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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 22 — Nov. 4, 2013
  • pp: 27402–27410
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Mutual mode control of short- and long-range surface plasmons

Junichi Takahara and Masashi Miyata  »View Author Affiliations


Optics Express, Vol. 21, Issue 22, pp. 27402-27410 (2013)
http://dx.doi.org/10.1364/OE.21.027402


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Abstract

A symmetric metal slab waveguide simultaneously supports two opposite types of propagation mode similar to a metal film: short-range surface plasmon (SRSP) like mode and long-range surface plasmon (LRSP) like mode. The strong field confinement of SRSP-like mode plays a crucial role for nano-optical integrated circuits in spite of short propagation length. In order to avoid the trade-off between field confinement and propagation length, we demonstrate selective mode excitation and mutual mode conversion for nanofocusing mediated by LRSP-like mode.

© 2013 Optical Society of America

1. Introduction

A plasmonic waveguide is a metal optical waveguide utilizing surface plasmon polariton (SPP). The waveguide is a promise candidate for nano-optical waveguiding since the optical beam diameter confined in the waveguide can be reduced to nanometer order beyond the diffraction limit of light [1

1. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22(7), 475–477 (1997). [CrossRef] [PubMed]

,2

2. J. Takahara and T. Kobayash, “Low-dimensional optical waves and nano-optical circuits,” Optics & Photonics News 15(10), 54–59 (2004). [CrossRef]

]. Many studies about plasmonic waveguides have been demonstrated as a key component of nano-optical integrated circuits (NOICs) so far [3

3. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010). [CrossRef]

,4

4. S. I. Bozhevolnyi, Plasmonic Nanoguides and Circuits (Pan Stanford Publishing, 2009).

].

Considering plasmonic waveguides for NOICs, a planar type of plasmonic waveguides such as a metal film (IMI; insulator-metal-insulator) or a metal gap (MIM; metal-insulator-metal) waveguide is suitable [5

5. F. Kusunoki, T. Yotsuya, J. Takahara, and T. Kobayashi, “Propagation properties of guided waves in index-guided two-dimensional optical waveguides,” Appl. Phys. Lett. 86(21), 211101 (2005). [CrossRef]

,6

6. J. Takahara and F. Kusunoki, “Guiding and nanofocusing of two-dimensional optical beam for nanooptical integrated circuits,” IEICE Trans. Electron. E90–C(1), 87–94 (2007). [CrossRef]

]. Especially, a symmetric (i.e. the clad layers are identical) metal film waveguide has a unique property such that it simultaneously supports two propagation modes with opposite characteristics without a cut-off: Long-Range Surface Plasmon polariton (LRSP) and Short-Range Surface Plasmon polariton (SRSP). The LRSP has been studied sine 1970’s and it enables us to achieve long-distance transmission in spite of weak field confinement [7

7. M. Fukui, V. So, and R. Normandin, “Lifetimes of surface plasmons in thin silver films,” Phys. Status Solidi 91(1), 61–64 (1979). [CrossRef]

9

9. P. Berini, “Long-range surface plasmon polaritons,” Adv. in Opt. and Photon. 1(3), 484–588 (2009). [CrossRef]

].

The propagation length of the LRSP is typically 100~300μm at visible frequency, which is more than 10 times longer than that of the SPP of single metal surface [9

9. P. Berini, “Long-range surface plasmon polaritons,” Adv. in Opt. and Photon. 1(3), 484–588 (2009). [CrossRef]

]. In contrast, the SRSP is extremely lossy, resulting in short propagation length of typically several microns. The SRSP, however, enables us to achieve strong field confinement to achieve nanoguiding and nanofocusing of optical beams [1

1. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22(7), 475–477 (1997). [CrossRef] [PubMed]

,2

2. J. Takahara and T. Kobayash, “Low-dimensional optical waves and nano-optical circuits,” Optics & Photonics News 15(10), 54–59 (2004). [CrossRef]

]. Such kind of trade-off relation between the field confinement and the propagation length limits the realization of NOICs. Thus, mutual mode control between LRSP and SRSP is needed. We have already proposed the selective excitation of LRSP/SRSP by two phase controlled incident beams [10

10. K. Yamamoto, K. Kurihara, J. Takahara, and A. Otomo, “Effective excitation of superfocusing surface plasmons using phase controlled waveguide modes,” Mater. Res. Soc. Symp. Proc. 1182–EE13–05, 55 (2009).

