3. Fiberized plasmonic Fresnel zone plates

Focusing light is invariably an important issue for numerous applications, including micromachining [23], optical tweezing [24, 25], bio-sensing [26, 27], etc. In particular, easy and accurate control of the focal point is one of the greatest factors to be considered for focusing apparatus from the perspective of practical implementation. A traditional method for shifting the focal point is to move either the focusing lens or the target object. Such mechanical adjustments tend to result in relatively large inaccuracies, which are undesirable by any means.

Recently, the author has proposed and demonstrated a simple and compact micro/ nanophotonic structure combining fiber-optic and metal-optic technologies in order for super-variable focusing of light [9], where the relatively high chromatic aberration properties of flat-metal-optical lenses were exploited for an alternative measure of varying its focal point in a wide range.

In this section, the author discusses the characteristics of metallic Fresnel zone plate (FZP/MFZP) structures implemented on a metal-coated optical fiber facet, that is, metallic Fresnel-zone-plated optical fiber facets (MFZP-OFFs), and shows that they can have novel super-variable focusing functionality [9]. Moreover, the author discusses another SPP-based MFZP-OFF scheme that can selectively focus light, depending on its polarization state [9, 28]. In particular, this novel SPPbased lens can be useful for some specific applications that inevitably require centrosymmetric optical force, such as optical trapping [29] and micro-machining [30].

### 3.1. MFZP-OFFs for super-variable focusing of light

Figure 4 illustrates the field intensity distributions of the total field, the C-SPP, and the NCDL for the CMNSs with no trench structure and the optimized RT and APT structures, respectively [8]. From the figure, one can observe that there are clear differences among the simple CMNS and the TA-CMNSs in terms of the NCDL suppression characteristics. With the TA structures, the NCDL noises were substantially canceled out at the center of the device. In particular, the peak and mean SNRs could reach 50.71 and 36.03 dB, respectively, for the APT-CMNS, which were more than one order of magnitude higher than those of the simple CMNS. The peak and

CMNS (dB) RT-CMNS (dB) APT-CMNS (dB)

mean SNRs of all the three devices are summarized in Table 1.

Peak SNR 34.27 38.58 50.71 Mean SNR 24.14 31.11 36.03

Table 1. Summary of the SNR values estimated within the main lobe of the C-SPP hotspots [8].

Figure 4. Top views of the total, plasmonic, and NCDL field intensity distributions [8].

186 Plasmonics

The focal position of a conventional lens, such as spherical lens, varies mainly by the chromatic dispersion of the lens material. For example, the focal length of a bi-convex lens is given by [31].

$$f = \frac{R\_1 R\_2}{R\_2 - R\_1} \frac{1}{n\_{\rm lens} - 1},\tag{3}$$

where f denotes the focal length, R<sup>1</sup> and R<sup>2</sup> the radii of the curvatures of both lens facets, and nlens the optical refractive index of the lens material. In general, the chromatic dispersion of nlens is given by a value in the order of �10�<sup>5</sup> /nm for fused silica [32], so that it results in a very limited focal length change with respect to incident wavelength. In contrast, a flat-metaloptical lens based on an FZP exhibits a drastically different aspect because the focusing of light is obtained from the constructive interference of light at a location where all the possible optical paths from the annular openings of the FZP become in phase, so that detuning of the condition is caused not by the material dispersion but by the direct change of the wavelength of incident light [31, 33].

In general, the product of the focal length and the incident wavelength is approximately invariant regardless of the given FZP geometry [9, 33], so that the general expression for the focal length f <sup>λ</sup> as a function of the incident wavelength λ can be given by

$$f\_{\lambda} \approx \frac{\lambda\_0 f\_0}{\lambda},\tag{4}$$

microscope system, and the measured focal points for RGB colors were at z = 18 (R), 20 (G), and 23 (B) μm, respectively. Numerical simulations were also performed to verify the experimental results, which are shown in Figure 5(c). The numerically calculated focal points for RGB colors were given by z = 17.6 (R), 21.0 (G), and 23.8 (B) μm, respectively, which were actually in good agreement with the experimental results. In fact, the focal length of the MFZP-OFF varied from 28.6 to 14.9 μm for the wavelength range from 400 to 700 nm, which means the relative focallength change per unit wavelength was as large as 45.5. It is highlighted that this relative change rate is over 20 times higher than the rate that can be obtained with a conventional silica-based lens [9, 31], as the latter can only be detuned from 20.2 to 19.6 μm for the same spectral detuning range. In addition, the mean beam radius averaged out over the whole visible range was calculated to be 768 nm with a standard deviation of 14.2 nm, which indicates that the relative change was only 1.84% over the whole visible range as expected from Eq. (5). Nevertheless, it should be noted that even though the super-variable focusing capability along with a nearly constant beam spot size at the focal point over the very wide spectral range was verified both numerically and experimentally, the depth of focus of the focal spot along the optical axis should

