2. Trench-assisted circular metallic nanoslits for low-noise plasmonic hotspot generation

Plasmonic focusing is beneficial to diverse novel applications, such as lithography [11], high harmonic generation [12], and sensing [13], etc. To date, various configurations have been suggested for plasmonic focusing, such as nanoparticles [14], circular nanoslits [15], bowtie structures [16], metal tips [17], etc. Among them, circular metallic nanoslits (CMNSs) engraved on a thin metal film are of great interest because of their capability of generating focused cylindrical SPPs (C-SPPs), that is, plasmonic hotspots, via modest fabrication procedures [8]. While various structures and schemes were extensively investigated to intensify the plasmonic hotspots, the effect of nonconfined diffracted light (NCDL) that accompanies C-SPPs has not been investigated rigorously [18]. In most cases of CMNSs, it is hard to avoid the disturbance of NCDL, so that its consequence increases the background noise, thereby degrading the signal-to-noise ratio (SNR) and sharpness of the C-SPP hotspot.

Recently, exploiting the multipole cancelation mechanism (MPCM) proposed for effective noise-canceling [19], the author has investigated novel trench-assisted circular metal nanoslits (TA-CMNSs) implemented onto optical fiber facets [20], where the use of the optical fiber platform leads to considerably simplified procedures to excite C-SPPs with low noise [21].

In this section, the author discusses the characteristics of TA-CMNS structures implemented on a metal-coated optical fiber facet and shows that they can have substantially improved SNR characteristics based on the MPCM. In particular, these structures are useful for plasmonic devices that particularly require high SNR characteristics, such as bio-sensing, imaging, surface-enhanced Raman spectroscopy, etc.

### 2.1. Fiberized circular metallic nanoslits

by the full accessibility to premium grade fiberized devices already combined with light sources, detectors, and various other components of optical functionalities. Once optical fiber platforms are considered for SPP research and applications, one most apparent effect obtained from them is the fact that the use of free-space optics can be eliminated or minimized as

In fact, a variety of plasmonic nanostructures implemented onto optical fiber platforms have been investigated to date: Most of them were based on metallic nanostructures constructed on the facet, tip, and polished or tapered side of optical fiber [4–7]. Among them, the author focuses on the optical fiber facet structures in that they inherently provide an easy and efficient access to light that the core of the optical fiber guides. Thus, in this chapter, the author investigates and discusses various optical fiber facet structures for an efficient platform for plasmonics research and applications: First, the author investigates trench-assisted circular metallic nanoslits on flat-cleaved optical fiber facets for the generation of axially symmetric SPP hotspots with significantly enhanced noise characteristics [8]. Second, the author investigates fiberized plasmonic Fresnel zone plates for super-variable focusing with incident wavelength and for selective focusing with incident polarization [9]. Third, the author investigates novel metal-coated angled optical fiber facets for a versatile optical-to-SPP mode converter, which provide high efficiency, unidirectionality, and perfect compatibility with fiberized light sources [10]. The detailed investigation and discussion with numerical and experimental demonstrations are given in the following sections. In addition, it is noteworthy that all the numerical simulations were done based on the finite element method (FEM: COMSOL Multiphysics®), and that all the metallic nanostructures were fabricated based on the electron-beam evaporation method and the focused ion beam (FIB) milling method, unless

Figure 1. Schematic illustrations of various nanostructured optical fiber facets for plasmonic applications.

illustrated in Figure 1.

182 Plasmonics

stated otherwise.

Different from one-dimensional nanoslits, a CMNS generates a plasmonic hotspot at its center by two-dimensionally focusing the inward-propagating C-SPP, so that the hotpot can be intensified to a substantial level. Moreover, its efficiency can also be enhanced if radially polarized light is utilized [22]. Indeed, the use of the optical fiber platform for CMNS applications can bring in a considerable advantage, because radially polarized fiber-optic modes (e.g., TM01 mode) are readily accessible.