,11

11. M. Miyata and J. Takahara, “Excitation control of long-range surface plasmons by two incident beams,” Opt. Express 20(9), 9493–9500 (2012). [CrossRef] [PubMed]

]. If efficient mode conversion is realized between LRSP and SRSP, we achieve optimum treatment of SPP modes in NOICs: excitation and transmission through LRSP and nanofocusing and nanoguiding through SRSP on demand.

A metal slab waveguide embed in a dielectric is one of major planer plasmon waveguides [12

12. R. Zia, A. Chandran, and M. L. Brongersma, “Dielectric waveguide model for guided surface polaritons,” Opt. Lett. 30(12), 1473–1475 (2005). [CrossRef] [PubMed]

]. The metal slab waveguide has attracted significant interest recently as a base for active plasmon components, such as a plasmon sources, modulators, amplifiers and interconnects [13

13. P. Berini and I. De Leon, “Surface plasmon–polariton amplifiers and lasers,” Nat. Photonics 6(1), 16–24 (2011). [CrossRef]

]. This is because of the existence of both LRSP- and SRSP-like mode similar to a metal film waveguide (a metal slab with infinite width); it enable us to realize the plasmon transmission for long distances as well as plasmon nanoguiding with strong localization. This means that a metal slab waveguide has a characteristic to severally satisfy two important goals of plasmonics: the bridge between photonics and electronics, and concentrating and delivering light energy into nanoscale regions [14

14. M. L. Brongersma and V. M. Shalaev, “Applied physics. The case for plasmonics,” Science 328(5977), 440–441 (2010). [CrossRef] [PubMed]

]. Furthermore, the ease of the fabrication and its integration has superiority for practical use. Therefore, the metal slab waveguides are now considered as a more important platform for active plasmonics and its potential applications [15

15. M. Miyata and J. Takahara, “Colloidal quantum dot-based plasmon emitters with planar integration and long-range guiding,” Opt. Express 21(7), 7882–7890 (2013). [CrossRef] [PubMed]

].

The optical waveguiding characteristics of symmetric and asymmetric metal slab waveguides have been studied numerically by Berini [16

16. P. Berini, “Plasmon polariton modes guided by a metal film of finite width,” Opt. Lett. 24(15), 1011–1013 (1999). [CrossRef] [PubMed]

18

18. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B 61(15), 10484–10503 (2000). [CrossRef]

]. Such studies, however, offered limited case of guiding structures, since they mainly analyzed slab structures with relatively wide width. Though a lot of experiments for plasmonic guiding are demonstrated in a metal slab waveguide, many of them have been performed in a simple metal slab formed on a dielectric substrate: i.e. an asymmetric metal slab [19

19. R. Charbonneau, P. Berini, E. Berolo, and E. Lisicka-Shrzek, “Experimental observation of plasmon polariton waves supported by a thin metal film of finite width,” Opt. Lett. 25(11), 844–846 (2000). [CrossRef] [PubMed]

21

21. E. Verhagen, M. Spasenović, A. Polman, and L. K. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett. 102(20), 203904 (2009). [CrossRef] [PubMed]

]. No LRSPs are supported in these asymmetric metal slabs.

