4. Metal-coated angled optical fiber facets

Efficient excitation of SPPs is invariably important because SPPs cannot be excited naturally, which means it requires some specific apparatus leading to the special boundary condition at the dielectric-metal interface [37]. The prism coupling technique based on the Kretschmann configuration is one of the most frequently used methods for this purpose [37]. This technique utilizes an oblique incidence toward a dielectric-metal interface, in which the real part of the dielectric material should be higher than that of the metal. In optical fiber platforms, the technique was not fully exploited, such that SPPs were normally excited via using tip structures, nanoslits or apertures, the polished or tapered side of the optical fiber, etc. [4–7].

Recently, the author has introduced a novel SPP coupling scheme in the optical fiber platform that is based on a metal-coated angled fiber facet (MCAFF) different from the aforementioned conventional schemes [10]. In fact, this scheme exploited the so-called Kretschmann configuration on the optical fiber platform, because the angle fiber facet can play exactly the same role as a prism to the optical mode guided in the core of the fiber [10, 37].

In this section, the author discusses the MCAFF configuration with corresponding numerical and experimental results, and also shows how it can be utilized for further applications, 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 an efficient alternative to the existing techniques.

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

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

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

Efficient excitation of SPPs is invariably important because SPPs cannot be excited naturally, which means it requires some specific apparatus leading to the special boundary condition at the dielectric-metal interface [37]. The prism coupling technique based on the Kretschmann configuration is one of the most frequently used methods for this purpose [37]. This technique utilizes an oblique incidence toward a dielectric-metal interface, in which the real part of the dielectric material should be higher than that of the metal. In optical fiber platforms, the technique was not fully exploited, such that SPPs were normally excited via using tip struc-

tures, nanoslits or apertures, the polished or tapered side of the optical fiber, etc. [4–7].

as a prism to the optical mode guided in the core of the fiber [10, 37].

Recently, the author has introduced a novel SPP coupling scheme in the optical fiber platform that is based on a metal-coated angled fiber facet (MCAFF) different from the aforementioned conventional schemes [10]. In fact, this scheme exploited the so-called Kretschmann configuration on the optical fiber platform, because the angle fiber facet can play exactly the same role

In this section, the author discusses the MCAFF configuration with corresponding numerical and experimental results, and also shows how it can be utilized for further applications,

MFZP-OFF discussed in the preceding section.

and for different incident polarization states.

190 Plasmonics

4. Metal-coated angled optical fiber facets

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

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

$$k\_{SP0} = n\_{\text{eff}} k\_0 \sin \theta = k\_0 \sqrt{\frac{\varepsilon\_d \varepsilon\_m}{\varepsilon\_d + \varepsilon\_m}},\tag{6}$$

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

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

fiber mode relative to the fiber-metal interface or simply the angle of the optical fiber facet relative to the optical fiber axis as illustrated in Figure 7(b).

suppress the decoupling of the SPP. In the latter case one may also alternatively consider choosing a thin layer nearby the core region and gradually increasing the thickness of the

Figure 9(a) illustrates an experimental setup to characterize the MCAFF [39]. An angle-cleaved optical fiber end supported in the substrate was metal (silver)-coated based on the electronbeam evaporation method. The optical fiber had a step-index core of a 5.3 μm diameter and of an NA of 0.14. The facet angle and the wavelength of incident light were given by <sup>θ</sup> <sup>¼</sup> <sup>46</sup>�

650 nm, respectively. Two samples with different metal thicknesses of 20 and 30 nm were fabricated. In order to decouple the SPP excited on the MCAFF surface out to free space, the surface was roughly ground to have some randomized texture. In addition, the incident polarization state was controlled by the rotation of the input polarizer, and the transmitted light was monitored and imaged by an optical microscope with a complementary metal-oxidesemiconductor (CMOS) camera. It should be noted that the SPP mode can only be excited by a transverse-magnetic (TM) mode. Thus, one can expect that the out-coupled light could only be observed if a TM optical mode were incident onto the MCAFF. In contrast, a transverse-electric (TE) mode would undergo substantial attenuation, so that it would be hard to observe its transmission. The facet images detected by the CMOS camera are shown in Figure 9(b) for the two MCAFF samples in the TM and TE incidence conditions. One can clearly see that significantly brighter transmission was detected when TM-polarized light was launched than when TE-polarized light was launched. Moreover, significantly brighter transmission was detected from the 30-nm-thickness MCAFF than the 20-nm-thickness MCAFF, which was due to the fact that the thinner (� 20 nm) metal layer caused relatively larger decoupling loss than the thicker (� 30 nm) metal layer, because the SPP was allowed to propagate a relatively long distance in

Figure 9. Experimental results of fabricated MCAFFs [39]: (a) Experimental arrangement for characterizing the fabricated MCAFFs. (b) Decoupled light from the MCAFFSs for incident light at 650 nm with different polarization modes.

and

193

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metal layer outside the core region.

this case, as already discussed.

In this scheme, two kinds of SPPs can be generated. One is the propagating SPP (P-SPP) mode that is the eigen mode of the given interface geometry, and the other is the localized SPP (L-SPP) mode directly induced by the incident wave [2, 10, 26, 37]. In order to verify the functional characteristics of the MCAPP, one can first perform numerical calculations of an example structure, assuming that the optical fiber is a step-index fiber with a core diameter of 3 μm and an NA of 0.1, and that the metal coating material is silver.

Figure 8(a) illustrates the field pattern of the MCAFF when the incident light was launched from the other end of the optical fiber, in which the metal thickness, the fiber-facet angle, and the incident wavelength were given by 20 nm, 45, and 600 nm, respectively [38]. It should be noted that the incident optical fiber mode was assumed to be an x-polarized LP01 mode. From the figure, one can see that an SPP mode was dominantly generated at the top surface of the metal layer, and a fraction of the incident light was immediately reflected by the dielectricmetal interface, and some of the SPP mode was decoupled back into the dielectric region after some propagation length. In fact, the decoupled component can also give rise to loss to the P-SPP, which can be observed at the right-top-corner indicated by a round-rectangle in a dashed-line. This is different from the direct reflection of the optical mode around the core region, and it can be avoided if the metal thickness increases considerably [10]. With the metal thickness of 20 nm, the spectral SPP coupling efficiency in terms of the fiber-facet angle is illustrated in Figure 8(b). The calculated efficiency reached close to 70% in the phase-matched condition. In addition, the given MCAFF structure showed a sufficiently broad spectral bandwidth covering the whole visible range with the given metal thickness of 20 nm. In fact, deciding the thickness of the metal layer is really dependent on the type of the application of the MCAFF. If the excitation of SPP is important only nearby the core region, one may choose a thin metal layer ( 20 nm) to intensify the direct coupling. In contrast, if it requires a relatively long propagation length, one may go for a considerably thick metal layer (> 30 nm) in order to

Figure 8. SPP coupling scheme based on the MCAFF [10]: (a) Field pattern of a specific MCAFF configuration. (b) Spectrum of the SPP coupling efficiency in terms of the fiber-facet angle and incident wavelength.

suppress the decoupling of the SPP. In the latter case one may also alternatively consider choosing a thin layer nearby the core region and gradually increasing the thickness of the metal layer outside the core region.

fiber mode relative to the fiber-metal interface or simply the angle of the optical fiber facet

In this scheme, two kinds of SPPs can be generated. One is the propagating SPP (P-SPP) mode that is the eigen mode of the given interface geometry, and the other is the localized SPP (L-SPP) mode directly induced by the incident wave [2, 10, 26, 37]. In order to verify the functional characteristics of the MCAPP, one can first perform numerical calculations of an example structure, assuming that the optical fiber is a step-index fiber with a core diameter of 3 μm and an NA

