (b) the FIB trimmed probe with high aspect ratio.

copyright ©2009 Optical Society of American.

**Figure 7.** Comparison of measured and theoretical cross sections at x=0 in Fig. 2 of the reference paper for (a) z=10 nm, (b) z=50 nm (c) z=1600 nm and (d) z=4000 nm.

Near-field measurement reveals unambiguously the light interaction with the slits and confirms the functionalities of the nanoplasmonic lens. The simple plasmonic lens demonstrated in this paper can find broad applications in ultra-compact photonic chips particularly for biosensing and high-resolution imaging. Among the three types metallic structures, the type of convave structure has best focusing performance.

In adition, V-shaped influence on focusing performance was analyzed in fabrication point of view [34]. The incident angle dependance on the focusing properties was discussed also in Ref. [35].

Regarding fabrication of the metallic structures with depth-tuned grooves, it is worthy to point out that the geometrical characrerization issue using atomic force microscope after focused ion beam direct milling [31]. Large measurement error is found during geometrical characterization of the nanostructures by use of an atomic force microscope (AFM) working in tapping mode. Apex wearing and 34° full cone angle of the probe generate the measurement errors during characterizing the nanostructures with the feature size of 200 nm and below. To solve this problem, a FIB trimmed AFM probe is employed in the geometrical characterization, as shown in Fig. 8. The results show that the error is improved greatly using the trimmed probe.

190 Plasmonics – Principles and Applications

**Figure 7.** Comparison of measured and theoretical cross sections at x=0 in Fig. 2 of the reference paper

Near-field measurement reveals unambiguously the light interaction with the slits and confirms the functionalities of the nanoplasmonic lens. The simple plasmonic lens demonstrated in this paper can find broad applications in ultra-compact photonic chips particularly for biosensing and high-resolution imaging. Among the three types metallic

In adition, V-shaped influence on focusing performance was analyzed in fabrication point of view [34]. The incident angle dependance on the focusing properties was discussed also in

Regarding fabrication of the metallic structures with depth-tuned grooves, it is worthy to point out that the geometrical characrerization issue using atomic force microscope after focused ion beam direct milling [31]. Large measurement error is found during geometrical characterization of the nanostructures by use of an atomic force microscope (AFM) working in tapping mode. Apex wearing and 34° full cone angle of the probe generate the measurement errors during characterizing the nanostructures with the feature size of 200 nm and below. To solve this problem, a FIB trimmed AFM probe is employed in the geometrical characterization, as shown in Fig. 8. The results show that the error is improved

for (a) z=10 nm, (b) z=50 nm (c) z=1600 nm and (d) z=4000 nm.

Ref. [35].

greatly using the trimmed probe.

structures, the type of convave structure has best focusing performance.

**Figure 8.** AFM probe for tapping mode. (a) the commercial probe with half cone angle of 17° and material of Si3N4. (b) the FIB trimmed probe with high aspect ratio.

Influence of polarization states on focusing properties of the depth-tuned metallic structures was reported [31]. The structure was designed with geometrical parameteres shown as Fig. 9. Figure 10 shows the total electric-field intensity |E|2=|Ex|2+|Ey|2+|Ez|2 at x-y plane along the longitudinal direction at z = 1.35 μm at λ=420 nm for the (a) elliptical polarization (EP), (b) circular polarization (CP), and (c) radial polarization (RP) cases. The intensity of transverse electric field, |Ex|2+|Ey|2, is significantly tuned. In the figure, the intensity along the horizontal (x) is equal to that along the vertical (y), while the intensity along the

**Figure 9.** An annular plasmonic lens having a depth-tuned structure (groove depths, t1= 130 nm, t2= 80 nm and t3=30 nm) milled in the output side of a Ag thin film (thickness, h = 200nm). Other structure parameters are: central hole diameter=200 nm, groove width=200 nm, and groove period=420 nm. The structure is incident with TM-polarized light having electric vector along the x direction. Reprinted with permission from "Jun Wang, Wei Zhou and Anand K. Asundi, Opt. Express 17, 8137-8143 (2009)." of copyright ©2009 Optical Society of American.

Plasmonic Lenses 193

diagonal directions (45° and 135° with respect to the *x* is tuned), the peak shift is observed at the side lobe, which is <0.1λ for the EP case. In Fig. 10 (a), in the direction of 45°. And the beam in 45° is narrower than that in the x- or y-directions. In addition, the phase function Re(exp(iθ)) indicates tuning capability. Re (exp(iθ)) = 0.5, where θ = π/3, for the EP case, and the phase function becomes 0 for the CP and 1 for the RP case. For example, in Fig. 10 (b), the uniformly distributed total-electric-field intensity is observed in the x-y plane, while, in Fig. 10 (c), the peak shifts 0.2λ in the 45° larger than that for the EP case, and much narrow beam is observed in the same direction. The same plasmonic modes are observed for CP, EP, or RP polarization cases as for TM case. Using a polarized plane wave the transverse electric field is tuned; the tuning 45° and 135° with respect to effect on focus spot is observed along the diagonal directions in 45° the x-direction. Of the cases, RP approach forms the smallest focus spot along the 45° using Re[exp(iθ)]=1, showing maximum tuning capability, while CP approach the phase function Re[exp(iθ)]=0 forms a symmetrically electric field distribution in the focal plane. Phase function indicates the

A novel method is proposed to manipulate beam by modulating light phase through a metallic film with arrayed nano-slits, which have constant depth but variant widths. The slits transport electro-magnetic energy in the form of surface plasmon polaritons (SPPs) in nanometric waveguides and provide desired phase retardations of beam manipulating with variant phase propagation constant. Numerical simulation of an illustrative lens design example is performed through finite-difference time-domain (FDTD) method and shows agreement with theory analysis result. In addition, extraordinary optical transmission of SPPs through sub-wavelength metallic slits is observed in the simulation and helps to

To illustrate the above idea of modulating phase, a metallic nano-slits lens is designed [24]. The parameters of the lens are as follows: *D* = 4 μm, *f* = 0.6 μm, λ= 0.65 μm, *d*=0.5 μm, where *D* is the diameter of the lens aperture, *f* the focus length, the wavelength and *d* the thickness of the film. The two sides of the lens is air. The schematic of lens is given in Fig. 11, where a metallic film is perforated with a great number of nano-slits with specifically designed

After numerous iterations of calculation using the FDTD algorithm, the resulting Poyinting vector is obtained and showed in Fig. 12 (a). A clear-cut focus appears about 0.6 micron away from the exit surface, which agrees with our design. The cross section of focus spot in x direction is given in Fig. 12 (b), indicating a full-width at half-maximum (FWHM) of 270 nm. The extraordinary light transmission effects of SPPs through sub-wavelength slits is also observed in the simulation with a transmission enhance factor of about 1.8 times. These advantages promise this method to find various potential applications in nano-scale beam

widths and transmitted light from slits is modulated and converges in free space.

shaping, integrate optics, date storage, and near-field imaging ect.

tuning capability.

*3.1.1.2. Width-tuned structures* 

improve elements's energy using factor.

**Figure 10.** Total electric field (left) transmitted through the structure under illumination using different polarization states, including (a) CP, (b) EP, and (c) RP, showing the phase modulation effect on the beam profile (right) along the transverse direction in x and y and diagonal directions along 45° and 135° with respect to the x. Refer to Fig. 1 for the directions. Reprinted with permission from "Jun Wang, Wei Zhou and Anand K. Asundi, Opt. Express 17, 8137-8143 (2009)." of copyright ©2009 Optical Society of American.

diagonal directions (45° and 135° with respect to the *x* is tuned), the peak shift is observed at the side lobe, which is <0.1λ for the EP case. In Fig. 10 (a), in the direction of 45°. And the beam in 45° is narrower than that in the x- or y-directions. In addition, the phase function Re(exp(iθ)) indicates tuning capability. Re (exp(iθ)) = 0.5, where θ = π/3, for the EP case, and the phase function becomes 0 for the CP and 1 for the RP case. For example, in Fig. 10 (b), the uniformly distributed total-electric-field intensity is observed in the x-y plane, while, in Fig. 10 (c), the peak shifts 0.2λ in the 45° larger than that for the EP case, and much narrow beam is observed in the same direction. The same plasmonic modes are observed for CP, EP, or RP polarization cases as for TM case. Using a polarized plane wave the transverse electric field is tuned; the tuning 45° and 135° with respect to effect on focus spot is observed along the diagonal directions in 45° the x-direction. Of the cases, RP approach forms the smallest focus spot along the 45° using Re[exp(iθ)]=1, showing maximum tuning capability, while CP approach the phase function Re[exp(iθ)]=0 forms a symmetrically electric field distribution in the focal plane. Phase function indicates the tuning capability.

#### *3.1.1.2. Width-tuned structures*

192 Plasmonics – Principles and Applications

**Figure 10.** Total electric field (left) transmitted through the structure under illumination using different polarization states, including (a) CP, (b) EP, and (c) RP, showing the phase modulation effect on the beam profile (right) along the transverse direction in x and y and diagonal directions along 45° and 135° with respect to the x. Refer to Fig. 1 for the directions. Reprinted with permission from "Jun Wang, Wei Zhou and Anand K. Asundi, Opt. Express 17, 8137-8143 (2009)." of copyright ©2009 Optical Society of American. A novel method is proposed to manipulate beam by modulating light phase through a metallic film with arrayed nano-slits, which have constant depth but variant widths. The slits transport electro-magnetic energy in the form of surface plasmon polaritons (SPPs) in nanometric waveguides and provide desired phase retardations of beam manipulating with variant phase propagation constant. Numerical simulation of an illustrative lens design example is performed through finite-difference time-domain (FDTD) method and shows agreement with theory analysis result. In addition, extraordinary optical transmission of SPPs through sub-wavelength metallic slits is observed in the simulation and helps to improve elements's energy using factor.

To illustrate the above idea of modulating phase, a metallic nano-slits lens is designed [24]. The parameters of the lens are as follows: *D* = 4 μm, *f* = 0.6 μm, λ= 0.65 μm, *d*=0.5 μm, where *D* is the diameter of the lens aperture, *f* the focus length, the wavelength and *d* the thickness of the film. The two sides of the lens is air. The schematic of lens is given in Fig. 11, where a metallic film is perforated with a great number of nano-slits with specifically designed widths and transmitted light from slits is modulated and converges in free space.

After numerous iterations of calculation using the FDTD algorithm, the resulting Poyinting vector is obtained and showed in Fig. 12 (a). A clear-cut focus appears about 0.6 micron away from the exit surface, which agrees with our design. The cross section of focus spot in x direction is given in Fig. 12 (b), indicating a full-width at half-maximum (FWHM) of 270 nm. The extraordinary light transmission effects of SPPs through sub-wavelength slits is also observed in the simulation with a transmission enhance factor of about 1.8 times. These advantages promise this method to find various potential applications in nano-scale beam shaping, integrate optics, date storage, and near-field imaging ect.

Plasmonic Lenses 195

widths milled using a focused ion beam. They found an excellent agreement between electromagnetic simulations of the design and confocal measurements on manufactured structures. They provide guidelines for lens design and show how actual lens behavior

**Figure 13.** Planar lens based on nanoscale slit array in metallic film. (a) Geometry of the lens consisting of a 400nm optically thick gold film (yellow) with air slits of different widths (80 to150 nm) (light blue) milled therein on a fused silica substrate (dark blue). The inset shows a scanning electron micrograph of the structure as viewed from the air-side. (b) Focusing pattern measured by confocal scanning optical microscopy (CSOM). (c) Finite-difference and frequency-domain (FDFD) simulated focusing pattern of the field intensity through the center of the slits. In order to show the features of the focus spotclearly, the field intensity inside the slits is saturated. Reprinted with permission from "LievenVerslegers et. al.,

The basic geometry consists of an array of nanoscale slits in an otherwise opaque metallic film (see Fig. 13 (a)). Figure13 shows the main results of the work, which combines fabrication, characterization, andsimulation. Pane l (a) shows the fabricated structure, while panels (b) and (c) represent the measured and simulated field intensity in across section through the center of the slits (along the x-direction). Both the measurement and the simulation clearly demonstrate focusing of the wave. The agreement between experiment and simulation is excellent. Moreover, the simulation image is generated using the designed parameters as the slit width rather than the actual slit width measured in the SEM, as is commonly done when comparing nanophotonics simulation and experiments. The agreemen there thus indicates the robustness in design and the fault tolerance of this

Nano Lett. 9, 235-238 (2009)" of copyright ©2009 Chemical Society of American.

deviates from simple theory.

**Figure 11.** A schematic of a nano-slit array with different width formed on thin metallic film. Metal thickness in this configuration is *d*, and each slit width is determined for required phase distribution on the exit side, respectively. A TM-polarized plane wave (consists of Ex, Hy and Ez field component, and Hy component parallel to the y-axis) is incident to the slit array from the left side. Reprinted with permission from "H. F. Shi, C. T. Wang, C. L. Du, X. G. Luo, X. C. Dong, and H. T. Gao, Opt. Express 13, 6815-6820 (2005)." of copyright ©2009 Optical Society of American.

**Figure 12.** (a) FDTD calculated result of normalized Poynting Vector Sz for designed metallic nano-slits lens. Film thickness is 500nm, and the total slits number is 65. The structure's exit side is posited at z=0.7 μm. (b) Cross m.section of the focus at z=1.5 μm. Reprinted with permission from "H. F. Shi, C. T. Wang, C. L. Du, X. G. Luo, X. C. Dong, and H. T. Gao, Opt. Express 13, 6815-6820 (2005)." of copyright ©2009 Optical Society of American.

As an experimentlal verification example, Lieven et. al. [37] experimentally demonstrated planar lenses based on nanoscale slit arrays in a metallic film. The lens structures consist of optically thick gold films with micron-size arrays of closely spaced, nanoscale slits of varying widths milled using a focused ion beam. They found an excellent agreement between electromagnetic simulations of the design and confocal measurements on manufactured structures. They provide guidelines for lens design and show how actual lens behavior deviates from simple theory.

194 Plasmonics – Principles and Applications

**Figure 11.** A schematic of a nano-slit array with different width formed on thin metallic film. Metal thickness in this configuration is *d*, and each slit width is determined for required phase distribution on the exit side, respectively. A TM-polarized plane wave (consists of Ex, Hy and Ez field component, and Hy component parallel to the y-axis) is incident to the slit array from the left side. Reprinted with permission from "H. F. Shi, C. T. Wang, C. L. Du, X. G. Luo, X. C. Dong, and H. T. Gao, Opt. Express 13,

**Figure 12.** (a) FDTD calculated result of normalized Poynting Vector Sz for designed metallic nano-slits lens. Film thickness is 500nm, and the total slits number is 65. The structure's exit side is posited at z=0.7 μm. (b) Cross m.section of the focus at z=1.5 μm. Reprinted with permission from "H. F. Shi, C. T. Wang, C. L. Du, X. G. Luo, X. C. Dong, and H. T. Gao, Opt. Express 13, 6815-6820 (2005)." of copyright

As an experimentlal verification example, Lieven et. al. [37] experimentally demonstrated planar lenses based on nanoscale slit arrays in a metallic film. The lens structures consist of optically thick gold films with micron-size arrays of closely spaced, nanoscale slits of varying

6815-6820 (2005)." of copyright ©2009 Optical Society of American.