A full-vectorial simulation of a CMNS constructed on top of an optical fiber facet is considered in the following, which was initially proposed and analyzed in [8]. It was assumed that the optical fiber had a step-index core with a diameter of 8 μm and a numerical aperture (NA) of 0.1, and that the metal was made of gold, the material parameters of which, that is, the refractive index and extinction coefficient, were given by n = 0.16918 and k = 3.8816, respectively. The wavelength of incident light was set as λ = 700 nm. The width of the slit and the thickness of the metal layer were set to 87.5 nm and 500 nm, respectively. The annular slit was concentric with the fiber core. In particular, the radius of the annular slit was matched with the intensity distribution of the TM01 mode of the optical fiber in order to maximize the modefield overlap with the opening of the annular slit.

First of all, a simple CMNS without having any trench structure was numerically analyzed [8]. The C-SPP (graded red/yellow) and NCDL (graded blue) field intensity patterns are illustrated in Figure 2. It is shown that while a plasmonic hotspot was formed at the center of the metal surface, the NCDL was also focused at the same position of the hotspot. In particular, the NCDL component at the center was hardly distinguishable with the C-SPP signal, so that the SNR (defined as the ratio of the C-SPP intensity to the NCDL intensity) of the device was inevitably degraded. The peak and mean SNRs within the central main lobe of the C-SPP hotspot were given by 22.74 and 14.70 dB, respectively.

### 2.2. Noise cancelation in trench-assisted CMNSs

As discussed in the preceding section, NCDL tends to be overlapped with the C-SPP hotspot. In particular, the NCDL propagating in the direction parallel to the metal surface can considerably degrade the SNR of the C-SPP hotspot. Thus, to improve the SNR, NCDL should be suppressed. As proposed in [8], a trench-assisted (TA) structure along with the conventional CMNS can be considered in order for minimizing the disturbance incurred by the unwanted NCDL. The proposed TA-CMNS structure and its operation principle are illustrated in Figure 3. The main strategy of exploiting the TA structure is such that a considerable portion of the primary NCDL (depicted in blue) from the slit is canceled out by the secondary NCDL (depicted in red) excited by the TA structure alongside the slit. The TA-CMNS was in fact designed in a way that the secondary NCDL destructively interferes with the primary NCDL, as shown in Figure 3. It should be further noted that the trench structure having a sharp edge at P<sup>2</sup> is

preferred, because P<sup>2</sup> is the location where charges are predominantly induced [14], so that it

In order to make the primary NCDL and the secondary NCDL out of phase completely, the phase difference between the primary NCDL (path l1) and the C-SPP (path l2) should be an odd integral multiple of λ, because the phase of the secondary NCDL is mostly determined by

where k and kC�SPP denote the wavenumbers of the NCDL and the C-SPP, respectively, Re the real part of the argument, and m an integer number. In addition, the location P<sup>1</sup> should also be determined carefully in order that the cavity formed between the two inner edges of the trench

Re kcsp <sup>d</sup> � <sup>φ</sup>Trench <sup>¼</sup> <sup>2</sup>m<sup>0</sup>

Here, two different types of TA-CMNSs are under consideration [8]: One is a rectangular trench (RT) and the other is an asymmetric parabolic trench (APT). While the RT-CMNS has a merit in terms of ease of fabrication, one can improve the SNR performance more significantly with the APT-CMNS because it facilitates increasing the charge concentration at P<sup>2</sup> relative to P<sup>1</sup> [8, 20]. All the detailed parameters can be optimized via iterative numerical procedures as

<sup>1</sup> satisfies the resonance condition maximizing the C-SPP transmission out of it, such

Reð Þ kC�SPP l<sup>2</sup> � kl<sup>1</sup> ¼ ð Þ 2m � 1 π, (1)

π, (2)

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<sup>1</sup>, φTrench the phase shift caused by the reflection

can be regarded as a "quasi-pole source" that generates secondary NCDL [8].

the phase of the C-SPP, such that [8].

Figure 3. Schematic of a TA-CMNS and its operation principle [8].

where d dentoes the distance between P<sup>1</sup> and P<sup>0</sup>

at the trench wall, and m<sup>0</sup> an integer number.

P<sup>1</sup> and P<sup>0</sup>

discussed in [8].

that [8].

Figure 2. Relative field intensity patterns in dB calculated for a simple CMNS with TM01 optical fiber mode incidence [8].