Plasmonics on Optical Fiber Platforms http://dx.doi.org/10.5772/intechopen.79146 189

If all the openings of the standard MFZP discussed in the preceding section are reduced down into the sub-wavelength scale [9, 28], its transmission starts to be dominated by the SPPmediated radiation, that is, the extraordinary optical transmission (EOT) via SPPs. Subsequently, such an MFZP (hereinafter SPP-MFZP) will bring in polarization-dependent characteristics because SPPs are normally excited in the direction perpendicular to the slit walls, so that only the radially polarized mode can lead to a hotspot. Thus, this SPP-MFZP can be utilized for focusing of radially polarized light, which has considerable advantages over the linearly polarized or un-polarized counterparts in various applications, thanks to its axially symmetric optical characteristics [30, 36]. The author has investigated the polarization-selective characteristics of the sub-wavelength-scale annular slit in [9], verifying that the transmission of azimuthally polarized (i.e., parallel-polarized) light was suppressed drastically if the relative slit width with respect to wavelength, that is, s/λ, was given by < 0.3, while the transmission of radially

Thus, building upon the principle, an SPP-MFZP was fabricated and characterized experimentally. A 195-nm-thickness gold layer was deposited on a fused-silica substrate, using the electron-beam evaporation method. A standard 6-ring FZP was designed for the reference wavelength of 660 nm and the reference focal length of 20-μm, and all the rings was filled with sub-wavelength-slits of a 120-nm width with a 50% duty ratio. Figure 6(a) illustrates the SEM image of the fabricated SPP-MFZP. To characterize its polarization-dependent functionality, linearly polarized light was illuminated on it. Rotating the axis of the incident polarization, its transmission through the SPP-MFZP was measured by the optical microscope. Considering that the linearly polarized light can be decomposed into a radial component and an azimuthal component with a different ratio depending on the location on the SPP-MFZP plane, the transmitted light pattern should be like a "figure of eight." Figure 6(b) illustrates the optical

still be inversely proportional to the wavelength of incident light [28, 33].

polarized (i.e., perpendicular-polarized) light remained nearly unchanged.

3.2. All-sub-wavelength-scaled MFZP

where λ<sup>0</sup> and f <sup>0</sup> denote the reference wavelength and focal length, respectively. It shows that an FZP has a focal length that is inversely proportional to the incident optical wavelength. In addition, one can also notice that the beam radius at the focal point of an FZP, that is, rr <sup>2</sup> tends to remain nearly consistent regardless of the incident wavelength, considering the optical diffraction principle [9, 31] such as

$$r\_{c^2} \propto \frac{1}{kNA} \approx \frac{\lambda f\_{\lambda}}{2\pi R'} \tag{5}$$

where k, NA, and R denote the wavenumber of the incident light, the effective numerical aperture of the lens, and the radius of the lens, respectively. Since the product of the wavelength and the focal length remains invariant from Eq. (4), Eq. (5) indicates that the beam radius at the focal point of an FZP is approximately preserved regardless of the wavelength of the incident light.

On the other hand, MFZP-OFFs can readily be fabricated using electron-beam and evaporation and FIB milling techniques [34, 35]. Figure 5 illustrates an MFZP-OFF fabricated in house based on the techniques and its focusing characteristics. Silver was initially deposited via an electron-beam evaporation system to form a 100-nm layer on the flat-cleaved multimode optical fiber facet. The multimode optical fiber had a 50-μm diameter step-index core with 0.22 NA. The silver layer was processed by FIB milling to have the FZP structure consisting of 6 rings [9]. It should be noted that this FZP was designed to produce a focal spot at 20 μm from the fiber facet when the wavelength of incident light was tuned at 550 nm.