©2009 Optical Society of American.

**Figure 13.** Planar lens based on nanoscale slit array in metallic film. (a) Geometry of the lens consisting of a 400nm optically thick gold film (yellow) with air slits of different widths (80 to150 nm) (light blue) milled therein on a fused silica substrate (dark blue). The inset shows a scanning electron micrograph of the structure as viewed from the air-side. (b) Focusing pattern measured by confocal scanning optical microscopy (CSOM). (c) Finite-difference and frequency-domain (FDFD) simulated focusing pattern of the field intensity through the center of the slits. In order to show the features of the focus spotclearly, the field intensity inside the slits is saturated. Reprinted with permission from "LievenVerslegers et. al., Nano Lett. 9, 235-238 (2009)" of copyright ©2009 Chemical Society of American.

The basic geometry consists of an array of nanoscale slits in an otherwise opaque metallic film (see Fig. 13 (a)). Figure13 shows the main results of the work, which combines fabrication, characterization, andsimulation. Pane l (a) shows the fabricated structure, while panels (b) and (c) represent the measured and simulated field intensity in across section through the center of the slits (along the x-direction). Both the measurement and the simulation clearly demonstrate focusing of the wave. The agreement between experiment and simulation is excellent. Moreover, the simulation image is generated using the designed parameters as the slit width rather than the actual slit width measured in the SEM, as is commonly done when comparing nanophotonics simulation and experiments. The agreemen there thus indicates the robustness in design and the fault tolerance of this approach for focusing. The effect of lens size can be exploited to control the focusing behavior as is shown clearly in Fig. 14. Both lenses introduce the same curvature to the incident plane wave as the lens from Fig. 13, since we consist of slits with the same width as the original design (2.5 μm long). By omitting one outer slit on each side for the lens in Fig. 14 (a), one gets the lens, as shown in Fig. 14 (b).

Plasmonic Lenses 197

and period) milled into a silver film [38]. The focusing mechanism is explained by using a simple coherent interference model of SPP generation on the circular grating by the incident field. Experimental results concur well with theoretical predictions and highlight the requirement for the phase matching of SPP sources in the grating to achieve the maximum enhancement of the SPP wave at the focal point. NSOM measurements show that the plasmonic lens achieves more than a 10-fold intensity enhancement over the intensity of a single ring of the in-plane field components at the focus when the grating design is tuned to

**Figure 15.** (a) Experimental scheme for near-field measurements. Circular gratings are cut into a silver film deposited on a quartz substrate. Laser light is normally incident from the quartz side, and the electromagnetic near-field is monitored with a metal coated NSOM tip. (b) SEM image of a sample with 15 rings. The scale bar is 5 microns. Reprinted with permission from "Jennifer M. Steele , Zhaowei Liu , Yuan Wang, and Xiang Zhang, Opt. Express 14, 5664-5670 (2006)." of copyright ©2006 Optical Society

To investigate this focusing experimentally, rings with different periods were cut into 150 nm thick silver films. Silver was evaporated onto a quartz plate at a high rate to ensure a surface with minimal roughness. Rings were milled into the metal using an FEI Strata 201 XP focused ion beam (FIB), with the inner most ring having a diameter of 8 microns. Additional rings were added with a period either close to or far from resonance with the excited SPP waves. The surface plasmons were excited with linearly polarized laser light incident from the quartz side. The electromagnetic near-field of these structures was recorded using near-field scanning optical microscopy (NSOM) in collection mode using a metal coated NSOM tip. A metal coated tip was chosen over an uncoated tip to increase the resolution of the scan. Previous experimental results on samples with similar geometry compare favorably with computer simulations, indicating the interaction of the SPP near field with the metal tip is negligible. The measurement scheme can be seen in Fig. 15 (a) with an SEM image of a typical sample shown in Fig. 15 (b). The phase change of SPP waves across a barrier is an interesting issue that has received very little attention. If the slit width

the SPP wavelength.

of American.

**Figure 14.** Control of the cylindrical lens behavior by design of nanoscale slit array parameters. Effect of lens size on focusing for (a) a lens with 13 slits (80-150nm by 2.5 μm) and (b) a lens with 11 slits (80- 120nm by 2.5 μm). The white line gives an estimate of the lens position. Both scanning electron micrographs are on the same saclew. Reprinted with permission from "LievenVerslegers et. al., Nano Lett. 9, 235-238 (2009)" of copyright ©2009 Chemical Society of American.

This first experimental demonstration is a crucial step in the realization of this potentially important technology form any applications in optoelectronics. Moreover, the design principles presented here for the specil case of a lens can be applied to construct a wide range of optical components that rely on tailoring of the optical phase front.

#### *3.1.2. Two-dimensional structures for focusing*

#### *3.1.2.1. Circular grating-based metallic structures for focusing*

Recently, Jennifer et. al. reported the generation and focusing of surface plasmon polariton (SPP) waves from normally incident light on a planar circular grating (constant slits width and period) milled into a silver film [38]. The focusing mechanism is explained by using a simple coherent interference model of SPP generation on the circular grating by the incident field. Experimental results concur well with theoretical predictions and highlight the requirement for the phase matching of SPP sources in the grating to achieve the maximum enhancement of the SPP wave at the focal point. NSOM measurements show that the plasmonic lens achieves more than a 10-fold intensity enhancement over the intensity of a single ring of the in-plane field components at the focus when the grating design is tuned to the SPP wavelength.

196 Plasmonics – Principles and Applications

14 (a), one gets the lens, as shown in Fig. 14 (b).

approach for focusing. The effect of lens size can be exploited to control the focusing behavior as is shown clearly in Fig. 14. Both lenses introduce the same curvature to the incident plane wave as the lens from Fig. 13, since we consist of slits with the same width as the original design (2.5 μm long). By omitting one outer slit on each side for the lens in Fig.

**Figure 14.** Control of the cylindrical lens behavior by design of nanoscale slit array parameters. Effect of lens size on focusing for (a) a lens with 13 slits (80-150nm by 2.5 μm) and (b) a lens with 11 slits (80- 120nm by 2.5 μm). The white line gives an estimate of the lens position. Both scanning electron micrographs are on the same saclew. Reprinted with permission from "LievenVerslegers et. al., Nano

This first experimental demonstration is a crucial step in the realization of this potentially important technology form any applications in optoelectronics. Moreover, the design principles presented here for the specil case of a lens can be applied to construct a wide

Recently, Jennifer et. al. reported the generation and focusing of surface plasmon polariton (SPP) waves from normally incident light on a planar circular grating (constant slits width

Lett. 9, 235-238 (2009)" of copyright ©2009 Chemical Society of American.

*3.1.2. Two-dimensional structures for focusing* 

*3.1.2.1. Circular grating-based metallic structures for focusing* 

range of optical components that rely on tailoring of the optical phase front.

**Figure 15.** (a) Experimental scheme for near-field measurements. Circular gratings are cut into a silver film deposited on a quartz substrate. Laser light is normally incident from the quartz side, and the electromagnetic near-field is monitored with a metal coated NSOM tip. (b) SEM image of a sample with 15 rings. The scale bar is 5 microns. Reprinted with permission from "Jennifer M. Steele , Zhaowei Liu , Yuan Wang, and Xiang Zhang, Opt. Express 14, 5664-5670 (2006)." of copyright ©2006 Optical Society of American.

To investigate this focusing experimentally, rings with different periods were cut into 150 nm thick silver films. Silver was evaporated onto a quartz plate at a high rate to ensure a surface with minimal roughness. Rings were milled into the metal using an FEI Strata 201 XP focused ion beam (FIB), with the inner most ring having a diameter of 8 microns. Additional rings were added with a period either close to or far from resonance with the excited SPP waves. The surface plasmons were excited with linearly polarized laser light incident from the quartz side. The electromagnetic near-field of these structures was recorded using near-field scanning optical microscopy (NSOM) in collection mode using a metal coated NSOM tip. A metal coated tip was chosen over an uncoated tip to increase the resolution of the scan. Previous experimental results on samples with similar geometry compare favorably with computer simulations, indicating the interaction of the SPP near field with the metal tip is negligible. The measurement scheme can be seen in Fig. 15 (a) with an SEM image of a typical sample shown in Fig. 15 (b). The phase change of SPP waves across a barrier is an interesting issue that has received very little attention. If the slit width

#### 198 Plasmonics – Principles and Applications

is much smaller than the SPP wavelength, the slit will have very little effect on the SPP and the phase change should be very small. However, if the slit width is on the order of the SPP wavelength, as the SPP waves cross a slit opposite charges will be induced on opposite sides of the slit, providing quasi-electrostatic coupling across the barrier. The authors calimed that it is possible that the phase change will be sensitive to the slit width. The number and period of rings, film material, and slit geometries provide experimental handles to tune the plasmonic lens to accommodate specific applications, making this technique a flexible plasmonic tool for sensing applications.

Plasmonic Lenses 199

Let **i**, **j**, **k** be the unit vectors in the direction of the co-ordinate axes. To be integral over the

0 0 , cos 1 cos sin exp cos sin ,

1 1 , cos sin sin exp cos sin ,

2 2 , cos 1 cos sin exp cos sin .

According to the equation, the intensity of lateral electric field component, |Ex|2, follows the zero-order Bessel function J0 of the first kind, while the intensity of longitudinal electric field component, |Ez|2, follows the first-order Bessel function J1 of the first kind. In the total electric field intensity distribution, all the field components add up. With high numerical aperture, this leads to not only asymmetry of the focus spot but also an enlarged focus spot. As shown in Figs. 17 (a)~(b), the total electric field and individual electric field components, |E|2, |Ex|2, &|Ez|2, emerged from λsp-launched FZP lens are in comparison with that the total electric field and individual electric field components from a λin-launched PMZP lens. It is found that the intensity ratio, |Ex|2/|Ez|2, can increase up to 10 times for the λsp-launched PMZP lens. A

**Figure 17.** The total electric field and electric field components, |E|2, |E*x*|2, and |E*z*|2, emerged from (a) a λsp-launched FZP lens and (b) a λin-launched FZP lens. It is observed that the proposed superlens enables to restrict the depolarization effect and produces a linearly- polarized focus spot having the

*I rz T J kr ikz d*

 θ

*I rz T J kr ikz d*

 θ

 θ

 θ  θ

 θ  θθ

 θ  θθ

 θθ

*I rz T J kr ikz d*

 θ

( ) ( )( ) ( )

( ) ( )( )

( ) ( )( ) ( )

θ θ

individual zones, *I0*, *I1*, *I2* are expressed as,

The wave vector *k* = 2π/λ.

polarization direction in the *x* direction.

1

1

−

*n n n*

α

1

− = −

*n n n*

α

*n*

α

*n*

α

− = +

θ

θ

focus spot having the polarization direction along the x direction is obtained.

*n n n*

α

<sup>=</sup>

*n*

α

The following two sections below introduce the metallic subwavelength structures with chirped (variant periods) slits and nanopinholes acted as the plasmonic lenses for the purpose of superfocusing.

#### *3.1.2.2. Illumination under linear polarization state*

A novel structure called plasmonic micro-zone plate-like (PMZP) or plasmonic lens with chirped slits is put forth to realize superfocusing. It was proposed by Fu's group [39,40]. Unlike conventional Fresnel zone plate (CFZP), a plasmonic structure was used and combined with a CFZP. Configuration of the PMZP is an asymmetric structure with variant periods in which a thin film of Ag is sandwiched between air and glass. The PMZP is a device that a quartz substrate coated with Ag thin film which is embedded with a zone plate structure with the zone number N < 10. Figure 16 is an example of schematic diagram of the structure.

**Figure 16.** Schematic of the plasmonic micro-zone plate for super-focusing.

Following the electromagnetic focusing theory of Richard and Wolf (Richards & Wolf, 1959)[41], the electric field vector in the focal region is given by,

$$\mathbf{E}\text{ (r, z, }\phi\text{)} = \text{-i}\left[\text{I}\alpha\text{ (r, z)}\text{-I}\text{z (r, z)}\cos 2\phi\text{] }\mathbf{i} - \text{i}\text{ 1z}\text{(r, z)}\sin 2\phi\text{)} - \text{2I}\text{-(r, z)}\cos \phi\text{ k}.\tag{2}$$

Let **i**, **j**, **k** be the unit vectors in the direction of the co-ordinate axes. To be integral over the individual zones, *I0*, *I1*, *I2* are expressed as,

$$I\_0\left(r,z\right) = \sum\_n T\_n \int\_{a\_{n-1}}^{a\_n} \sqrt{\cos\theta} \left(1+\cos\theta\right) I\_0\left(kr\sin\theta\right) \exp\left(ikz\cos\theta\right) \sin\theta d\theta,$$

$$I\_1\left(r,z\right) = \sum\_n T\_n \int\_{a\_{n-1}}^{a\_n} \sqrt{\cos\theta} \sin\theta f\_1\left(kr\sin\theta\right) \exp\left(ikz\cos\theta\right) \sin\theta d\theta,$$

$$I\_2\left(r,z\right) = \sum\_n T\_n \int\_{a\_{n-1}}^{a\_n} \sqrt{\cos\theta} \left(1-\cos\theta\right) I\_2\left(kr\sin\theta\right) \exp\left(ikz\cos\theta\right) \sin\theta d\theta.$$

The wave vector *k* = 2π/λ.

198 Plasmonics – Principles and Applications

plasmonic tool for sensing applications.

*3.1.2.2. Illumination under linear polarization state* 

**Figure 16.** Schematic of the plasmonic micro-zone plate for super-focusing.

1959)[41], the electric field vector in the focal region is given by,

) = -*i* [*I0* (*r*, *z*)+*I2* (*r*, *z*) cos2

Following the electromagnetic focusing theory of Richard and Wolf (Richards & Wolf,

] **i** – *i I2* (*r*, *z*) sin2

ϕ

**j** - 2*I1* (*r*, *z*) cos

ϕ

**k**. (2)

ϕ

purpose of superfocusing.

structure.