One of the most unique prospects of plasmonic waveguides is their potential to concentrate light energy and its field enhancement in nanoscale regions as small as a few nanometres. This plasmonic nanofocusing [22

22. A. J. Babadjanyan, N. L. Margaryan, and Kh. V. Nerkararyan, “Superfocusing of surface polaritons in the conical structure,” J. Appl. Phys. 87(8), 3785–3788 (2000). [CrossRef]

,23

23. M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93(13), 137404 (2004). [CrossRef] [PubMed]

] has been achieved using tapered metallic guiding nanostructures such as tapered metal rods [24

24. C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: a nanoconfined light source,” Nano Lett. 7(9), 2784–2788 (2007). [CrossRef] [PubMed]

,25

25. F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, “Nanoscale chemical mapping using three-dimensional adiabatic compression of surface plasmon polaritons,” Nat. Nanotechnol. 5(1), 67–72 (2010). [CrossRef] [PubMed]

], sharp metal wedges [26

26. M. Durach, A. Rusina, M. I. Stockman, and K. Nelson, “Toward full spatiotemporal control on the nanoscale,” Nano Lett. 7(10), 3145–3149 (2007). [CrossRef] [PubMed]

], tapered metal gaps [27

27. H. Choi, D. F. P. Pile, S. Nam, G. Bartal, and X. Zhang, “Compressing surface plasmons for nano-scale optical focusing,” Opt. Express 17(9), 7519–7524 (2009). [CrossRef] [PubMed]

] and lateral tapered metal films on a dielectric [28

28. E. Verhagen, L. Kuipers, and A. Polman, “Enhanced nonlinear optical effects with a tapered plasmonic waveguide,” Nano Lett. 7(2), 334–337 (2007). [CrossRef] [PubMed]

,29

29. E. Verhagen, A. Polman, and L. K. Kuipers, “Nanofocusing in laterally tapered plasmonic waveguides,” Opt. Express 16(1), 45–57 (2008). [CrossRef] [PubMed]

]. Plasmon nanofocusing can typically occur in an adiabatic tapered waveguide with a SPP mode that shows increasing wavenumber to infinity as the thickness and/or width decreases. In order to achieve nanoguiding or nanofocusing, it is needed that the selective excitations of appropriate mode in a symmetric slab waveguide.

In this paper, we propose mutual mode control of SRSP- and LRSP-like modes propagating in a metal slab waveguide. Selective mode excitation by two phase controlled beams and a mode converter for LSRP/SRSP is demonstrated experimentally and theoretically.

2. Propagation mode in symmetric metal slab waveguide

2.1 Symmetric metal film

Since some propagation modes in a metal slab are similar to those of a metal film, we briefly show basic results of a metal film. The structures of a metal film and a metal slab are shown in Fig. 1
Fig. 1 The cross sectional view of (a) a metal film (a metal slab with infinite width) and (b) a metal slab.
. The Cartesian coordinate axes used for the analysis are also shown, and propagation takes place along the z-axis, which is upward out of the page. The metal film and slab are said to by symmetric and asymmetric when ε1 = ε3 and otherwise, respectively [9

9. P. Berini, “Long-range surface plasmon polaritons,” Adv. in Opt. and Photon. 1(3), 484–588 (2009). [CrossRef]

]. In this study, only the symmetric case is studied: the structure consists of a metal (silver) slab of thickness h and width w surrounded by a dielectric (SiO2).

Effective refractive index β/k0 of a lossless silver film is shown in Fig. 2
Fig. 2 Propagation modes in the lossless silver film waveguide (the slab with infinite width): Effective index versus the normalized film thickness. The relative permittivity of the clad and core are 2.13 (n = 1.46) and −19 at λ0 = 635nm, respectively.
with respect to normalized film thickness h0 at the vacuum wavelength of λ0 = 635nm, where β is wavenumber of SPP mode along z-axis and k0 = 2π/λ0 is the vacuum wavenumber. A metal film waveguide supports only TM (Transverse Magnetic field) mode as a propagation mode of SPP. For relatively thick metal film (h0 > 0.2), SPPs at two metal-dielectric interface propagates separately. As the thickness decreases, SPPs at the interface couple to form even and odd coupled modes: symmetric (s) and antisymmetric (a) mode [9

9. P. Berini, “Long-range surface plasmon polaritons,” Adv. in Opt. and Photon. 1(3), 484–588 (2009). [CrossRef]

]. In this paper, we classify propagation mode by the symmetry of Ey field component of the TM mode, i.e. the Ey is symmetric or antisymmetric along the y-axis (normal to the interface).