To characterize the MFZP-OFF, visible light of three different colors (RGB) was launched into the other end of the optical fiber. The center wavelengths of them were given by 612 (R), 527 (G), 473 (B) nm, respectively. The focal length of the MFZP-OFF was measured by an optical

Figure 5. Experimental results of the fabricated MFZP-OFF [9]: (a) Scanning electron microscope (SEM) image of the fabricated MFZP-OFF. (b) Optical microscope images of the transmitted light at various incidence and distance conditions. (c) Numerical results on the normalized field intensity distributions along the z-axis with respect to the wavelength of incident light.

microscope system, and the measured focal points for RGB colors were at z = 18 (R), 20 (G), and 23 (B) μm, respectively. Numerical simulations were also performed to verify the experimental results, which are shown in Figure 5(c). The numerically calculated focal points for RGB colors were given by z = 17.6 (R), 21.0 (G), and 23.8 (B) μm, respectively, which were actually in good agreement with the experimental results. In fact, the focal length of the MFZP-OFF varied from 28.6 to 14.9 μm for the wavelength range from 400 to 700 nm, which means the relative focallength change per unit wavelength was as large as 45.5. It is highlighted that this relative change rate is over 20 times higher than the rate that can be obtained with a conventional silica-based lens [9, 31], as the latter can only be detuned from 20.2 to 19.6 μm for the same spectral detuning range. In addition, the mean beam radius averaged out over the whole visible range was calculated to be 768 nm with a standard deviation of 14.2 nm, which indicates that the relative change was only 1.84% over the whole visible range as expected from Eq. (5). Nevertheless, it should be noted that even though the super-variable focusing capability along with a nearly constant beam spot size at the focal point over the very wide spectral range was verified both numerically and experimentally, the depth of focus of the focal spot along the optical axis should still be inversely proportional to the wavelength of incident light [28, 33].

### 3.2. All-sub-wavelength-scaled MFZP

<sup>f</sup> <sup>λ</sup> <sup>≈</sup> <sup>λ</sup>0<sup>f</sup> <sup>0</sup>

where λ<sup>0</sup> and f <sup>0</sup> denote the reference wavelength and focal length, respectively. It shows that an FZP has a focal length that is inversely proportional to the incident optical wavelength. In addition, one can also notice that the beam radius at the focal point of an FZP, that is, rr

to remain nearly consistent regardless of the incident wavelength, considering the optical

kNA <sup>≈</sup> <sup>λ</sup><sup>f</sup> <sup>λ</sup>

where k, NA, and R denote the wavenumber of the incident light, the effective numerical aperture of the lens, and the radius of the lens, respectively. Since the product of the wavelength and the focal length remains invariant from Eq. (4), Eq. (5) indicates that the beam radius at the focal point of an FZP is approximately preserved regardless of the wavelength of

On the other hand, MFZP-OFFs can readily be fabricated using electron-beam and evaporation and FIB milling techniques [34, 35]. Figure 5 illustrates an MFZP-OFF fabricated in house based on the techniques and its focusing characteristics. Silver was initially deposited via an electron-beam evaporation system to form a 100-nm layer on the flat-cleaved multimode optical fiber facet. The multimode optical fiber had a 50-μm diameter step-index core with 0.22 NA. The silver layer was processed by FIB milling to have the FZP structure consisting of 6 rings [9]. It should be noted that this FZP was designed to produce a focal spot at 20 μm from

To characterize the MFZP-OFF, visible light of three different colors (RGB) was launched into the other end of the optical fiber. The center wavelengths of them were given by 612 (R), 527 (G), 473 (B) nm, respectively. The focal length of the MFZP-OFF was measured by an optical

Figure 5. Experimental results of the fabricated MFZP-OFF [9]: (a) Scanning electron microscope (SEM) image of the fabricated MFZP-OFF. (b) Optical microscope images of the transmitted light at various incidence and distance conditions. (c) Numerical results on the normalized field intensity distributions along the z-axis with respect to the wavelength

the fiber facet when the wavelength of incident light was tuned at 550 nm.

re<sup>2</sup> <sup>∝</sup> <sup>1</sup>

diffraction principle [9, 31] such as

the incident light.

188 Plasmonics

of incident light.