 **E** (*r*, *z*,

ϕ

is much smaller than the SPP wavelength, the slit will have very little effect on the SPP and the phase change should be very small. However, if the slit width is on the order of the SPP wavelength, as the SPP waves cross a slit opposite charges will be induced on opposite sides of the slit, providing quasi-electrostatic coupling across the barrier. The authors calimed that it is possible that the phase change will be sensitive to the slit width. The number and period of rings, film material, and slit geometries provide experimental handles to tune the plasmonic lens to accommodate specific applications, making this technique a flexible

The following two sections below introduce the metallic subwavelength structures with chirped (variant periods) slits and nanopinholes acted as the plasmonic lenses for the

A novel structure called plasmonic micro-zone plate-like (PMZP) or plasmonic lens with chirped slits is put forth to realize superfocusing. It was proposed by Fu's group [39,40]. Unlike conventional Fresnel zone plate (CFZP), a plasmonic structure was used and combined with a CFZP. Configuration of the PMZP is an asymmetric structure with variant periods in which a thin film of Ag is sandwiched between air and glass. The PMZP is a device that a quartz substrate coated with Ag thin film which is embedded with a zone plate structure with the zone number N < 10. Figure 16 is an example of schematic diagram of the

According to the equation, the intensity of lateral electric field component, |Ex|2, follows the zero-order Bessel function J0 of the first kind, while the intensity of longitudinal electric field component, |Ez|2, follows the first-order Bessel function J1 of the first kind. In the total electric field intensity distribution, all the field components add up. With high numerical aperture, this leads to not only asymmetry of the focus spot but also an enlarged focus spot. As shown in Figs. 17 (a)~(b), the total electric field and individual electric field components, |E|2, |Ex|2, &|Ez|2, emerged from λsp-launched FZP lens are in comparison with that the total electric field and individual electric field components from a λin-launched PMZP lens. It is found that the intensity ratio, |Ex|2/|Ez|2, can increase up to 10 times for the λsp-launched PMZP lens. A focus spot having the polarization direction along the x direction is obtained.

**Figure 17.** The total electric field and electric field components, |E|2, |E*x*|2, and |E*z*|2, emerged from (a) a λsp-launched FZP lens and (b) a λin-launched FZP lens. It is observed that the proposed superlens enables to restrict the depolarization effect and produces a linearly- polarized focus spot having the polarization direction in the *x* direction.

The chirped slits can form a focal region in free space after the exit plane. The final intensity at the focal point is synthesized by iteration of each zone focusing and interference each other, and can be expressed as

$$I = \alpha \sum\_{i=1}^{N} CI\_0 \frac{4r\_i}{\lambda\_{SP}} e^{-(r\_{\hat{\mathbf{I}}} / l\_{SP})} \tag{3}$$

Plasmonic Lenses 201

**Figure 18.** The simulation result of the example of the PMZP. The propagation direction is z. Electric field intensity |Ex|2 at (a) y-z plane, (b) x-z plane, and (c) x-y plane. Electric field transmission in the line z=-0.65 μm (calculated focal plane) at (d) x-z plane, y=0; (e) y-z plane, x=0; and (f) y-z plane, x=0. The designed focal length and outmost zone width using scalar theory is f=1μm and 53 nm, respectively. The calculated DOF is ~700 nm (scalar theory designed value is 8.85 nm) the site z=0 is the exit plane of the Ag film.

where *I*0 is the incident intensity, *r*i is the inner radius of each zone, *i* is the number of the zones, *l*SP is the propagation length for the SPP wave, α is interference factor, and *C* is the coupling efficiency of the slits. *C* is a complicated function of the slit geometry and will likely have a different functional form when the slit width is much larger or much smaller than the incident wavelength

The PMZPs is an asymmetric structure. For an evanescent wave with given kx, we have 2 2 1/2 [ ( /) ] *zj j <sup>x</sup> k ck* =+ − ε ω for j=1 (air) and j=3 (glass) and <sup>2</sup> 2 1/2 [ ( / )] *zj x j k ik c* =+ − ε ω for j=2 (Ag film). Superfocusing requires regenerating the evanescent waves. Thus the PMZP needs to be operated with the condition 11 22 22 33 | / / || / / | 0 *zz z z kk k k* εε εε + +→ . Physically, this would require exciting a surface plasmon at either the air or the glass side. For *E*⊥ wave, a negative permittivity is sufficient for focusing evanescent waves if the metal film thickness and object are much smaller than the incident wavelength. Because electric permittivity ε < 0 occurs naturally in silver and other noble metals at visible wavelengths, a thin metallic film can act as an optical super lens. In the electrostatic limit, the p-polarized light, dependence on permeability μ is eliminated and only permittivity ε is relevant. In addition, diffraction and interference contribute to the transition from the evanescent waves to the propagation waves in the quasi-far-field region. Above all, the PMZPs form super focusing by interference of the localized SPP wave which is excited from the zones. This makes it possibly work at near and quasi-far-field with lateral resolution beyond diffraction limit. Also the PMZP has several zones only, its dimension is decreased greatly compared the CFZP.

As an example, an appropriate numerical computational analysis of a PMZP structure's electromagnetic field is carried out using finite-difference and time-damain (FDTD). It is illuminated by a plane wave with a 633 nm incident where Ag film has permittivity ' " 17.6235 0.4204 *mm m* εε ε = + =− + *i i* . An Ag film with thickness 300 *Ag h nm* = centered at z=150 nm has an embedded micro-zone-plate structure. Zone number *N*=8, and outer diameter *OD*=11.93 μm. The widths of each zone from first ring to last ring, calculated by using the conventional zone plate equations, are 245, 155, 116, 93, 78, 67, 59, and 52 nm. In the FDTD simulations, the perfectly

matched layer boundary condition was applied at the grid boundaries. Figure 17 is the simulation result. From the result, the simulated focal length of the PMZP, *f*PMZP and depth of focus (*DOF*) are larger than those of the designed values using the classical equations 2 2 1/2 ( / 4) *n FZP r nf n* = + λ λ and <sup>2</sup> *DOF r* =± Δ2 / λ , where *n*=1, 2, 3,…, *f*PMZP is the designed principal focal length of Fresnel zone plates and given in terms of radius *R* of the inner ring

200 Plasmonics – Principles and Applications

other, and can be expressed as

than the incident wavelength

2 2 1/2 [ ( /) ] *zj j <sup>x</sup> k ck* =+ − ε ω

ε

CFZP.

εε

 ε

simulations, the perfectly

2 2 1/2 ( / 4) *n FZP*

 λ

*r nf n* = + λ

The chirped slits can form a focal region in free space after the exit plane. The final intensity at the focal point is synthesized by iteration of each zone focusing and interference each

*<sup>N</sup>* 4 (/ ) *SP*

<sup>−</sup> <sup>=</sup> (3)

is interference factor, and *C* is the

for j=2 (Ag

ε ω

, where *n*=1, 2, 3,…, *f*PMZP is the designed

α

εε+ +→ . Physically, this

0 1

λ=

where *I*0 is the incident intensity, *r*i is the inner radius of each zone, *i* is the number of the

coupling efficiency of the slits. *C* is a complicated function of the slit geometry and will likely have a different functional form when the slit width is much larger or much smaller

The PMZPs is an asymmetric structure. For an evanescent wave with given kx, we have

film). Superfocusing requires regenerating the evanescent waves. Thus the PMZP needs to

would require exciting a surface plasmon at either the air or the glass side. For *E*⊥ wave, a negative permittivity is sufficient for focusing evanescent waves if the metal film thickness and object are much smaller than the incident wavelength. Because electric permittivity

 < 0 occurs naturally in silver and other noble metals at visible wavelengths, a thin metallic film can act as an optical super lens. In the electrostatic limit, the p-polarized light, dependence on permeability μ is eliminated and only permittivity ε is relevant. In addition, diffraction and interference contribute to the transition from the evanescent waves to the propagation waves in the quasi-far-field region. Above all, the PMZPs form super focusing by interference of the localized SPP wave which is excited from the zones. This makes it possibly work at near and quasi-far-field with lateral resolution beyond diffraction limit. Also the PMZP has several zones only, its dimension is decreased greatly compared the

As an example, an appropriate numerical computational analysis of a PMZP structure's electromagnetic field is carried out using finite-difference and time-damain (FDTD). It is

illuminated by a plane wave with a 633 nm incident where Ag film has permittivity ' " 17.6235 0.4204 *mm m*

matched layer boundary condition was applied at the grid boundaries. Figure 17 is the simulation result. From the result, the simulated focal length of the PMZP, *f*PMZP and depth of focus (*DOF*) are larger than those of the designed values using the classical equations

λ

principal focal length of Fresnel zone plates and given in terms of radius *R* of the inner ring

and <sup>2</sup> *DOF r* =± Δ2 /

 = + =− + *i i* . An Ag film with thickness 300 *Ag h nm* = centered at z=150 nm has an embedded micro-zone-plate structure. Zone number *N*=8, and outer diameter *OD*=11.93 μm. The widths of each zone from first ring to last ring, calculated by using the conventional zone plate equations, are 245, 155, 116, 93, 78, 67, 59, and 52 nm. In the FDTD

εε

for j=1 (air) and j=3 (glass) and <sup>2</sup> 2 1/2 [ ( / )] *zj x j k ik c* =+ −

*i SP <sup>r</sup> r l <sup>i</sup> <sup>i</sup> I CI e*

α

be operated with the condition 11 22 22 33 | / / || / / | 0 *zz z z kk k k*

zones, *l*SP is the propagation length for the SPP wave,

**Figure 18.** The simulation result of the example of the PMZP. The propagation direction is z. Electric field intensity |Ex|2 at (a) y-z plane, (b) x-z plane, and (c) x-y plane. Electric field transmission in the line z=-0.65 μm (calculated focal plane) at (d) x-z plane, y=0; (e) y-z plane, x=0; and (f) y-z plane, x=0. The designed focal length and outmost zone width using scalar theory is f=1μm and 53 nm, respectively. The calculated DOF is ~700 nm (scalar theory designed value is 8.85 nm) the site z=0 is the exit plane of the Ag film.

and incident wavelength by <sup>2</sup> / *FZP f R*<sup>=</sup> λ , Δ*r* is the outmost zone width, and λ is the incident wavelength. It may be attributed to the SPPs wave coupling through the cavity mode and is involved for the contribution of the beam focusing. The focusing is formed by interference between the SPPs wave and the diffraction waves from the zones.

Plasmonic Lenses 203

**Figure 19.** (a) Schematic diagram of the sandwiched plasmonic lens with chirped circular slits corrugated on Au film. Width of the outmost circular slit is 95 nm. Lens dimension (outer diameter) is 12 μm. (b) Scanning electron microscope image of the lens fabricated using focused ion beam milling technique. The scale bar is 4 μm. (c) AFM measurement result: topography of the fabricated lens. (d) NSOM characterization result of the lens: 2D E-field intensity distribution at propagation distance of 2.5 μm

**Figure 20.** Measured 3D E-field intensity distribution of the plasmonic lens vs. lateral *x* and propagation distance *z* using NSOM. The figure was replotted using the NSOM probed data.

Figures 18 (a)~(f) are electric intensity distribution |*E*x|2 for *E*<sup>⊥</sup> wave in z-y, x-z, and x-y plane, respectively. The numerical computational analysis of the electromagnetic field is carried out using finite-difference and time-domain (FDTD) algorithm. It can be seen that focused spot size [full width at half maximum (FWHM)] at y-z plane is smaller than the one at x-y plane. For conventional Fresenl zone plate, when zone numbers are few, the first sidelobe is large. In contrast, our PMZP has much lower first sidelobe. Suppressed sidelobe at y-z plane is higher than the one at XOZ plane due to the incident wave with *E*<sup>⊥</sup> wave. Transmission with the *E*<sup>⊥</sup> wave illumination is extraordinarily enhanced due to the excited SPP wave coupling which is then converted to propagation wave by diffraction. Figure 2 (f) shows that there is only one peak transmission after exit plane of the Ag film. Furthermore, Fabry-Pérot-like phenomenon is found through the central aperture during the SPP wave coupling and propagation in cavity mode, as shown in Figs.17 (a), (b) and (f). It plays a positive role for the enhancement transmission.

Further characterization of the plasmonic lens was done,as shown in Figs. 19 (a)-(d) [42]. The Au thin film of 200 nm in thickness was coated on quart substrate using e-beam evaporation technique. The lens was fabricated using focused ion beam (FEI Quanta 200 3D dual beam system) direct milling technique, as shown in Fig. 19 (b). Geometrical characterization was performed using an atomic force microscope (Nanoscope 2000 from DI company). Figure 19 (c) shows topography of the FIB fabricated plasmonic lens. The optical measurement was performed with a near-field optical microscope (MultiView 2000TS from Nanonics Inc. in Israel) where a tapered single mode fiber probe, with an aperture diameter of 100 nm, was used working in collection mode. The fiber tip was raster scanned at a discrete constant height of 500 nm, 1.0 μm, 1.5 μm, 2.0 μm, 2.5 μm, 3.0 μm, 3.2 μm, 3.5 μm, 3.7 μm, 4 μm, 4.5 μm, and 5 μm, respectively, above the sample surface, and allowing us to map the optical intensity distribution over a grid of 256×256 points spanning an area of 20×20 μm2. Working wavelength of the light source is 532 nm (Nd: YAG laser with power of 20 mW). Additionally, a typical lock-in amplifier and optical chopper were utilized to maximize the signal-to-noise ratio. Figure 19 (d) shows the measured three-dimensional (3D) electric field intensity distribution of the lens at propagation distance of 2.5 μm.

Figure 20 is a re-plotted 3D image of the NSOM measured intensity profiles along *x*-axis probed at the different propagation distance *z* ranging from 5 nm to 5 μm. It intuitively shows the intensity distribution along propagation distance. It can be seen that the peak intensity is significantly enhanced from 0.01 μm to 1 μm, and then degraded gradually in near-field region because of SPP-enhanced wave propagation on Au surface vanished in free space when z >1 μm. Only the interference-formed beam focusing region exits in near-field region. It is also in agreement with our calculated results. For more information, please see Ref. [43].

202 Plasmonics – Principles and Applications

and incident wavelength by <sup>2</sup> / *FZP f R*<sup>=</sup>

positive role for the enhancement transmission.

Ref. [43].