Figure 8(a) illustrates the field pattern of the MCAFF when the incident light was launched from the other end of the optical fiber, in which the metal thickness, the fiber-facet angle, and the incident wavelength were given by 20 nm, 45, and 600 nm, respectively [38]. It should be noted that the incident optical fiber mode was assumed to be an x-polarized LP01 mode. From the figure, one can see that an SPP mode was dominantly generated at the top surface of the metal layer, and a fraction of the incident light was immediately reflected by the dielectricmetal interface, and some of the SPP mode was decoupled back into the dielectric region after some propagation length. In fact, the decoupled component can also give rise to loss to the P-SPP, which can be observed at the right-top-corner indicated by a round-rectangle in a dashed-line. This is different from the direct reflection of the optical mode around the core region, and it can be avoided if the metal thickness increases considerably [10]. With the metal thickness of 20 nm, the spectral SPP coupling efficiency in terms of the fiber-facet angle is illustrated in Figure 8(b). The calculated efficiency reached close to 70% in the phase-matched condition. In addition, the given MCAFF structure showed a sufficiently broad spectral bandwidth covering the whole visible range with the given metal thickness of 20 nm. In fact, deciding the thickness of the metal layer is really dependent on the type of the application of the MCAFF. If the excitation of SPP is important only nearby the core region, one may choose a thin metal layer ( 20 nm) to intensify the direct coupling. In contrast, if it requires a relatively long propagation length, one may go for a considerably thick metal layer (> 30 nm) in order to

Figure 8. SPP coupling scheme based on the MCAFF [10]: (a) Field pattern of a specific MCAFF configuration.

(b) Spectrum of the SPP coupling efficiency in terms of the fiber-facet angle and incident wavelength.

relative to the optical fiber axis as illustrated in Figure 7(b).

of 0.1, and that the metal coating material is silver.

192 Plasmonics

Figure 9(a) illustrates an experimental setup to characterize the MCAFF [39]. An angle-cleaved optical fiber end supported in the substrate was metal (silver)-coated based on the electronbeam evaporation method. The optical fiber had a step-index core of a 5.3 μm diameter and of an NA of 0.14. The facet angle and the wavelength of incident light were given by <sup>θ</sup> <sup>¼</sup> <sup>46</sup>� and 650 nm, respectively. Two samples with different metal thicknesses of 20 and 30 nm were fabricated. In order to decouple the SPP excited on the MCAFF surface out to free space, the surface was roughly ground to have some randomized texture. In addition, the incident polarization state was controlled by the rotation of the input polarizer, and the transmitted light was monitored and imaged by an optical microscope with a complementary metal-oxidesemiconductor (CMOS) camera. It should be noted that the SPP mode can only be excited by a transverse-magnetic (TM) mode. Thus, one can expect that the out-coupled light could only be observed if a TM optical mode were incident onto the MCAFF. In contrast, a transverse-electric (TE) mode would undergo substantial attenuation, so that it would be hard to observe its transmission. The facet images detected by the CMOS camera are shown in Figure 9(b) for the two MCAFF samples in the TM and TE incidence conditions. One can clearly see that significantly brighter transmission was detected when TM-polarized light was launched than when TE-polarized light was launched. Moreover, significantly brighter transmission was detected from the 30-nm-thickness MCAFF than the 20-nm-thickness MCAFF, which was due to the fact that the thinner (� 20 nm) metal layer caused relatively larger decoupling loss than the thicker (� 30 nm) metal layer, because the SPP was allowed to propagate a relatively long distance in this case, as already discussed.

Figure 9. Experimental results of fabricated MCAFFs [39]: (a) Experimental arrangement for characterizing the fabricated MCAFFs. (b) Decoupled light from the MCAFFSs for incident light at 650 nm with different polarization modes.