Figure 3. Schematic of a TA-CMNS and its operation principle [8].

intensity distribution of the TM01 mode of the optical fiber in order to maximize the modefield

First of all, a simple CMNS without having any trench structure was numerically analyzed [8]. The C-SPP (graded red/yellow) and NCDL (graded blue) field intensity patterns are illustrated in Figure 2. It is shown that while a plasmonic hotspot was formed at the center of the metal surface, the NCDL was also focused at the same position of the hotspot. In particular, the NCDL component at the center was hardly distinguishable with the C-SPP signal, so that the SNR (defined as the ratio of the C-SPP intensity to the NCDL intensity) of the device was inevitably degraded. The peak and mean SNRs within the central main lobe of the C-SPP

As discussed in the preceding section, NCDL tends to be overlapped with the C-SPP hotspot. In particular, the NCDL propagating in the direction parallel to the metal surface can considerably degrade the SNR of the C-SPP hotspot. Thus, to improve the SNR, NCDL should be suppressed. As proposed in [8], a trench-assisted (TA) structure along with the conventional CMNS can be considered in order for minimizing the disturbance incurred by the unwanted NCDL. The proposed TA-CMNS structure and its operation principle are illustrated in Figure 3. The main strategy of exploiting the TA structure is such that a considerable portion of the primary NCDL (depicted in blue) from the slit is canceled out by the secondary NCDL (depicted in red) excited by the TA structure alongside the slit. The TA-CMNS was in fact designed in a way that the secondary NCDL destructively interferes with the primary NCDL, as shown in Figure 3. It should be further noted that the trench structure having a sharp edge at P<sup>2</sup> is

Figure 2. Relative field intensity patterns in dB calculated for a simple CMNS with TM01 optical fiber mode incidence [8].

overlap with the opening of the annular slit.

184 Plasmonics

hotspot were given by 22.74 and 14.70 dB, respectively.

2.2. Noise cancelation in trench-assisted CMNSs

preferred, because P<sup>2</sup> is the location where charges are predominantly induced [14], so that it can be regarded as a "quasi-pole source" that generates secondary NCDL [8].

In order to make the primary NCDL and the secondary NCDL out of phase completely, the phase difference between the primary NCDL (path l1) and the C-SPP (path l2) should be an odd integral multiple of λ, because the phase of the secondary NCDL is mostly determined by the phase of the C-SPP, such that [8].

$$\operatorname{Re}(k\_{\mathbb{C}-SPP})l\_2 - kl\_1 = (2m - 1)\pi,\tag{1}$$

where k and kC�SPP denote the wavenumbers of the NCDL and the C-SPP, respectively, Re the real part of the argument, and m an integer number. In addition, the location P<sup>1</sup> should also be determined carefully in order that the cavity formed between the two inner edges of the trench P<sup>1</sup> and P<sup>0</sup> <sup>1</sup> satisfies the resonance condition maximizing the C-SPP transmission out of it, such that [8].

$$2\operatorname{Re}\left(k\_{\text{csp}}\right)d - \varphi\_{Trench} = 2m'\pi,\tag{2}$$

where d dentoes the distance between P<sup>1</sup> and P<sup>0</sup> <sup>1</sup>, φTrench the phase shift caused by the reflection at the trench wall, and m<sup>0</sup> an integer number.

Here, two different types of TA-CMNSs are under consideration [8]: One is a rectangular trench (RT) and the other is an asymmetric parabolic trench (APT). While the RT-CMNS has a merit in terms of ease of fabrication, one can improve the SNR performance more significantly with the APT-CMNS because it facilitates increasing the charge concentration at P<sup>2</sup> relative to P<sup>1</sup> [8, 20]. All the detailed parameters can be optimized via iterative numerical procedures as discussed in [8].

3. Fiberized plasmonic Fresnel zone plates

point in a wide range.

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

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

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

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].

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

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

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

1 nlens � 1

, (3)

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/nm for fused silica [32], so that it results in a very

<sup>f</sup> <sup>¼</sup> <sup>R</sup>1R<sup>2</sup> R<sup>2</sup> � R<sup>1</sup>

to result in relatively large inaccuracies, which are undesirable by any means.

optical force, such as optical trapping [29] and micro-machining [30].

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

is given by a value in the order of �10�<sup>5</sup>

of incident light [31, 33].

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

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


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