λ , Δ

interference between the SPPs wave and the diffraction waves from the zones.

incident wavelength. It may be attributed to the SPPs wave coupling through the cavity mode and is involved for the contribution of the beam focusing. The focusing is formed by

Figures 18 (a)~(f) are electric intensity distribution |*E*x|2 for *E*<sup>⊥</sup> wave in z-y, x-z, and x-y plane, respectively. The numerical computational analysis of the electromagnetic field is carried out using finite-difference and time-domain (FDTD) algorithm. It can be seen that focused spot size [full width at half maximum (FWHM)] at y-z plane is smaller than the one at x-y plane. For conventional Fresenl zone plate, when zone numbers are few, the first sidelobe is large. In contrast, our PMZP has much lower first sidelobe. Suppressed sidelobe at y-z plane is higher than the one at XOZ plane due to the incident wave with *E*<sup>⊥</sup> wave. Transmission with the *E*<sup>⊥</sup> wave illumination is extraordinarily enhanced due to the excited SPP wave coupling which is then converted to propagation wave by diffraction. Figure 2 (f) shows that there is only one peak transmission after exit plane of the Ag film. Furthermore, Fabry-Pérot-like phenomenon is found through the central aperture during the SPP wave coupling and propagation in cavity mode, as shown in Figs.17 (a), (b) and (f). It plays a

Further characterization of the plasmonic lens was done,as shown in Figs. 19 (a)-(d) [42]. The Au thin film of 200 nm in thickness was coated on quart substrate using e-beam evaporation technique. The lens was fabricated using focused ion beam (FEI Quanta 200 3D dual beam system) direct milling technique, as shown in Fig. 19 (b). Geometrical characterization was performed using an atomic force microscope (Nanoscope 2000 from DI company). Figure 19 (c) shows topography of the FIB fabricated plasmonic lens. The optical measurement was performed with a near-field optical microscope (MultiView 2000TS from Nanonics Inc. in Israel) where a tapered single mode fiber probe, with an aperture diameter of 100 nm, was used working in collection mode. The fiber tip was raster scanned at a discrete constant height of 500 nm, 1.0 μm, 1.5 μm, 2.0 μm, 2.5 μm, 3.0 μm, 3.2 μm, 3.5 μm, 3.7 μm, 4 μm, 4.5 μm, and 5 μm, respectively, above the sample surface, and allowing us to map the optical intensity distribution over a grid of 256×256 points spanning an area of 20×20 μm2. Working wavelength of the light source is 532 nm (Nd: YAG laser with power of 20 mW). Additionally, a typical lock-in amplifier and optical chopper were utilized to maximize the signal-to-noise ratio. Figure 19 (d) shows the measured three-dimensional

(3D) electric field intensity distribution of the lens at propagation distance of 2.5 μm.

Figure 20 is a re-plotted 3D image of the NSOM measured intensity profiles along *x*-axis probed at the different propagation distance *z* ranging from 5 nm to 5 μm. It intuitively shows the intensity distribution along propagation distance. It can be seen that the peak intensity is significantly enhanced from 0.01 μm to 1 μm, and then degraded gradually in near-field region because of SPP-enhanced wave propagation on Au surface vanished in free space when z >1 μm. Only the interference-formed beam focusing region exits in near-field region. It is also in agreement with our calculated results. For more information, please see

*r* is the outmost zone width, and λ is the

**Figure 19.** (a) Schematic diagram of the sandwiched plasmonic lens with chirped circular slits corrugated on Au film. Width of the outmost circular slit is 95 nm. Lens dimension (outer diameter) is 12 μm. (b) Scanning electron microscope image of the lens fabricated using focused ion beam milling technique. The scale bar is 4 μm. (c) AFM measurement result: topography of the fabricated lens. (d) NSOM characterization result of the lens: 2D E-field intensity distribution at propagation distance of 2.5 μm

**Figure 20.** Measured 3D E-field intensity distribution of the plasmonic lens vs. lateral *x* and propagation distance *z* using NSOM. The figure was replotted using the NSOM probed data.

A hybrid Au-Ag subwavelength metallic zone plate-like structure was put forth for the purpose of preventing oxidation and sulfuration of Ag film, as well as realizing superfocusing, as shown in Fig. 21 [43]. The Au film acts as both a protector and modulator in the structure. Focusing performance is analyzed by means of three-dimensional (3D) finite-difference and time-domain (FDTD) algorithm-based computational numerical calculation. It can be tuned by varying thicknesses of both Au and Ag thin films. The calculated results show that thickness difference between the Au and Ag thin films plays an important role for transmission spectra. The ratio of Au to Ag film thicknesses, *h*Au/*h*Ag, is proportional to the relevant peak transmission intensity. In case of *h*Au ≈ *h*Ag=50 nm, both transmission intensity and focusing performance are improved. In addition, the ratio *h*Au/*h*Ag strongly influences position of peak wavelengths λAu and λAg generated from beaming through the metallic structures.

Plasmonic Lenses 205

film, fixing *h*Au = 50 nm and 200 nm respectively and varying *h*Ag, the corresponding

4. Ratio α = *h*Au/*h*Ag strongly influences position of peak wavelengths λAu and λAg

The calculation results show that thickness of both the Au and Ag thin films has significant tailoring function due to the great contribution to superfocusing and transmission. Improved focusing performance and enhanced transmission can be obtained if *h*Au and *h*Ag match each other. This hybrid subwavelength structure has potential applications in data

However, the rings-based structures have higher sidelobes. To supress the sidelobes, a circular holes-based plasmonic lens was reported, as shown in Fig. 22 [44]. In the plasmonic lens with fixed pinhole diameters, propagation waves still exist for much reduced periodicity of pinholes due to the SPPs wave coupling, which interferes with the diffraction wavelets from the pinholes to form a focusing region in free space. Increasing incident wavelength is equivalent to reducing the pinhole diameters, and rapid decay of the EM field intensity will occur accordingly. The superlens proposed by the authors has the advantages of possessing micron scale focal length and large depth of focus along the propagation direction. It should be especially noted that the structure of the superlens can be easily fabricated using the current nanofabrication techniques, e.g. focused ion beam milling and e-beam lithography.

To further improve focusing quality of the circular holes-based plasmonic lens, an elliptical nanoholes-based plasmonic lens was put forth, as shown in Fig. 9 [45]. The plasmonic lens is

**Figure 22.** (a) Schematic of the pinhole array with focal length *f*. Lateral central distance *L* determines wave coupling between the neighboring holes. The pinholes are uniformly distributed in the zones. It is illuminated by a plane wave with 633 nm incident wavelength and p-polarization (transverse-magnetic field with components of Ex, Hy, and Ez). The perfectly matched layer (PML) boundary condition was applied at the grid boundaries in the three-dimensional FDTD simulation. (b) Nanofabrication of the

(a) (b)

lens using focused ion beam.

optical performances are not improved gradually with increasing *h*Ag.

generated from the metallic subwavelength structures.

storage, nanophotolithography, nanometrology, and bio-imaging etc.

**Figure 21.** Schematic of the plasmonic micro-zone plate super-focusing with focal length *f*. It is illuminated by a plane wave with 633 nm incident wavelength. In our FDTD simulations the perfectly matched layer (PML) boundary condition was applied at the grid boundaries.

The following features were found from the calculation results:


film, fixing *h*Au = 50 nm and 200 nm respectively and varying *h*Ag, the corresponding optical performances are not improved gradually with increasing *h*Ag.

4. Ratio α = *h*Au/*h*Ag strongly influences position of peak wavelengths λAu and λAg generated from the metallic subwavelength structures.

204 Plasmonics – Principles and Applications

A hybrid Au-Ag subwavelength metallic zone plate-like structure was put forth for the purpose of preventing oxidation and sulfuration of Ag film, as well as realizing superfocusing, as shown in Fig. 21 [43]. The Au film acts as both a protector and modulator in the structure. Focusing performance is analyzed by means of three-dimensional (3D) finite-difference and time-domain (FDTD) algorithm-based computational numerical calculation. It can be tuned by varying thicknesses of both Au and Ag thin films. The calculated results show that thickness difference between the Au and Ag thin films plays an important role for transmission spectra. The ratio of Au to Ag film thicknesses, *h*Au/*h*Ag, is proportional to the relevant peak transmission intensity. In case of *h*Au ≈ *h*Ag=50 nm, both transmission intensity and focusing performance are improved. In addition, the ratio *h*Au/*h*Ag strongly influences position of peak

wavelengths λAu and λAg generated from beaming through the metallic structures.

**Figure 21.** Schematic of the plasmonic micro-zone plate super-focusing with focal length *f*. It is illuminated by a plane wave with 633 nm incident wavelength. In our FDTD simulations the perfectly

the resonant wavelength of the hybrid structure which is proportional to α.

1. Thickness difference between the Au and Ag thin films plays important role for transmission spectra. It determines peak transmission intensity. Ratio of film thicknesses α = *h*Au/*h*Ag is proportional to the relevant peak intensity. It may attributed to

2. In the case of *h*Au ≈ *h*Ag = 50 nm, α≈1, both transmission intensity and focusing performance are improved in comparison to the other cases (fixing *h*Au = 50 nm and

3. For *h*Ag = 200 nm, both transmission intensity and focusing performance are improved gradually with increasing *h*Au. However, unlike the fixed 200 nm thickness of the Ag

matched layer (PML) boundary condition was applied at the grid boundaries.

The following features were found from the calculation results:

varying *h*Ag from 10 nm to 200 nm).

The calculation results show that thickness of both the Au and Ag thin films has significant tailoring function due to the great contribution to superfocusing and transmission. Improved focusing performance and enhanced transmission can be obtained if *h*Au and *h*Ag match each other. This hybrid subwavelength structure has potential applications in data storage, nanophotolithography, nanometrology, and bio-imaging etc.

However, the rings-based structures have higher sidelobes. To supress the sidelobes, a circular holes-based plasmonic lens was reported, as shown in Fig. 22 [44]. In the plasmonic lens with fixed pinhole diameters, propagation waves still exist for much reduced periodicity of pinholes due to the SPPs wave coupling, which interferes with the diffraction wavelets from the pinholes to form a focusing region in free space. Increasing incident wavelength is equivalent to reducing the pinhole diameters, and rapid decay of the EM field intensity will occur accordingly. The superlens proposed by the authors has the advantages of possessing micron scale focal length and large depth of focus along the propagation direction. It should be especially noted that the structure of the superlens can be easily fabricated using the current nanofabrication techniques, e.g. focused ion beam milling and e-beam lithography.

To further improve focusing quality of the circular holes-based plasmonic lens, an elliptical nanoholes-based plasmonic lens was put forth, as shown in Fig. 9 [45]. The plasmonic lens is

**Figure 22.** (a) Schematic of the pinhole array with focal length *f*. Lateral central distance *L* determines wave coupling between the neighboring holes. The pinholes are uniformly distributed in the zones. It is illuminated by a plane wave with 633 nm incident wavelength and p-polarization (transverse-magnetic field with components of Ex, Hy, and Ez). The perfectly matched layer (PML) boundary condition was applied at the grid boundaries in the three-dimensional FDTD simulation. (b) Nanofabrication of the lens using focused ion beam.

Plasmonic Lenses 207

distribute in different rings with variant periods. It can generate ultra-enhanced lasing effect and realize a long focal length in free space accordingly with extraordinarily elongated depth of focus (*DOF*) of as long as 13 μm under illumination of plane wave in linear y-

Figure 24 shows our computational results: E-field intensity distribution |Ey|2 at x-z and y-z planes for (a) and (b) δ=0.1; (c) and (d) δ=0.2; and (e) and (f) δ=0.4, respectively. It can be seen that E-field intensity distribution is symmetric due to linear y-polarization which is formed by uniformly rotating linear polarization radiating along radial directions. By means of interfering constructively, and the Ez component interferes destructively and vanishes at the focus. Thus we have |E|2=|Ex|2+|Ey|2+|Ez|2=|Ey|2, whereas Ex=0, and Ez=0. The lasing effect-induced ultra-long *DOF* is 7 μm, 12 μm, and 13 μm for δ=0.1, 0.2, and 0.4, respectively. It is three orders of magnitude in comparison to that of the conventional microlenses. The ultra-enhanced lasing effect may attribute to the surface plasmon (SP) wave coupling in the micro- and nano-cavity which form Fabry**-**Pérot resonance while the beam passing through the constructive pinholes. Calculated full-width and half-maximum (FWHM) at propagation distance z= -7 μm in free space is 330 nm, 510 nm, and 526 nm for δ=0.1, 0.2, and 0.4,

Lasing effect of the plasmonic lens with extraordinarily elongated *DOF* has the following

1. In bioimaging systems such as confocal optical microscope, three-dimensional (3D) image of cells or molecular is possible to be obtained and conventional multilayer focal

2. In online optical metrology systems, feed-back control system can be omitted because height of surface topography of the measured samples as large as ten micron is still

3. In plasmonic structures-based photolithography systems, the reported experimental results were obtained at near-field with tens nanometers gap between the structure and substrate surface. Apparently, it is difficult to control the gap in practical operation. However, using this plasmonic lens, the working distance between the structure and substrate surface can be as long as 12 μm and even longer. Practical control and operation process will be much easier and simplified than the approaches before in case

Like the discussion above regarding illumination with different polarization states, influence of polarization states on focusing properties of the the plasmonic lenses with both

The lens was fabricated using focused ion beam directly milling technique, and characterization of the elliptical nanopinholes-based plasmonic lens was carried out using NSOM, as shown in Figs. 25 (a) and (b). Currently, this work is still in progress in the research

within the extraordinarily elongated *DOF* of the plasmonic lenses.

chirped circular slits and elliptical nanopinholes were reported [46, 47].

polarization.

respectively.

unique features in practical applications:

plane scanning is unnecessary.

of using this lens.

group.

**Figure 23.** (a) Schematization of the pinhole array with focal length *f*. Lateral central distance *L* determines of wave coupling between the neighbored holes. The pinholes are uniformly distributed along the zones. It is illuminated by various waves with 633 nm incident wavelength. And we have different polarization states such as TM, EP and RP. (b) layout of elliptical pinholes with total 8 rings δ= 0.6 being used in our computational numerical calculation.

composed of elliptical pinholes with different sizes distributed in different rings with variant periods. Long-axis of the ellipse is defined as *an*=3*wn*, whereas *w*n is width of the corresponding ring width, and *n* is the number of rings. A thin film of Ag coated on the glass substrate is perforated by the pinholes. The numbers of *w*n and radius for different rings are listed in Table1.


**Table 1.** The numbers of *w*n for different rings with orders from inner to outer (designed *f*=1μm)

As an example, the authors studied the case of 200 nm thickness Ag film coated on quartz substrate and designed a nanostructure with 8 rings on the metal film (see Fig. 23). The pinholes are completely penetrated through the Ag film. The number of pinholes from inner to outer rings is 8, 20, 36, 55, 70, 96, 107, and 140, respectively. Outer diameter of the ring is 12.05 μm. Radius of the rings can be calculated by the formula <sup>2</sup> 2 2 <sup>2</sup> *<sup>n</sup> r nf n* = + λ λ , where *f* is the focal length for working wavelength of λ =633 nm which we used in our works. For simplicity, we define a ratio of short-axis to long-axis δ= *b*/*a* (where *a* is the length of longaxis of the elliptical pinholes, and *b* the short-axis). The used metal here is Ag with dielectric constant of 17.24 0.498 *<sup>m</sup>*ε =− + *i* at λ =633 nm, and εd=1.243 for glass. The incident angle θ is 0° (normal incidence). In our analysis, we simulated the cases of the ratios: δ = 0.1, 0.2, and 0.4, respectively. The ultra-enhanced lasing effect disappears when the ratio δ→1 (circular pinholes). Orientation of the pinholes is along radial direction. The pinholes symmetrically distribute in different rings with variant periods. It can generate ultra-enhanced lasing effect and realize a long focal length in free space accordingly with extraordinarily elongated depth of focus (*DOF*) of as long as 13 μm under illumination of plane wave in linear ypolarization.