### 4.2. Application of the MCAFF scheme: corrugation-assisted MCAFF for wavelength-dependent off-axis beaming

In this section, the author discusses a corrugation-assisted MCAFF (CA-MCAFF) structure, which has wavelength-dependent off-axis directional beaming (WODB) functionality [40–42]. The schematic of the CA-MCAFF is shown in Figure 10. It is noteworthy that the incident optical fiber mode can be coupled into both P-SPP and L-SPP at the top surface of the metal layer, which can be decoupled into free-space mode through the periodic corrugation structure depending on the phase-matching condition given by [10, 42]:

$$k\_{SPP} \pm mk\_{\varepsilon} + k\_0 \text{sin}\phi = 0,\tag{7}$$

depending on what characteristic of the CA-MCAFF is most desired, for example, the overall out-coupling efficiency, spectral bandwidth, etc. [10]. Figure 11 illustrates the calculated far-field magnitude distribution through the CA-MCAFF, in which the thickness of the metal layer and the fiber-facet angle were set to 20 nm and 50�, respectively, and the period, modulation depth, and duty ratio of the corrugation were set to 380 nm, 40 nm, and 47%, respectively. These parameters were determined after going through iterative calculations from the perspective of maximizing the overall out-coupling efficiency [10]. In the figure, there are a few virtual lines drawn: The solid white line and dashed black line denote the theoretically calculated output beaming angles when phase-matched with the L-SPP and the P-SPP, respectively. As already explained that the L-SPP mode should be the dominant SPP mode in the given structure, one can see that the actual beaming angle was better fitted with the beaming angle trace by the L-SPP mode than with the trace by the P-SPP mode. In particular, higher out-coupling took places where both traces are matched or close to each other, which peaked at � 500 nm as depicted in Figure 11. This means that the wavenumber of L-SPP and P-SPP was close to each other in the given condition, which eventually enhanced the aggregate coupling efficiency of the SPPs. In addition, it is noteworthy that the beaming angle exhibited good linearity with wavelength, which in fact justifies that the CA-MCAFF can efficiently be used for WODB. On the other hand, the dash-dotted blue and red lines represent the case when the incident fiber optical mode was phase matched with unwanted backward-propagating SPP modes, such as the SPP modes excited at the metal-fiber interface and the air-metal interface, respectively, for m ¼ �2 in Eq. (7). The second-order coupling should be possible because the periodic corrugation was formed in an asymmetrically layered structure in the transverse (or vertical) direction [10]. When the main beaming line passed across these two traces, the out-coupling efficiency dropped a bit, because the phase-matching conditions for the L-SPP and for the backward-propagating SPPs were satisfied at the same time. However, this unwanted consequence had already been mini-

Plasmonics on Optical Fiber Platforms http://dx.doi.org/10.5772/intechopen.79146 195

Figure 11. Numerical results of the far-field magnitude distribution and the analytical results of the primary beaming angle of the optical radiation from the CA-MCAFF with respect to the wavelength of incident light and the azimuthal

mized while optimizing the duty ratio of the corrugation [10].

angle ϕ [10].

where kSPP denotes the wavenumber of the SPP (either P-SPP or L-SPP), k<sup>0</sup> the wavenumber of the optical radiation in free space, kc the reciprocal lattice vector (i.e., kc ¼ 2π=Λ) of the corrugation having a period of Λ and ϕ the azimuthal angle of the out-coupled optical radiation in free space relative to the surface-normal vector of the MCAFF as shown in Figure 10(a). If the period of the corrugation Λ is fixed, the angle of the out-coupling ϕ will subsequently vary with wavelength [10, 42]. It is noteworthy that the L-SPP is excited owing to the localized plasmonic oscillation in the trough segment of the corrugation whereas the P-SPP is excited owing to the nonlocalized, normal SPP oscillation spread out along the whole metalair interface of the periodical corrugation. Therefore, in the given condition, one can expect that the L-SPP will become the dominant mode rather than the P-SPP, because the latter will undergo significantly higher attenuation by ohmic loss in the metal than the former [37].