The effective index of the upper branch increases to infinity while that of the lower branch asymptotically approaches the refractive index of SiO2 (n = 1.46). The coupled mode of the lower branch (s) is LRSP which has weak field confinement with long propagation length even in lossy metals. The coupled mode of the upper branch (a) is SRSP which has strong field confinement with short propagation length. Such opposite properties of the coupled modes are useful for manipulating optical beams for opposite demands from long-range propagation to strong field confinement to form extremely narrow optical beams.

2.2 Symmetric metal slab

The symmetric metal slab considered here is shown in Fig. 1(b). The propagation modes supported by the structure are obtained by Finite Element Method (FEM). Since mode characteristics of metal slabs as a function of h and w are complicated, we focus on very thin symmetric metal slab (h0 << 1) here. Unlike metal films (metal slabs with infinite width), pure TM modes are not supported by metal slabs, but hybrid modes are supported: all six field components are present for all modes. Neither LRSP nor SRSP mode is supported in the slab. Hence, identifying the modes that are supported by a symmetric metal slab, the mode nomenclature as [symmetric or antisymmetric of Ey in horizontal x-axis] [symmetric or antisymmetric of Ey in vertical y-axis] (order number in y-axis) is used according to Berini [9

9. P. Berini, “Long-range surface plasmon polaritons,” Adv. in Opt. and Photon. 1(3), 484–588 (2009). [CrossRef]

].

The results for the lossy silver slab with h = 30 nm at λ0 = 635 nm are shown in Fig. 3
Fig. 3 Propagation modes in the lossy silver slab waveguide with h = 30nm for λ0 = 635nm: (a) Real and (b) imaginary part of the effective index versus normalized slab width. ss0(blue solid line), as0 (light blue solid line), sa0(red solid line), aa0 (green solid line), sa1 (orange dashed line), aa1(green dashed line). s (LRSP) and a (SRSP) for infinite width waveguide are also plotted for comparison as dash-dotted lines.
. Note that the symmetry of the Ey field component along the x-axis is fixed to the symmetric mode in this study, since antisymmetric modes in x-axis are nearly impossible to excite in practical cases. Furthermore, although the first mode for ss0 and the first and second modes for sa (sa0 and sa1) are presented here, the existence of higher-order modes that have a number of field extrema along the x-axis has been observed for the present structure. Leaky modes are known to exist in metal slab structures, and although they have not been searched for in the present study, their existence is anticipated.

For relatively wide metal slabs (w0 > 1), as the width increases, ss0 and sa1 modes asymptotically approach the value of the effective index of LRSP (s) and SRSP (a) mode supported by a metal film with h = 30 nm (the values are presented as dash-dotted lines in Fig. 3). Their field distribution for w = 5μm are shown in Fig. 4(a)
Fig. 4 The distributions of electric field of propagation modes shown in Fig. 3: Ey of (a) ss0 (LRSP-like mode) at w = 5μm, (b) sa1 at w = 5μm, (c) ss0 at w = 200nm, (d) sa0 (SRSP-like mode) at w = 200nm, and (e) Ex, (f) Ey, (g) Ez of sa0 at w = 30nm. Note that each scale bar is normalized by the field maximum. The maxima are not equal each other.
and 4(b). These modes correspond to vertically coupled SPP mode bound in x-z interfaces. On the other hand, as the width increases, the effective indices of sa0 and aa0 modes asymptotically approach β/k0~2.4. This is the similar value of a SPP mode supported by an isolated corner (the side edge) in a semi-infinite metal film. Thus, these modes correspond to horizontally coupled SPP mode bound in y-z interfaces and edges [18

18. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B 61(15), 10484–10503 (2000). [CrossRef]

].

Metal slabs with small width (w0 < 1), however, strong mode coupling between left and right edges occurs: it leads to unique propagation modes including super long-range guiding as well as nanolocalized guiding. Note that a metal slab is sometimes called a metal stripe in such region. As the width of the slab decreases, ss0 and sa0 modes begin to change in character while sa1 mode has a cutoff level at w0~0.5.