206 Plasmonics – Principles and Applications

δ

rings are listed in Table1.

**Figure 23.** (a) Schematization of the pinhole array with focal length *f*. Lateral central distance *L* determines of wave coupling between the neighbored holes. The pinholes are uniformly distributed along the zones. It is illuminated by various waves with 633 nm incident wavelength. And we have different polarization states such as TM, EP and RP. (b) layout of elliptical pinholes with total 8 rings

composed of elliptical pinholes with different sizes distributed in different rings with variant periods. Long-axis of the ellipse is defined as *an*=3*wn*, whereas *w*n is width of the corresponding ring width, and *n* is the number of rings. A thin film of Ag coated on the glass substrate is perforated by the pinholes. The numbers of *w*n and radius for different

(a) (b)

Ring No. 1 3 3 4 5 6 7 8 Ring radius(μm) 1.41 2.11 2.78 3.43 4.08 4.73 5.37 6.01 *w*n (nm) 245 155 116 93 78 67 59 53 **Table 1.** The numbers of *w*n for different rings with orders from inner to outer (designed *f*=1μm)

12.05 μm. Radius of the rings can be calculated by the formula <sup>2</sup> 2 2 <sup>2</sup> *<sup>n</sup>*

λ

As an example, the authors studied the case of 200 nm thickness Ag film coated on quartz substrate and designed a nanostructure with 8 rings on the metal film (see Fig. 23). The pinholes are completely penetrated through the Ag film. The number of pinholes from inner to outer rings is 8, 20, 36, 55, 70, 96, 107, and 140, respectively. Outer diameter of the ring is

λ

simplicity, we define a ratio of short-axis to long-axis δ= *b*/*a* (where *a* is the length of longaxis of the elliptical pinholes, and *b* the short-axis). The used metal here is Ag with dielectric

0° (normal incidence). In our analysis, we simulated the cases of the ratios: δ = 0.1, 0.2, and 0.4, respectively. The ultra-enhanced lasing effect disappears when the ratio δ→1 (circular pinholes). Orientation of the pinholes is along radial direction. The pinholes symmetrically

*r nf n* = + λ

=633 nm which we used in our works. For

=633 nm, and εd=1.243 for glass. The incident angle

 λ

, where *f* is

θis

= 0.6 being used in our computational numerical calculation.

the focal length for working wavelength of

=− + *i* at

constant of 17.24 0.498 *<sup>m</sup>*ε

Figure 24 shows our computational results: E-field intensity distribution |Ey|2 at x-z and y-z planes for (a) and (b) δ=0.1; (c) and (d) δ=0.2; and (e) and (f) δ=0.4, respectively. It can be seen that E-field intensity distribution is symmetric due to linear y-polarization which is formed by uniformly rotating linear polarization radiating along radial directions. By means of interfering constructively, and the Ez component interferes destructively and vanishes at the focus. Thus we have |E|2=|Ex|2+|Ey|2+|Ez|2=|Ey|2, whereas Ex=0, and Ez=0. The lasing effect-induced ultra-long *DOF* is 7 μm, 12 μm, and 13 μm for δ=0.1, 0.2, and 0.4, respectively. It is three orders of magnitude in comparison to that of the conventional microlenses. The ultra-enhanced lasing effect may attribute to the surface plasmon (SP) wave coupling in the micro- and nano-cavity which form Fabry**-**Pérot resonance while the beam passing through the constructive pinholes. Calculated full-width and half-maximum (FWHM) at propagation distance z= -7 μm in free space is 330 nm, 510 nm, and 526 nm for δ=0.1, 0.2, and 0.4, respectively.

Lasing effect of the plasmonic lens with extraordinarily elongated *DOF* has the following unique features in practical applications:


Like the discussion above regarding illumination with different polarization states, influence of polarization states on focusing properties of the the plasmonic lenses with both chirped circular slits and elliptical nanopinholes were reported [46, 47].

The lens was fabricated using focused ion beam directly milling technique, and characterization of the elliptical nanopinholes-based plasmonic lens was carried out using NSOM, as shown in Figs. 25 (a) and (b). Currently, this work is still in progress in the research group.

Plasmonic Lenses 209

**Figure 25.** (a) SEM micrograph of the elliptical nanopinholes-based plasmonic lens. (b) 2D image of NSOM probing along propagation distance at *z*=20nm in free space. The arrow indicates direction of

(a) (b)

Here we addressed an issue here from fabrication point of view. Real part of Au permittivity εAu will be increased due to Ga+ implantation of the FIB directly etching process. Theoretically, propagation constant *k*SP will be increased due to the large real part of

light in vacuum, εm and εd is dielectric constant of metal and dielectric, respectively. The increased *k*SP will cause strong transmission enhancement and generate extended skin depth

ω

is the incident frequency, *c* is the speed of

(c)

, whereas

linear polarization. (c) 3D image of NSOM probing.

*SP*

*c* ω

*k*

*m d*

ε ε

ε ε

<sup>=</sup> <sup>+</sup>

dielectric constant as *m d*

**Figure 24.** E-field intensity distribution |Ey|2 at x-z and y-z planes for (a) and (b) δ=0.1; (c) and (d) δ=0.2; and (e) and (f) δ=0.4, respectively.

208 Plasmonics – Principles and Applications

**Figure 24.** E-field intensity distribution |Ey|2 at x-z and y-z planes for (a) and (b) δ=0.1; (c) and (d)

δ=0.2; and (e) and (f) δ=0.4, respectively.

**Figure 25.** (a) SEM micrograph of the elliptical nanopinholes-based plasmonic lens. (b) 2D image of NSOM probing along propagation distance at *z*=20nm in free space. The arrow indicates direction of linear polarization. (c) 3D image of NSOM probing.

Here we addressed an issue here from fabrication point of view. Real part of Au permittivity εAu will be increased due to Ga+ implantation of the FIB directly etching process. Theoretically, propagation constant *k*SP will be increased due to the large real part of dielectric constant as *m d SP m d k c* ω ε ε ε ε <sup>=</sup> <sup>+</sup> , whereas ω is the incident frequency, *c* is the speed of light in vacuum, εm and εd is dielectric constant of metal and dielectric, respectively. The increased *k*SP will cause strong transmission enhancement and generate extended skin depth

#### 210 Plasmonics – Principles and Applications

in free space which is helpful for formation of the focusing region and makes a positive contribution on the plasmonic focusing accordingly.

Plasmonic Lenses 211

<sup>2</sup> 22 22 ( ) 2 (0) ( *x n ab a x b x* ) π

where *n* is an integer number. Therefore, the key point of designing the metallic lens is to

**Figure 26.** NSOM measurement showing SPP focusing in the plasmonic lens illuminated by radially polarized light. The NSOM probe was at a constant height of 2 μm above the PL. (a) 2D NSOM scan. Bright regions correspond to high intensity. (b) Normalized experimental (blue, cross markers) and theoretical (red, solid line) cross sections through the center of the PL. The sharp focus can be clearly observed. Reprinted with permission from "Gilad M.Lerman, Avner Yanai,and Uriel Levy, Nano Lett.

9, 2139-2143 (2009)." of copyright ©2009 Chemical Society of American.

Δ = +Δ + + − + − + (4)

λ

determine the width and position of slits for appropriate phase retardation.

ϕ

 πϕ

An elliptical nano-pinholes-based plasmonic lens was studied experimentally by means of FIB nanofabrication, AFM imaging, and NSOM characterization for the purpose of proof of plasmonic finely focusing. Both modes of sample scan and tip scan were employed for the lens probing. For the NSOM-based optical characterization of the plasmonic lenses, both of them have their own characteristics. The former can generate a bright-field like image with strong and uniform illumination; and the latter can produce a dark-field like image with high contrast which is helpful for checking focusing performance of the lenses. Our experimental results demonstrated that the lens is capable of realizing a subwavelength focusing with elongated depth of focus.

#### *3.1.2.3. Illumination under radial polarization state*

Most recently, the circular rings-based plasmonic lens was experimentally demonstrated [48, 49]. The focusing of surface plasmon polaritons by a plasmonic lens illuminated with radially polarized light was investigated. The field distribution is characterized by near-field scanning optical microscope. A sharp focal spot corresponding to a zero-order Bessel function is observed. For comparison, the plasmonic lens is also measured with linearly polarized light illumination, resulting in two separated lobes. Finally, the authors verify that the focal spot maintain sits width along the optical axis of the plasmonic lens. The results demonstrate the advantage of using radially polarized light for nanofocusing applications involving surface plasmon polaritons. Figures 26 (a) and (b) are reported NSOM characterization results. For comparison purposes, this theoretical cross section is also shownin Figure 26 (b). The profile of the Bessel function can be clearly observed. Neglecting the contribution of the E component, the theoretical spot size (based on full width halfmaximum criterion) is 380nm. The measured spot size is slightly larger, 410 ± 39nm (error was estimated by taking several cross sections through the center of the PL along different directions).

### **3.2. Subwavelength metallic structure for imaging**

A planar lens based on nanoscale slit arrays in a metallic film is present here for subwavelength imaging in the far field. Figure 27 is the schematic of the optical imaging with metallic slab lens [51]. To illustrate the design, both object distance a and image distance b are set to be 1 μm. The aperture and the thickness of silver slab lens are 3μm and 300 nm respectively. The permittivity εm=-29.26+i1.348 is used for silver at 810 nm.

When the light with magnetic field polarized in the y direction impinged on the surface of silver slab, SPPs can be excited at the slit entrance. The SPPs propagate inside the slits in the specific waveguide modes until reaching the export where we radiate into free space and form the optical image at the desired position. For the imaging of object localized on the axis x=0, the phase retardation of light transmitted through the lens is giver by

Plasmonic Lenses 211

$$
\Delta\varphi(\mathbf{x}) = 2n\pi + \Delta\varphi(0) + \frac{2\pi}{\lambda}(a+b-\sqrt{a^2+x^2}-\sqrt{b^2+x^2})\tag{4}
$$

where *n* is an integer number. Therefore, the key point of designing the metallic lens is to determine the width and position of slits for appropriate phase retardation.

210 Plasmonics – Principles and Applications

contribution on the plasmonic focusing accordingly.

focusing with elongated depth of focus.

directions).

*3.1.2.3. Illumination under radial polarization state* 

**3.2. Subwavelength metallic structure for imaging** 

in free space which is helpful for formation of the focusing region and makes a positive

An elliptical nano-pinholes-based plasmonic lens was studied experimentally by means of FIB nanofabrication, AFM imaging, and NSOM characterization for the purpose of proof of plasmonic finely focusing. Both modes of sample scan and tip scan were employed for the lens probing. For the NSOM-based optical characterization of the plasmonic lenses, both of them have their own characteristics. The former can generate a bright-field like image with strong and uniform illumination; and the latter can produce a dark-field like image with high contrast which is helpful for checking focusing performance of the lenses. Our experimental results demonstrated that the lens is capable of realizing a subwavelength

Most recently, the circular rings-based plasmonic lens was experimentally demonstrated [48, 49]. The focusing of surface plasmon polaritons by a plasmonic lens illuminated with radially polarized light was investigated. The field distribution is characterized by near-field scanning optical microscope. A sharp focal spot corresponding to a zero-order Bessel function is observed. For comparison, the plasmonic lens is also measured with linearly polarized light illumination, resulting in two separated lobes. Finally, the authors verify that the focal spot maintain sits width along the optical axis of the plasmonic lens. The results demonstrate the advantage of using radially polarized light for nanofocusing applications involving surface plasmon polaritons. Figures 26 (a) and (b) are reported NSOM characterization results. For comparison purposes, this theoretical cross section is also shownin Figure 26 (b). The profile of the Bessel function can be clearly observed. Neglecting the contribution of the E component, the theoretical spot size (based on full width halfmaximum criterion) is 380nm. The measured spot size is slightly larger, 410 ± 39nm (error was estimated by taking several cross sections through the center of the PL along different

A planar lens based on nanoscale slit arrays in a metallic film is present here for subwavelength imaging in the far field. Figure 27 is the schematic of the optical imaging with metallic slab lens [51]. To illustrate the design, both object distance a and image distance b are set to be 1 μm. The aperture and the thickness of silver slab lens are 3μm and

When the light with magnetic field polarized in the y direction impinged on the surface of silver slab, SPPs can be excited at the slit entrance. The SPPs propagate inside the slits in the specific waveguide modes until reaching the export where we radiate into free space and form the optical image at the desired position. For the imaging of object localized on the axis

300 nm respectively. The permittivity εm=-29.26+i1.348 is used for silver at 810 nm.

x=0, the phase retardation of light transmitted through the lens is giver by

**Figure 26.** NSOM measurement showing SPP focusing in the plasmonic lens illuminated by radially polarized light. The NSOM probe was at a constant height of 2 μm above the PL. (a) 2D NSOM scan. Bright regions correspond to high intensity. (b) Normalized experimental (blue, cross markers) and theoretical (red, solid line) cross sections through the center of the PL. The sharp focus can be clearly observed. Reprinted with permission from "Gilad M.Lerman, Avner Yanai,and Uriel Levy, Nano Lett. 9, 2139-2143 (2009)." of copyright ©2009 Chemical Society of American.

**Figure 27.** A schematic of optical imaging by a metallic slab lens with nanoslits. Reprinted with permission from "Ting Xu, et. al. Appl. Phys. Lett. 91,201501 (2007)" of copyright ©2007 American Institute of Physics.

Because of the complexity of the accurate description of the processes of SPPs' excitation, propagation, and coupling in metallic slits, the convenient and effective way is the approximation of these processed and making sure of good accuracy simultaneously. The coupling of SPPs during the propagation in slits is neglected, provided that the metallic wall between any two adjacent slits is larger than the skin depth in metal, about 24 nm for silver at a wavelength of 810 nm giver by

$$Z = \frac{1}{k\_0} \left[ \frac{\text{Re}(\mathcal{E}\_m) + \mathcal{E}\_d}{\text{Re}(\mathcal{E}\_m)^2} \right]^{1/2} \tag{5}$$

Plasmonic Lenses 213

of *β* determine the phase velocity and the propagation loss of SPPs inside the metallic slit,

**Figure 28.** (a) Dependence of phase retardation on the slit width. Red and blue tags represent the contributions for phase retardation from the real part of propagation constant and multiple reflections. The wavelength of incident light is 810 nm. (b) Transmittance of optical field (810 nm wavelength) through a nanoslit vs the slit depth ranging from 100 to 500 nm. Slit widths are 10, 20, 40, and 60 nm. Reprinted with permission from "Ting Xu, et. al. Appl. Phys. Lett. 91,201501 (2007)" of copyright ©2007

To illustrate the validity of metallic slab lens, finite-difference time-domain simulations are performed. Figure 28 (a) illuminates the dependence of phase retardation on slit width. Figure 28 (b) plots the finite-difference time-domain (FDTD) simulated transmittance of light through a slit with variant thickness as ranging from 100 to 500 nm by normal incidence at the wavelength of 810 nm. Calculated steady optical field (the magnetic field |Hy|2) of the simulation result is shown in Fig. 29. Obvious image spot can be seen at the position around Z=2.43 μm with the full width at half maximum of 396 nm approximately half of the incident wavelength. The slight focal shift of about 60 nm. Above all, the metallic slab lens displays a considerably good performance for imaging objects in the far field

respectively.