<sup>λ</sup> , (4)

<sup>2</sup>π<sup>R</sup> , (5)

<sup>2</sup> tends

If all the openings of the standard MFZP discussed in the preceding section are reduced down into the sub-wavelength scale [9, 28], its transmission starts to be dominated by the SPPmediated radiation, that is, the extraordinary optical transmission (EOT) via SPPs. Subsequently, such an MFZP (hereinafter SPP-MFZP) will bring in polarization-dependent characteristics because SPPs are normally excited in the direction perpendicular to the slit walls, so that only the radially polarized mode can lead to a hotspot. Thus, this SPP-MFZP can be utilized for focusing of radially polarized light, which has considerable advantages over the linearly polarized or un-polarized counterparts in various applications, thanks to its axially symmetric optical characteristics [30, 36]. The author has investigated the polarization-selective characteristics of the sub-wavelength-scale annular slit in [9], verifying that the transmission of azimuthally polarized (i.e., parallel-polarized) light was suppressed drastically if the relative slit width with respect to wavelength, that is, s/λ, was given by < 0.3, while the transmission of radially polarized (i.e., perpendicular-polarized) light remained nearly unchanged.

Thus, building upon the principle, an SPP-MFZP was fabricated and characterized experimentally. A 195-nm-thickness gold layer was deposited on a fused-silica substrate, using the electron-beam evaporation method. A standard 6-ring FZP was designed for the reference wavelength of 660 nm and the reference focal length of 20-μm, and all the rings was filled with sub-wavelength-slits of a 120-nm width with a 50% duty ratio. Figure 6(a) illustrates the SEM image of the fabricated SPP-MFZP. To characterize its polarization-dependent functionality, linearly polarized light was illuminated on it. Rotating the axis of the incident polarization, its transmission through the SPP-MFZP was measured by the optical microscope. Considering that the linearly polarized light can be decomposed into a radial component and an azimuthal component with a different ratio depending on the location on the SPP-MFZP plane, the transmitted light pattern should be like a "figure of eight." Figure 6(b) illustrates the optical

including a corrugation-assisted MCAFF for wavelength-dependent off-axis directional beaming. Unlike the conventional SPP-coupling techniques having trade-offs and limitations from various perspectives, such as efficiency, compactness, unidirectional coupling, alignment, etc., the MCAFF configuration can readily resolve the aforementioned issues, so that it can be

In general, optical-fiber-based SPP generation has mostly been done based on nanoslit structures [4, 6, 9, 38]. However, its coupling efficiency tends to be considerably low by the following factors: the generation of NCDL, the excitation of multidirectional SPPs, and the reflection of the incident light by aperture [10] as illustrated in Figure 7(a). In fact, such issues can be overcome if the Kretschmann configuration [37] is directly exploited on an angled

In fact, the Kretschmann's prism coupling configuration should still be valid for an angled fiber facet, because it can be regarded as a prism to the optical mode guided in the core of the fiber [10, 37]. Subsequently, an MCAFF can excite SPPs along the dielectric-metal interface as

where k<sup>0</sup> denotes the wavenumber of the optical radiation in free space, kSP<sup>0</sup> the wavenumber of the SPP, ε<sup>d</sup> and ε<sup>m</sup> the electric permittivities of the dielectric and the metal, respectively, neff the effective refractive index of the optical fiber mode, and θ the incidence angle of the optical

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi εdε<sup>m</sup> ε<sup>d</sup> þ ε<sup>m</sup>

, (6)

Plasmonics on Optical Fiber Platforms http://dx.doi.org/10.5772/intechopen.79146 191

r

kSP<sup>0</sup> ¼ neff k<sup>0</sup> sinθ ¼ k<sup>0</sup>

Figure 7. Fiber-SPP-mode coupling schemes [10]: (a) Nanoslit coupling scheme and (b) MCAFF scheme.

an efficient alternative to the existing techniques.

optical fiber facet as illustrated in Figure 7(b).

4.1. SPP coupling scheme based on a metal-coated angled fiber facet

long as the following phase-matching condition is satisfied [10]:

Figure 6. Experimental results of the fabricated SPP-MFZP [9]: (a) SEM image of the SPP-MFZP fabricated on a goldcoated fused-silica substrate. (b) Dark-field optical microscope images of the transmitted light at different image planes and for different incident polarization states.

microscope images of the transmitted light patterns at the top surface of the SPP-MFZP and at the focal plane for two different linear polarization states. The results suggest that the SPP-MFZP functioned as expected, such that only the radial-polarization mode could efficiently pass through the SPP-MFZP, being selectively focused down at the focal plane. It is noteworthy that the SPP-MFZP can readily be implemented onto a fiber facet in a way similar to the MFZP-OFF discussed in the preceding section.