It is noteworthy that the CA-MCAFF requires high coupling efficiency nearby the core region, so that a thin metal layer of 20 nm should be a relevant choice. In addition, the initial fiber-facet angle θ and the duty ratio of the unit corrugation should also be determined carefully,

Figure 10. CA-MCAFF and its corresponding SPP modes [10]: (a) Schematic of the CA-MCAFF. (b) Two different types of SPP modes excited at the periodically corrugated metal surface.

depending on what characteristic of the CA-MCAFF is most desired, for example, the overall out-coupling efficiency, spectral bandwidth, etc. [10]. Figure 11 illustrates the calculated far-field magnitude distribution through the CA-MCAFF, in which the thickness of the metal layer and the fiber-facet angle were set to 20 nm and 50�, respectively, and the period, modulation depth, and duty ratio of the corrugation were set to 380 nm, 40 nm, and 47%, respectively. These parameters were determined after going through iterative calculations from the perspective of maximizing the overall out-coupling efficiency [10]. In the figure, there are a few virtual lines drawn: The solid white line and dashed black line denote the theoretically calculated output beaming angles when phase-matched with the L-SPP and the P-SPP, respectively. As already explained that the L-SPP mode should be the dominant SPP mode in the given structure, one can see that the actual beaming angle was better fitted with the beaming angle trace by the L-SPP mode than with the trace by the P-SPP mode. In particular, higher out-coupling took places where both traces are matched or close to each other, which peaked at � 500 nm as depicted in Figure 11. This means that the wavenumber of L-SPP and P-SPP was close to each other in the given condition, which eventually enhanced the aggregate coupling efficiency of the SPPs. In addition, it is noteworthy that the beaming angle exhibited good linearity with wavelength, which in fact justifies that the CA-MCAFF can efficiently be used for WODB. On the other hand, the dash-dotted blue and red lines represent the case when the incident fiber optical mode was phase matched with unwanted backward-propagating SPP modes, such as the SPP modes excited at the metal-fiber interface and the air-metal interface, respectively, for m ¼ �2 in Eq. (7). The second-order coupling should be possible because the periodic corrugation was formed in an asymmetrically layered structure in the transverse (or vertical) direction [10]. When the main beaming line passed across these two traces, the out-coupling efficiency dropped a bit, because the phase-matching conditions for the L-SPP and for the backward-propagating SPPs were satisfied at the same time. However, this unwanted consequence had already been minimized while optimizing the duty ratio of the corrugation [10].

4.2. Application of the MCAFF scheme: corrugation-assisted MCAFF for

depending on the phase-matching condition given by [10, 42]:

In this section, the author discusses a corrugation-assisted MCAFF (CA-MCAFF) structure, which has wavelength-dependent off-axis directional beaming (WODB) functionality [40–42]. The schematic of the CA-MCAFF is shown in Figure 10. It is noteworthy that the incident optical fiber mode can be coupled into both P-SPP and L-SPP at the top surface of the metal layer, which can be decoupled into free-space mode through the periodic corrugation structure

where kSPP denotes the wavenumber of the SPP (either P-SPP or L-SPP), k<sup>0</sup> the wavenumber of the optical radiation in free space, kc the reciprocal lattice vector (i.e., kc ¼ 2π=Λ) of the corrugation having a period of Λ and ϕ the azimuthal angle of the out-coupled optical radiation in free space relative to the surface-normal vector of the MCAFF as shown in Figure 10(a). If the period of the corrugation Λ is fixed, the angle of the out-coupling ϕ will subsequently vary with wavelength [10, 42]. It is noteworthy that the L-SPP is excited owing to the localized plasmonic oscillation in the trough segment of the corrugation whereas the P-SPP is excited owing to the nonlocalized, normal SPP oscillation spread out along the whole metalair interface of the periodical corrugation. Therefore, in the given condition, one can expect that the L-SPP will become the dominant mode rather than the P-SPP, because the latter will undergo significantly higher attenuation by ohmic loss in the metal than the former [37].