American Institute of Physics.

region.

The coupling effect occurred at the exit surface from neighboring slits is also omitted, compared with the intensity of directly radiated light from slits. The design above also displays that only a slight deviation is produced by coupling effect and it affects the image profile insignificantly. Assuming that the slit width is much smaller than a wavelength, it is justified to only consider the fundamental mode in the slit. Its complex propagation constant β in the slit is determined by the following equation:

$$\tanh(\sqrt{\beta^2 - k\_0^2 \varepsilon\_d} w \mid \text{2}) = \frac{-\varepsilon\_d \sqrt{\beta^2 - k\_0^2 \varepsilon\_m}}{\varepsilon\_m \sqrt{\beta^2 - k\_0^2 \varepsilon\_d}} \tag{6}$$

where *k*0 is the wave vector of light in free space, *m*ε and *<sup>d</sup>* ε are the permittivity of the metal and dielectric material inside the slits, and *w* is the slit width. The real and imaginary parts of *β* determine the phase velocity and the propagation loss of SPPs inside the metallic slit, respectively.

212 Plasmonics – Principles and Applications

Institute of Physics.

at a wavelength of 810 nm giver by

**Figure 27.** A schematic of optical imaging by a metallic slab lens with nanoslits. Reprinted with permission from "Ting Xu, et. al. Appl. Phys. Lett. 91,201501 (2007)" of copyright ©2007 American

0

*Z k*

β in the slit is determined by the following equation:

where *k*0 is the wave vector of light in free space, *m*

1 Re( )

Re( ) *m d m*

ε

2 2 0 <sup>0</sup> 2 2

ε

− − − =

tanh( / 2) *d m d*

and dielectric material inside the slits, and *w* is the slit width. The real and imaginary parts

*k w*

 ε

β

ε

The coupling effect occurred at the exit surface from neighboring slits is also omitted, compared with the intensity of directly radiated light from slits. The design above also displays that only a slight deviation is produced by coupling effect and it affects the image profile insignificantly. Assuming that the slit width is much smaller than a wavelength, it is justified to only consider the fundamental mode in the slit. Its complex propagation constant

 <sup>+</sup> <sup>=</sup> 

Because of the complexity of the accurate description of the processes of SPPs' excitation, propagation, and coupling in metallic slits, the convenient and effective way is the approximation of these processed and making sure of good accuracy simultaneously. The coupling of SPPs during the propagation in slits is neglected, provided that the metallic wall between any two adjacent slits is larger than the skin depth in metal, about 24 nm for silver

1/2

2 2

*k*

 ε

*m d*

 and *<sup>d</sup>* ε

−

εβ

εβ

0

 ε

*k*

(5)

(6)

are the permittivity of the metal

2

 ε

**Figure 28.** (a) Dependence of phase retardation on the slit width. Red and blue tags represent the contributions for phase retardation from the real part of propagation constant and multiple reflections. The wavelength of incident light is 810 nm. (b) Transmittance of optical field (810 nm wavelength) through a nanoslit vs the slit depth ranging from 100 to 500 nm. Slit widths are 10, 20, 40, and 60 nm. Reprinted with permission from "Ting Xu, et. al. Appl. Phys. Lett. 91,201501 (2007)" of copyright ©2007 American Institute of Physics.

To illustrate the validity of metallic slab lens, finite-difference time-domain simulations are performed. Figure 28 (a) illuminates the dependence of phase retardation on slit width. Figure 28 (b) plots the finite-difference time-domain (FDTD) simulated transmittance of light through a slit with variant thickness as ranging from 100 to 500 nm by normal incidence at the wavelength of 810 nm. Calculated steady optical field (the magnetic field |Hy|2) of the simulation result is shown in Fig. 29. Obvious image spot can be seen at the position around Z=2.43 μm with the full width at half maximum of 396 nm approximately half of the incident wavelength. The slight focal shift of about 60 nm. Above all, the metallic slab lens displays a considerably good performance for imaging objects in the far field region.

Plasmonic Lenses 215

from the tip, grows relatively much stronger. The 3D energy concentration occurs at the tip of a smoothly tapered metal nanoplasmonic waveguide. This causes the local field increase

**Figure 30.** Geometry of the nanoplasmonic waveguide. The radius of the waveguide gradually decreases from 50 nm to 2 nm. Reprinted with permission from "Mark I. Stockman, Phys. Rev. Lett. 93,

**Figure 31.** Snapshot of instanteneous fields (at some arbitrary moment *t*=0): longitudinal component *Ez*  of the local optical electric field are shown in the longitudinal cross section (*xz*) plane of the system. The fields are in the units of the far-zone (excitation) field. Reprinted with permission from "Mark I. Stockman, Phys. Rev. Lett. 93, 137404 (2004)" with copyright © 2004 of American Society of Physics.

Most recently, Ewold *et. al*. reported our tapered waveguid structure for nanofocusing, as shown in Fig. 32 [54]. It was used for focusing of surface plasmon polaritons (SPPs) excited with 1.5 μm light in a tapered Au waveguide on a planar dielectric substrate by experiments and simulations. We find that nanofocusing can be obtained when the asymmetric bound mode at the substrate side of the metal film is excited. The propagation and concentration of this mode to the tip is demonstrated. No sign of a cutoff waveguide width is observed as the SPPs propagate along the tapered waveguide. Simulations show that such concentrating behavior is not possible for excitation of the mode at the low-index side of the film. The mode that enables the focusing exhibits a strong resemblance to the asymmetric mode responsible for focusing in conical waveguides. This work demonstrates a practical

137404 (2004)" with copyright © 2004 of American Society of Physics.

implementation of plasmonic nanofocusing on a planar substrate.

by 3 orders of magnitude in intensity and four orders in energy density.

**Figure 29.** Calculated steady magnetic field intensity |Hy|2 of the simulation results using FDTD method. The spirce is localized at X=0 and Z=0.2 μm. The metallic slab lens ranged from Z=1.2 μm to Z=1.5 μm. The radiated light from the source is TM polarized with a wavelength of 810nm. The curve at the right side represents the cross section of image plane at Z=2.435 μm. Reprinted with permission from "Ting Xu, et. al. Appl. Phys. Lett. 91,201501 (2007)" of copyright ©2007 American Institute of Physics.

In addition, nanorod array was reported being used for imaging [51]. Mark et. al reported parallel conducting wires as a lens for subwavelength microwave imaging [52].

### **4. Plasmonic Lens on the basis of waveguide modes**

Another structure that can realize nanofocusing was theoretically reported [53]. SPPs propagating toward the tip of a tapered plasmonic waveguide are slowed down and asymptotically stopped when we tend to the tip, never actually reaching it (the travel time to the tip is logarithmically divergent). This phenomenon causes accumulation of energy and giant local fields at the tip. Focusing of fundamental cylindrical SPP wave is formed at apex of the taper tip, as shown in Fig. 30. Figure 31 displays the amplitudes of the local optical fields in the cross section of the system for the normal and longitudinal (with respect to the axis) components of the optical electric field. As SPP's move toward the tip, the SPP fields start to localize at the metal surface, and simultaneously, our wavelength is progressively reducing and amplitude growing. The field magnitudes grow significantly at small |Z|. The transverse x component grows by an order of magnitude as the SPP's approach the tip of the guide, while the longitudinal z component, which is very small far from the tip, grows relatively much stronger. The 3D energy concentration occurs at the tip of a smoothly tapered metal nanoplasmonic waveguide. This causes the local field increase by 3 orders of magnitude in intensity and four orders in energy density.

214 Plasmonics – Principles and Applications

Physics.

**Figure 29.** Calculated steady magnetic field intensity |Hy|2 of the simulation results using FDTD method. The spirce is localized at X=0 and Z=0.2 μm. The metallic slab lens ranged from Z=1.2 μm to Z=1.5 μm. The radiated light from the source is TM polarized with a wavelength of 810nm. The curve at the right side represents the cross section of image plane at Z=2.435 μm. Reprinted with permission from "Ting Xu, et. al. Appl. Phys. Lett. 91,201501 (2007)" of copyright ©2007 American Institute of

In addition, nanorod array was reported being used for imaging [51]. Mark et. al reported

Another structure that can realize nanofocusing was theoretically reported [53]. SPPs propagating toward the tip of a tapered plasmonic waveguide are slowed down and asymptotically stopped when we tend to the tip, never actually reaching it (the travel time to the tip is logarithmically divergent). This phenomenon causes accumulation of energy and giant local fields at the tip. Focusing of fundamental cylindrical SPP wave is formed at apex of the taper tip, as shown in Fig. 30. Figure 31 displays the amplitudes of the local optical fields in the cross section of the system for the normal and longitudinal (with respect to the axis) components of the optical electric field. As SPP's move toward the tip, the SPP fields start to localize at the metal surface, and simultaneously, our wavelength is progressively reducing and amplitude growing. The field magnitudes grow significantly at small |Z|. The transverse x component grows by an order of magnitude as the SPP's approach the tip of the guide, while the longitudinal z component, which is very small far

parallel conducting wires as a lens for subwavelength microwave imaging [52].

**4. Plasmonic Lens on the basis of waveguide modes** 

**Figure 30.** Geometry of the nanoplasmonic waveguide. The radius of the waveguide gradually decreases from 50 nm to 2 nm. Reprinted with permission from "Mark I. Stockman, Phys. Rev. Lett. 93, 137404 (2004)" with copyright © 2004 of American Society of Physics.

**Figure 31.** Snapshot of instanteneous fields (at some arbitrary moment *t*=0): longitudinal component *Ez*  of the local optical electric field are shown in the longitudinal cross section (*xz*) plane of the system. The fields are in the units of the far-zone (excitation) field. Reprinted with permission from "Mark I. Stockman, Phys. Rev. Lett. 93, 137404 (2004)" with copyright © 2004 of American Society of Physics.

Most recently, Ewold *et. al*. reported our tapered waveguid structure for nanofocusing, as shown in Fig. 32 [54]. It was used for focusing of surface plasmon polaritons (SPPs) excited with 1.5 μm light in a tapered Au waveguide on a planar dielectric substrate by experiments and simulations. We find that nanofocusing can be obtained when the asymmetric bound mode at the substrate side of the metal film is excited. The propagation and concentration of this mode to the tip is demonstrated. No sign of a cutoff waveguide width is observed as the SPPs propagate along the tapered waveguide. Simulations show that such concentrating behavior is not possible for excitation of the mode at the low-index side of the film. The mode that enables the focusing exhibits a strong resemblance to the asymmetric mode responsible for focusing in conical waveguides. This work demonstrates a practical implementation of plasmonic nanofocusing on a planar substrate.

Plasmonic Lenses 217

**Figure 33.** Scanning electron microscope (SEM) (a) the top image of the structure, (b) the image of the structure obtained with view angle 45°. The radius of curved chains of nanoparticles is equal to 10μm. The particle in-plane size (diameter) and inter-particle distance are estimated to be about 350nm and 850nm, respectively, the particle height is 300nm. Reprinted with permission from "A. B. Evlyukhin, et.

**Figure 34.** Magnitude of scattered electric field calculated above the gold surface with a curved chain (with *R*=10 μm and β=60°) of spheroid gold nanoparticles illuminated by a light beam at the wavelength of 800nm being incident perpendicular to the gold surface and polarized along x-direction. The waist W of the incident beam and the inter-particle (center-to-center) spacing *D* in the chain are (a) W=10μm, *D*=400nm; (b)W=10μm, *D*=800nm; (c)W =1.5 μm, *D*=400nm; (d)W =1.5 μm, *D*=800nm. Reprinted with permission from "A. B. Evlyukhin, et. al, Opt. Exp. 15, 16667-16680 (2007)." of copyright ©2007 Optical

Society of American.

al, Opt. Exp. 15, 16667-16680 (2007)." of copyright ©2007 Optical Society of American.

**Figure 32.** Schematic of the experimental geometry in the case of upconversion luminescence detection through the substrate (a), or from the air side of the sample (b). In both cases the SPPs are excited with infrared light at the Au/Al2O3 interface in the direction of the arrow. The red line schematically indicates the Er depth profile. Reprinted with permission from "Ewold Verhagen, Albert Polman, and L. (Kobus) Kuipers, Opt. Express 16, 45-57 (2008)." of copyright ©2008 Optical Society of American.

A fiber-pigtailed 1.48 μm diode pump laser is used as excitation source. Figure 32 shows a schematic of the hole array/taper geometry. The pitch of the hole array is chosen such that ppolarized light with a wavelength of 1.48 μm is diffracted to generate SPPs propagatin at the substrate side of the film. To maximize the excitation of the desired SPP mode, the excitation beam is focused to a 10 μm wide spot near the edge of the array. The triangularl shaped tapered waveguide starts at a distance of 6 μm from the edge of the excitation arra and has a base width of 12 μm and a length of 60 μm (taper angle 11°).

### **5. Plasmonic lens on the basis of curved chains of nanoparticles**

Focusing of surface plasmon polaritons (SPPs) beams with parabolic chains of gold nanoparticles fabricated on thin gold films was reported [55]. SPP focusing with different parabolic chains is investigated in the wavelength range of 700-860nm, both experimentally and thoretically. Mapping of SPP fields is accomplished by making use of leakage radiation microscopy, demonstrating robust and efficient SPP focusing into submicron spots. Numerical simulations based on the Green's tenor formalism show very good agreement with the experimental results, suggesting the usage of elliptical corrections for parabolic structures to improve our focusing of slightly divergent SPP beams.

Shortly after the above work, excitation,focusing and directing of surface plasmon polaritons (SPPs) with curved chains of nanoparticles located on a metal surface is investigated both experimentally and theoretically by Evlyukhin et. al., as shown in Fig. 33 [56]. We demonstrate that, by using a relatively narrow laser beam (at normal incidence) interacting only with a portion of a curved chain of nanoparticles, one can excite an SPPs beam whose divergence and propagation direction are dictated by the incident light spot size and its position along the chain. It is also found that the SPPs focusing regime is strongly influenced by the chain inter-particle distance. Extensive numerical simulations of

216 Plasmonics – Principles and Applications

**Figure 32.** Schematic of the experimental geometry in the case of upconversion luminescence detection through the substrate (a), or from the air side of the sample (b). In both cases the SPPs are excited with infrared light at the Au/Al2O3 interface in the direction of the arrow. The red line schematically indicates the Er depth profile. Reprinted with permission from "Ewold Verhagen, Albert Polman, and L. (Kobus)

A fiber-pigtailed 1.48 μm diode pump laser is used as excitation source. Figure 32 shows a schematic of the hole array/taper geometry. The pitch of the hole array is chosen such that ppolarized light with a wavelength of 1.48 μm is diffracted to generate SPPs propagatin at the substrate side of the film. To maximize the excitation of the desired SPP mode, the excitation beam is focused to a 10 μm wide spot near the edge of the array. The triangularl shaped tapered waveguide starts at a distance of 6 μm from the edge of the excitation arra and has a

Focusing of surface plasmon polaritons (SPPs) beams with parabolic chains of gold nanoparticles fabricated on thin gold films was reported [55]. SPP focusing with different parabolic chains is investigated in the wavelength range of 700-860nm, both experimentally and thoretically. Mapping of SPP fields is accomplished by making use of leakage radiation microscopy, demonstrating robust and efficient SPP focusing into submicron spots. Numerical simulations based on the Green's tenor formalism show very good agreement with the experimental results, suggesting the usage of elliptical corrections for parabolic

Shortly after the above work, excitation,focusing and directing of surface plasmon polaritons (SPPs) with curved chains of nanoparticles located on a metal surface is investigated both experimentally and theoretically by Evlyukhin et. al., as shown in Fig. 33 [56]. We demonstrate that, by using a relatively narrow laser beam (at normal incidence) interacting only with a portion of a curved chain of nanoparticles, one can excite an SPPs beam whose divergence and propagation direction are dictated by the incident light spot size and its position along the chain. It is also found that the SPPs focusing regime is strongly influenced by the chain inter-particle distance. Extensive numerical simulations of

Kuipers, Opt. Express 16, 45-57 (2008)." of copyright ©2008 Optical Society of American.

**5. Plasmonic lens on the basis of curved chains of nanoparticles** 

base width of 12 μm and a length of 60 μm (taper angle 11°).

structures to improve our focusing of slightly divergent SPP beams.

**Figure 33.** Scanning electron microscope (SEM) (a) the top image of the structure, (b) the image of the structure obtained with view angle 45°. The radius of curved chains of nanoparticles is equal to 10μm. The particle in-plane size (diameter) and inter-particle distance are estimated to be about 350nm and 850nm, respectively, the particle height is 300nm. Reprinted with permission from "A. B. Evlyukhin, et. al, Opt. Exp. 15, 16667-16680 (2007)." of copyright ©2007 Optical Society of American.

**Figure 34.** Magnitude of scattered electric field calculated above the gold surface with a curved chain (with *R*=10 μm and β=60°) of spheroid gold nanoparticles illuminated by a light beam at the wavelength of 800nm being incident perpendicular to the gold surface and polarized along x-direction. The waist W of the incident beam and the inter-particle (center-to-center) spacing *D* in the chain are (a) W=10μm, *D*=400nm; (b)W=10μm, *D*=800nm; (c)W =1.5 μm, *D*=400nm; (d)W =1.5 μm, *D*=800nm. Reprinted with permission from "A. B. Evlyukhin, et. al, Opt. Exp. 15, 16667-16680 (2007)." of copyright ©2007 Optical Society of American.

the configuration investigated experimentally are carried out for a wide set of system parameters by making use of the Green's tensor formalism and dipole approximation. Comparison of numerical results with experimental data shows good agreement with respect to the observed features in SPP focusing and directing, providing the guidelines for aproper choice of the system parameters.

Plasmonic Lenses 219

**Figure 35.** (a) SEM image of the focusing array coupled to a 250-nm-wide Ag strip guide; light gray, Ag; dark gray, Cr; scale bar, 2 μm.(b) NSOM image of the SPPs intensity showing focusing and guiding. Reprinted with permission from "Leilei Yin, et. al., Nano Lett. 2005, *5*, 1399–1402." of copyright ©2005

a type of imaging by diffraction rather than an ordinary imaging of a lens. Actually, some researchers are still interested in the self-imaging effect since H. F. Talbot discovered it in 1836. And intensive theoretical and experimental studies regarding Talbot effect have been done since then. For example, the plasmon analogue of the self-imaging Talbot effect of a row of holes drilled in a metal film was described and theoretically analyzed, and suggested the potential applications in sensing, imaging, and optical interconnects on the basis of plasmon focal spots aimed at plasmon waveguides [63]. Subsequently, the Talbot effect regarding SPPs imaging on the basis of a rather different system by a quite different approach was studied theoretically and experimentally [62-64]. Furthermore, the Talbot effect for volume electromagnetic waves has been used in a variety of applications. And it is expected that the analogue for SPPs will be found applications in numerous nanoscale plasmonic devices.

Chemical Society of American.

When the inter-particle distance is smaller than the light wavelength, the pattern of the field magnitude distribution is relatively smooth [Fig. 34 (a)]. In this case, the illuminated part of the chain exhibits scattering properties that are similar to those of a continuous ridge. Note that straight ridges are frequently used for excitation of a divergent SPP beam on a metal surface in SPP experiments. When increasing the inter-particle distance, the individual particles of the chain become relatively independent sources of the scattered waves whose phases differ considerably, resulting in a complex interference pattern [Fig. 34 (b)] – a system of divergent SPPs rays. A similar trend is also seen for a relatively narrow incident light beam [see Figs. 34 (c) and (d)]. If the light spot size being determined by *W* is sufficiently small in comparison with the chain curvature radius *R* so that the diffraction angle of a SPPs beam is approximately equal to the focusing angle *W/R*, the focusing effect decreases and the maximum of SPPs intensity moves toward the nanoparticle chain. Strong SPPs focusing effects have been obtained for relatively lager *W/R*.

Apart from the chain particle-based plasmonic structures for nanofocusing, the reverse pattern: nanoholes, constructed in curved chains can also realize focusing of SPP wave, as shown in Fig. 35 [57]. The focused SPPs can be directly coupled into a waveguide located at the focal plane. The constructive interference of SPPs launched by nanometric holes allows us to focus SPP into a spot of high near-field intensity having subwavelength width. Nearfield scanning optical microscopy is used to map the local SPP intensity. The resulting SPPs patterns and our polarization dependence are accurately described in model calculations based on a dipolar model for the SPP emission at each hole. Furthermore, we show that the high SPPs intensity in the focal spot can be launched and propagated on a Ag strip guide with a 250 × 50 nm2 cross section, thus overcoming the diffraction limit of conventional optics. The combination of focusing arrays and nano-waveguides may serve as a basic element in planar nano-photonic circuits.

Not only focusing and imaging, the similar plasmonic structures can be used as beam sppliters [58] and beam shaping [59]. Nanofabrication of the plasmonic lenses were reported in Ref. [60-62].

### **6. Plasmonic Talbot effect of nanolenses**

Previous introduction in Section 3 shows a common phenomenon which there several focal points exist along central axis in free space after exit plane of the nanolenses.

To explore its physical mechanism, we compared the phenomenon to another well-known story: Talbot effect, *i.e.* self-imaging. The self-imaging means that when a one-dimensional (1D) periodic structure is illuminated by the monochromatic plane wave, the image of that structure can be observed at the periodical distance from the back side of the structure. It is

218 Plasmonics – Principles and Applications

aproper choice of the system parameters.

element in planar nano-photonic circuits.

**6. Plasmonic Talbot effect of nanolenses** 

in Ref. [60-62].

SPPs focusing effects have been obtained for relatively lager *W/R*.

the configuration investigated experimentally are carried out for a wide set of system parameters by making use of the Green's tensor formalism and dipole approximation. Comparison of numerical results with experimental data shows good agreement with respect to the observed features in SPP focusing and directing, providing the guidelines for

When the inter-particle distance is smaller than the light wavelength, the pattern of the field magnitude distribution is relatively smooth [Fig. 34 (a)]. In this case, the illuminated part of the chain exhibits scattering properties that are similar to those of a continuous ridge. Note that straight ridges are frequently used for excitation of a divergent SPP beam on a metal surface in SPP experiments. When increasing the inter-particle distance, the individual particles of the chain become relatively independent sources of the scattered waves whose phases differ considerably, resulting in a complex interference pattern [Fig. 34 (b)] – a system of divergent SPPs rays. A similar trend is also seen for a relatively narrow incident light beam [see Figs. 34 (c) and (d)]. If the light spot size being determined by *W* is sufficiently small in comparison with the chain curvature radius *R* so that the diffraction angle of a SPPs beam is approximately equal to the focusing angle *W/R*, the focusing effect decreases and the maximum of SPPs intensity moves toward the nanoparticle chain. Strong

Apart from the chain particle-based plasmonic structures for nanofocusing, the reverse pattern: nanoholes, constructed in curved chains can also realize focusing of SPP wave, as shown in Fig. 35 [57]. The focused SPPs can be directly coupled into a waveguide located at the focal plane. The constructive interference of SPPs launched by nanometric holes allows us to focus SPP into a spot of high near-field intensity having subwavelength width. Nearfield scanning optical microscopy is used to map the local SPP intensity. The resulting SPPs patterns and our polarization dependence are accurately described in model calculations based on a dipolar model for the SPP emission at each hole. Furthermore, we show that the high SPPs intensity in the focal spot can be launched and propagated on a Ag strip guide with a 250 × 50 nm2 cross section, thus overcoming the diffraction limit of conventional optics. The combination of focusing arrays and nano-waveguides may serve as a basic

Not only focusing and imaging, the similar plasmonic structures can be used as beam sppliters [58] and beam shaping [59]. Nanofabrication of the plasmonic lenses were reported

Previous introduction in Section 3 shows a common phenomenon which there several focal

To explore its physical mechanism, we compared the phenomenon to another well-known story: Talbot effect, *i.e.* self-imaging. The self-imaging means that when a one-dimensional (1D) periodic structure is illuminated by the monochromatic plane wave, the image of that structure can be observed at the periodical distance from the back side of the structure. It is

points exist along central axis in free space after exit plane of the nanolenses.

**Figure 35.** (a) SEM image of the focusing array coupled to a 250-nm-wide Ag strip guide; light gray, Ag; dark gray, Cr; scale bar, 2 μm.(b) NSOM image of the SPPs intensity showing focusing and guiding. Reprinted with permission from "Leilei Yin, et. al., Nano Lett. 2005, *5*, 1399–1402." of copyright ©2005 Chemical Society of American.

a type of imaging by diffraction rather than an ordinary imaging of a lens. Actually, some researchers are still interested in the self-imaging effect since H. F. Talbot discovered it in 1836. And intensive theoretical and experimental studies regarding Talbot effect have been done since then. For example, the plasmon analogue of the self-imaging Talbot effect of a row of holes drilled in a metal film was described and theoretically analyzed, and suggested the potential applications in sensing, imaging, and optical interconnects on the basis of plasmon focal spots aimed at plasmon waveguides [63]. Subsequently, the Talbot effect regarding SPPs imaging on the basis of a rather different system by a quite different approach was studied theoretically and experimentally [62-64]. Furthermore, the Talbot effect for volume electromagnetic waves has been used in a variety of applications. And it is expected that the analogue for SPPs will be found applications in numerous nanoscale plasmonic devices.

Here, as an example, the Talbot effect of an Ag nanolens with five periodic concentric through the rings illuminated by a radially polarized light was computationally studied. Rigorous finite-difference and time-domain (FDTD) algorithm was employed in the computational numerical calculation. The results indicate that several focal points can be obtained at different locations due to the SPPs-related Talbot effect at λinc.=248 nm. The positions are quite different from that of values calculated by the Talbot distance equation reported in Ref. [65]. A minimum diameter of 100 nm at site of full width and half maximum (FWHM) was derived at the propagation distance of Z=396 nm. To further study the phenomenon in physics, it was compared with the traditional Talbot distance calculated using the scalar diffraction theory in the sections below.

Plasmonic Lenses 221

According to the frequency domain analysis method, the diffraction eld distribution *Uz* at

( ) ( )

<sup>2</sup> <sup>2</sup> (m 1,2,3, ) *md*

exp <sup>1</sup> *<sup>n</sup> j z <sup>d</sup>* πλ

− =

( ) exp 2 exp( ) () ( ) exp *z n*

( ) ( ) 2 2

<sup>2</sup> 2

*d*

λ

Substituting *d* and λ with their corresponding values of 500 nm and 248 nm, respectively, we can get the Talbot distance of *z*T=2.016 μm. It indicates that self-imaging of the periodic grating structures can be observed at positions of *Z*=2.016 μm, 4.032 μm, and 6.048 μm, etc.,

It was found that the result analyzed above by the scalar diffraction theory is quite different from the results calculated by the FDTD numerical analysis method. The former is far field diffraction, but the latter is SPPs coupling and interfering at near field. Thus the focal points do not repeat at the same positions as that of the scalar one along the propagation direction. The phenomenon described before can be attributed to that of the surface plasmons (SP). SPPs is excited at all azimuthal directions that interferes each other constructively and creates a strongly enhanced localized elds at the focal points. The size of the focal spots is less than half a wavelength and the focal positions are not determined by the Talbot

*T*

*z*

*<sup>n</sup> U x c j x jkz U x jkz <sup>d</sup>* π

2

exp 2 exp exp *z n*

= −

*n n U x c j x j z jkz d d* π

2

= =… (9)

= = (11)

*<sup>z</sup> I U x Ux* = = (12)

<sup>=</sup> (13)

(10)

(8)

πλ

a free-space propagation distance *Z* is given by

Note that when

*Uz* can be written as

then

*n*

*n*

Intensity distribution equals to the original intensity

The Talbot distance of a grating with a period of *d* is

which is integral number times of *Tz* .

distance.

∞

=−∞

∞

=−∞

*z*

λ

For simplification of the analyses, the structure is simplified that is equivalent to a onedimensional grating structure with the same geometrical parameters as the nanolens mentioned before due to its symmetry, as shown in Fig. 36.

The scalar field immediately behind an infinite grating at the original position (Z = 0) when it is illuminated by an unit intensity plane wave can be described by a Fourier series representing a weighted set of plane wave components as:

**Figure 36.** Self-imaging of the grating structure with the same geometrical parameters as the nanolens mentioned before.

$$\mathcal{U}\left(\mathbf{x}\right) = \sum\_{n=-\infty}^{\infty} c\_n \exp\left(j2\pi\frac{n}{d}x\right) \tag{7}$$

where *d* is the grating period (is 500 nm here) and *nc* is the nth Fourier coefficient. The coefficients represent the complex intensity and the phase.