It is noteworthy that the CA-MCAFF requires high coupling efficiency nearby the core region, so that a thin metal layer of 20 nm should be a relevant choice. In addition, the initial fiber-facet angle θ and the duty ratio of the unit corrugation should also be determined carefully,

Figure 10. CA-MCAFF and its corresponding SPP modes [10]: (a) Schematic of the CA-MCAFF. (b) Two different types of

SPP modes excited at the periodically corrugated metal surface.

kSPP � mkc þ k0sinϕ ¼ 0, (7)

wavelength-dependent off-axis beaming

194 Plasmonics

Figure 11. Numerical results of the far-field magnitude distribution and the analytical results of the primary beaming angle of the optical radiation from the CA-MCAFF with respect to the wavelength of incident light and the azimuthal angle ϕ [10].

radial-polarization selectivity owing to the EOT effect from the auxiliary subwavelength annular slits inserted in the openings of the FZP structure. Numerical and experimental analyses verified their novel functionality. These schemes will be useful for various applications that require accurate, flexible, and centrosymmetric optical focusing with a broad focal-length tuning range, such as in micro/nanomachining and optical trapping. In addition, these schemes can also be

Plasmonics on Optical Fiber Platforms http://dx.doi.org/10.5772/intechopen.79146 197

Third, a fiberized SPP coupling scheme and its application to a CA-MCAFF were introduced and discussed. The former realized the Kretschmann SPP coupling scheme in the optical fiber platform, and the latter exhibited novel WODB functionality. Numerical and experimental analyses verified that the MCAFF-based SPP coupling scheme worked efficiently and has great potential for being used as an excellent, alternative SPP generation method, which provides high efficiency, unidirectionality, and full compatibility with fiber-based optical sources. The CA-MCAFF scheme will also be very useful for various plasmonic and optical applications where WODB functionality is required, such as a nanophotonic wavelength-division-multiplexer, a compact

Optical fibers are an excellent platform for plasmonics studies and applications. The novel plasmonic nanostructures realized on various optical fiber platforms successfully demonstrated fascinating characteristics of plasmonics in a compact, flexible, and cost-effective format. The author believes that the investigations and discussions given in this chapter will broaden the fiber-optic and plasmonics research fields, as well as expecting further advances

Optoelectronics Research Centre, University of Southampton, Southampton, United Kingdom

[1] Ghatak A, Thyagarajan K. An Introduction to Fiber Optics. Cambridge: Cambridge Uni-

[2] Agrawal G. Nonlinear fiber optics. San Diego, California: Academic Press; 1995

The author acknowledges the useful discussion with Prof. Y. Jeong.

Address all correspondence to: H.Kim@soton.ac.uk

exploited for mono-chromatic-multi-focal or multi-chromatic-mono-focal lenses [43, 44].

spectrometer, etc.

and convergence of them to come.

Acknowledgements

Author details

Hyuntai Kim

References

versity Press; 1998

Figure 12. Field magnitude patterns of a specific CA-MCAFF for RGB incidence conditions [10].

Figure 12 illustrates the resultant field pattern nearby the core region for different incident wavelengths, which justifies the spatial beaming characteristics of the out-coupled optical radiation from the CA-MCAFF. It is clearly shown that the L-SPP mode was dominantly generated above the core region, and a fraction of it propagates along the air-metal interface and another fraction was out-coupled into free space. They show different beaming angles with incident wavelength, confirming the WODB characteristics. In particular, for 550 nm, one can see that the incident light was also coupled to the counter-directionally propagating SPP, which has also been denoted by the dash-dotted blue line in Figure 11. The overall out-coupling efficiency for WODB was estimated to be as high as 30% [10] for the given CA-MCAFF.