According to the frequency domain analysis method, the diffraction eld distribution *Uz* at a free-space propagation distance *Z* is given by

$$\mathcal{U}I\_z\left(\mathbf{x}\right) = \sum\_{n=-\infty}^{\infty} c\_n \exp\left(j2\pi \frac{n}{d} \mathbf{x}\right) \exp\left[-j\pi \lambda z \left(\frac{n}{d}\right)^2\right] \exp\left(jkz\right) \tag{8}$$

Note that when

$$z = \frac{2md^2}{\lambda} \qquad \qquad \text{(m=1,2,3,...)} \tag{9}$$

then

220 Plasmonics – Principles and Applications

mentioned before.

using the scalar diffraction theory in the sections below.

mentioned before due to its symmetry, as shown in Fig. 36.

representing a weighted set of plane wave components as:

Here, as an example, the Talbot effect of an Ag nanolens with five periodic concentric through the rings illuminated by a radially polarized light was computationally studied. Rigorous finite-difference and time-domain (FDTD) algorithm was employed in the computational numerical calculation. The results indicate that several focal points can be obtained at different locations due to the SPPs-related Talbot effect at λinc.=248 nm. The positions are quite different from that of values calculated by the Talbot distance equation reported in Ref. [65]. A minimum diameter of 100 nm at site of full width and half maximum (FWHM) was derived at the propagation distance of Z=396 nm. To further study the phenomenon in physics, it was compared with the traditional Talbot distance calculated

For simplification of the analyses, the structure is simplified that is equivalent to a onedimensional grating structure with the same geometrical parameters as the nanolens

The scalar field immediately behind an infinite grating at the original position (Z = 0) when it is illuminated by an unit intensity plane wave can be described by a Fourier series

**Figure 36.** Self-imaging of the grating structure with the same geometrical parameters as the nanolens

( ) exp 2 *<sup>n</sup> n*

∞

=−∞

coefficients represent the complex intensity and the phase.

*<sup>n</sup> Ux c j x <sup>d</sup>*

where *d* is the grating period (is 500 nm here) and *nc* is the nth Fourier coefficient. The

<sup>=</sup>

π

(7)

$$\mathbb{E}\exp\left[-j\pi\mathfrak{A}z\left(\frac{n}{d}\right)^2\right] = 1\tag{10}$$

*Uz* can be written as

$$\mathcal{U}I\_z\left(\mathbf{x}\right) = \sum\_{n=-\infty}^{\infty} c\_n \exp\left(j2\pi \frac{n}{d} \mathbf{x}\right) \exp\left(jkz\right) = \mathcal{U}\left(\mathbf{x}\right) \exp\left(jkz\right) \tag{11}$$

Intensity distribution equals to the original intensity

$$I = \left| \mathcal{U}\_z \left( \mathbf{x} \right) \right|^2 = \left| \mathcal{U} \left( \mathbf{x} \right) \right|^2 \tag{12}$$

The Talbot distance of a grating with a period of *d* is

$$z\_T = \frac{2d^2}{\lambda} \tag{13}$$

Substituting *d* and λ with their corresponding values of 500 nm and 248 nm, respectively, we can get the Talbot distance of *z*T=2.016 μm. It indicates that self-imaging of the periodic grating structures can be observed at positions of *Z*=2.016 μm, 4.032 μm, and 6.048 μm, etc., which is integral number times of *Tz* .

It was found that the result analyzed above by the scalar diffraction theory is quite different from the results calculated by the FDTD numerical analysis method. The former is far field diffraction, but the latter is SPPs coupling and interfering at near field. Thus the focal points do not repeat at the same positions as that of the scalar one along the propagation direction. The phenomenon described before can be attributed to that of the surface plasmons (SP). SPPs is excited at all azimuthal directions that interferes each other constructively and creates a strongly enhanced localized elds at the focal points. The size of the focal spots is less than half a wavelength and the focal positions are not determined by the Talbot distance.

In comparison to the results of above mentioned Talbot distances from scalar theory, only the contribution from the eld of SPPs is taken into account in the calculations of the interference pattern. In the geometry considered in this paper, the conversion of the incident SPPs into the volume electromagnetic waves is weak. The Talbot distance of 2.016 μm (first order) calculated by formula *zT=k*Λ*2/*π (it is the same as Eq. (13) actually. They were written in two different forms.) from Maradudin *et. al.* [63] and van Oosten [64] is different also from our calculated value of 0.3962 μm (first order) here. The reason we get a different answer compared to the other two methods is because the other two methods use the paraxial approximation in far-field regime, which state that the pitch of the structure is much greater than the incident wavelength. However, the near-field regime in which we operate is when the wavelength is about half the period. For our structures, the paraxial approximation does not hold anymore. Therefore, we can draw a conclusion that the theoretical equations deduced for the structures of metallic dot arrays [63, 65] are not suitable to our nanolens structures. The approach of computational numerical calculation must be employed for the study of the Talbot distance. For more information regarding theoretical calculation, readers can see Ref.[65].

Plasmonic Lenses 223

the measured and calculated results coincide with each other very well. It can be explained that the interaction between the NSOM probe and the nanolenses surface is weak at the farfield. The influence on the probing is significantly degraded and can be ignored accordingly. In comparison to a standard diffraction experiment, if the wavelength is large the slit is subwavelength, surely there will be no diffracted waves (also known as cylindrical waves) and therefore, the distinction between short wavelength and long wavelength is obvious. For the standard diffraction, transmission intensity decays exponentially with slit size (Bethe's theory was put forth in 1944). However, for our plasmonic lenses, the transmission intensity can be enhanced due to inherent advantage of plasmonic resonance which is well known already. Here, we used metallic subwavelength structure to generate the selfimaging. It is more apparent in near field region. The contribution of plasmonic resonance here is that enhancing the intensity of the plasmonic Talbot-based focusing (see Fig. 36). It is especially important for nano-photolithography for which large working distance and high exposure intensity are crucial issues. Our previous FDTD calculation results [66] demonstrated that only one focal point can be observed for the case of λ>300 nm, which is a threshold value for the SPPs-based Talbot effect. For the short wavelength, it is smaller than the slit width. Thus it is consistent to the Talbot effect condition. For more information

In summary, the main reason of the diffraction limit of a conventional optical lens is that a conventional lens is only capable of transmitting the propagating. The evanescent carry subwavelength information about the object decay, but it decay exponentially and cannot be collected in far field region. In contrast, plasmonic lens is an alternative to these problems. There are two key concepts about plasmonic lens. One is the concept of negative refractive index. The other is the transmission enhancement of evanescent waves. The concept of negative refractive index is the basic issue of plasmonic lens. And this is very common for

The scalar Talbot effect cannot interpret the Talbot effect phenomenon for the metallic nanolenses. It may attribute to the paraxial approximation applied in the Talbot effect theory in far-field region. However, the approximation does not hold in our nanolenses structures during the light propagation. In addition, the Talbot effect appears at the short

Also plasmonic lenses provide excellent optical property for us. We can shape the beam beyond the diffraction limit, such as superfocusing, imaging and so on. Also we can exist in various forms. And in this paper, we show them in three form generally. Some new ideas will be produced while we design the plasmonic lenses to resolve practical problems. Currently, applications of the plasmonic lenses reported include photodetector [67] and ring resonator [68]. With rapid development of the plasmonic lenses, it is reasonable to believe

wavelength regime only, especially in the ultra-violet wavelength region.

that extensive applications will be found in the near future.

regarding experimental characterization, readers can see Ref.[67].

**7. Summary** 

noble metal in specific frequency.

To compare the experimental results with the theoretically calculated results, we plotted Efield intensity profiles versus propagation distance z together with that of the numerically calculated in the same figure, as shown in Fig. 37. It can be seen that variation tendency of the E-field intensity of the measured results is in agreement with the theoretically calculated results in general. As can be seen from Fig. 36, the positions of the measured first three focal points are slightly in advance of the calculated values due to the interaction of the metal surfaces between the NSOM probe and nanolenses at near-field. But for the last two ones,

**Figure 37.** Comparison of E-field intensity distribution along propagation axis between experimental and theoretical results.

the measured and calculated results coincide with each other very well. It can be explained that the interaction between the NSOM probe and the nanolenses surface is weak at the farfield. The influence on the probing is significantly degraded and can be ignored accordingly.

In comparison to a standard diffraction experiment, if the wavelength is large the slit is subwavelength, surely there will be no diffracted waves (also known as cylindrical waves) and therefore, the distinction between short wavelength and long wavelength is obvious. For the standard diffraction, transmission intensity decays exponentially with slit size (Bethe's theory was put forth in 1944). However, for our plasmonic lenses, the transmission intensity can be enhanced due to inherent advantage of plasmonic resonance which is well known already. Here, we used metallic subwavelength structure to generate the selfimaging. It is more apparent in near field region. The contribution of plasmonic resonance here is that enhancing the intensity of the plasmonic Talbot-based focusing (see Fig. 36). It is especially important for nano-photolithography for which large working distance and high exposure intensity are crucial issues. Our previous FDTD calculation results [66] demonstrated that only one focal point can be observed for the case of λ>300 nm, which is a threshold value for the SPPs-based Talbot effect. For the short wavelength, it is smaller than the slit width. Thus it is consistent to the Talbot effect condition. For more information regarding experimental characterization, readers can see Ref.[67].

### **7. Summary**

222 Plasmonics – Principles and Applications

order) calculated by formula *zT=k*

theoretical calculation, readers can see Ref.[65].

0.0

0.2

0.4

Normalized intensity

and theoretical results.

0.6

0.8

1.0

In comparison to the results of above mentioned Talbot distances from scalar theory, only the contribution from the eld of SPPs is taken into account in the calculations of the interference pattern. In the geometry considered in this paper, the conversion of the incident SPPs into the volume electromagnetic waves is weak. The Talbot distance of 2.016 μm (first

in two different forms.) from Maradudin *et. al.* [63] and van Oosten [64] is different also from our calculated value of 0.3962 μm (first order) here. The reason we get a different answer compared to the other two methods is because the other two methods use the paraxial approximation in far-field regime, which state that the pitch of the structure is much greater than the incident wavelength. However, the near-field regime in which we operate is when the wavelength is about half the period. For our structures, the paraxial approximation does not hold anymore. Therefore, we can draw a conclusion that the theoretical equations deduced for the structures of metallic dot arrays [63, 65] are not suitable to our nanolens structures. The approach of computational numerical calculation must be employed for the study of the Talbot distance. For more information regarding

To compare the experimental results with the theoretically calculated results, we plotted Efield intensity profiles versus propagation distance z together with that of the numerically calculated in the same figure, as shown in Fig. 37. It can be seen that variation tendency of the E-field intensity of the measured results is in agreement with the theoretically calculated results in general. As can be seen from Fig. 36, the positions of the measured first three focal points are slightly in advance of the calculated values due to the interaction of the metal surfaces between the NSOM probe and nanolenses at near-field. But for the last two ones,

0 2 4 6 8 10

 measured calculated

Propogation distance, Z (μm)

**Figure 37.** Comparison of E-field intensity distribution along propagation axis between experimental

(it is the same as Eq. (13) actually. They were written

Λ*2/*π

> In summary, the main reason of the diffraction limit of a conventional optical lens is that a conventional lens is only capable of transmitting the propagating. The evanescent carry subwavelength information about the object decay, but it decay exponentially and cannot be collected in far field region. In contrast, plasmonic lens is an alternative to these problems. There are two key concepts about plasmonic lens. One is the concept of negative refractive index. The other is the transmission enhancement of evanescent waves. The concept of negative refractive index is the basic issue of plasmonic lens. And this is very common for noble metal in specific frequency.

> The scalar Talbot effect cannot interpret the Talbot effect phenomenon for the metallic nanolenses. It may attribute to the paraxial approximation applied in the Talbot effect theory in far-field region. However, the approximation does not hold in our nanolenses structures during the light propagation. In addition, the Talbot effect appears at the short wavelength regime only, especially in the ultra-violet wavelength region.

> Also plasmonic lenses provide excellent optical property for us. We can shape the beam beyond the diffraction limit, such as superfocusing, imaging and so on. Also we can exist in various forms. And in this paper, we show them in three form generally. Some new ideas will be produced while we design the plasmonic lenses to resolve practical problems. Currently, applications of the plasmonic lenses reported include photodetector [67] and ring resonator [68]. With rapid development of the plasmonic lenses, it is reasonable to believe that extensive applications will be found in the near future.

## **Author details**

### Yongqi Fu

*School of Physical Electronics, University of Electronic Science and Technology of China, China* 

Plasmonic Lenses 225

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#### Jun Wang and Daohua Zhang

*School of Electronic and Electrical Engineering, Nanyang Technological University, Republic of Singapore* 

## **Acknowledgement**

Some reported research works in this chapter were supported by National Natural Science Foundation of China (No. 11079014 and 61077010).

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**Chapter 9** 

© 2012 Lee and Kim, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

**Fundamental Role of Periodicity and Geometric** 

Optical properties of the plasmonic structures based on the surface of variously structured metal plates became a subject of intense research ever since Ebbesen et al. reported the enhanced optical transmission through subwavelength hole arrays [1]. Their experimental results provided evidence that the enhanced optical properties originate from the coupling between the incident light and surface plasmon modes. Studies of such plasmonic structures and its mechanisms have a long history in the development of electromagnetism, though it

In the 1900s, Wood and Rayleigh reported the anomalous optical properties of reflection gratings [2,3], which are intimately connected with the excitation of surface bound waves on the metal-dielectric interfaces [4]. Hessel and Oliner presented two types of the anomalies occurring in the reflection grating surface: a Rayleigh wavelength type attributed to the usual propagating surface plasmon modes and a resonance type which is related to the guided waves supported by the grating itself [5]. On the other hand, since the 1970s, the optical properties of transmission gratings or grids have been occasionally studied in the microwave, terahertz (THz), and infrared regions [6-10]. In particular, Lochbihler and Depine in 1993 presented a theoretical approach for calculating the fields diffracted by the gratings made of highly conducting wires [11]. Here they calculated Maxwell's equations based on modal expansions inside the metal and Rayleigh expansions outside the metal, applying the theoretical treatments by means of surface impedance boundary condition

This research field reinvigorated after the Ebbesen's pioneering work which was focused on the understanding of mechanisms of the enhanced transmission through periodically perforated holes or slits on metallic plates. The one-dimensional plasmonic structures with periodic arrays of slits have been studied by some groups with theoretical and experimental

and reproduction in any medium, provided the original work is properly cited.

**Shape to Resonant Terahertz Transmission** 

Joong Wook Lee and DaiSik Kim

http://dx.doi.org/10.5772/48243

**1. Introduction** 

method [11,12].

Additional information is available at the end of the chapter

has been an intense subject of research in recent years.

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