As shown in Fig. 3(b), ss0 mode for w0 < 0.5 presents the extremely lower loss factor than that of a metal film (s) and have the expanded fields into a dielectric layer as clearly shown in Fig. 4(c). Thus, ss0 mode is LRSP-like mode and is so to speak “super-LRSP mode”. In contrast, although sa0 mode show relatively strong dissipation and significantly smaller propagation length rather than the ss0 mode, the effective index increases to infinity for w0 < 0.1; it presents strong subwavelength localization in two dimensions (the x-y plane) as shown in Fig. 4(d). Thus, sa0 mode is SRSP-like mode. From the field distribution shown in Fig. 4 (e), (f) and (g), the property of the sa0 mode is very similar to that of a metal rod [1

1. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22(7), 475–477 (1997). [CrossRef] [PubMed]

]. Also, this mode can be understood as the reverse case for a metal slot with small gap: the SPP mode coupled wedge plasmons along the four edges. Note that these two modes supported by the metal slabs with small width do not have a cutoff width; thus their specific characteristics can further be highlighted by decreasing the slab width. Although it is reported that nonlocal effect diminishes the field enhancement at the apex in a smooth metal surface, it also increases the robustness in a real rough metal surface, resulting in improving the performance of nanofocusing [30

30. A. Wiener, A. I. Fernández-Domínguez, A. P. Horsfield, J. B. Pendry, and S. A. Maier, “Nonlocal effects in the nanofocusing performance of plasmonic tips,” Nano Lett. 12(6), 3308–3314 (2012). [CrossRef] [PubMed]

].

The ss0 (LRSP-like) mode can be used for optical signal transmission with long distances, and it has the superiority to standard LRSPs in a metal film or a wider metal slab waveguide for long-range guiding. The sa0 (SRSP-like) mode has the potential for strong subwavelength localization and can be considered as one of the candidates for plasmon nanoguiding. The existence of the LRSP-like and the SRSP-like modes as well as their interesting characteristics makes a metal nano-slab waveguide attractive for applications requiring extremely long-range guiding or nanoguiding.

3. Selective mode excitation

3.1 Selective mode excitation by two incident beams

In order to control propagation modes in a metal slab waveguide, we perform numerical simulation of selective mode excitation by finite-difference time domain (FDTD) method. The waveguide consists of a lateral tapered lossless silver slab of 30 nm thickness with taper angle 17.8◦, surrounded by SiO2, and the fields of guiding SPPs are calculated. Firstly, a conventional end-fire method using single beam irradiated from the single side of the slab is used to excite SPP. The simulations show many modes are excited by the single beam and complicated interference patterns are observed (not shown). Instead, by using two incident beams with phase difference between the beams, the symmetry of excited modes can be controlled selectively by the symmetry of incident electric field [10

10. K. Yamamoto, K. Kurihara, J. Takahara, and A. Otomo, “Effective excitation of superfocusing surface plasmons using phase controlled waveguide modes,” Mater. Res. Soc. Symp. Proc. 1182–EE13–05, 55 (2009).

,11

11. M. Miyata and J. Takahara, “Excitation control of long-range surface plasmons by two incident beams,” Opt. Express 20(9), 9493–9500 (2012). [CrossRef] [PubMed]

].

Figure 5
Fig. 5 Simulated results of electric field intensity (|E|2 on the Ag surface) in a tapered lossless silver slab waveguide with h = 30nm: (a) selective excitation of ss0 mode in both sides with phase difference of 0 and (b) selective excitation of sa0 mode in both sides with phase difference of π. Note that each scale bar is normalized by the field maximum. The maxima are not equal each other.
shows the simulated results of the ss0 (LRSP-like) and the sa0 (SRSP-like) modes propagating in a lateral tapered waveguide. The each SPP mode is excited selectively by using two indent beams (λ0 = 635 nm) illuminated at a metal edge. For the case of ss0 mode, the optical energy can reach the tip without a cutoff, but the beam at the tip shows a finite width and the remarkable field enhancement cannot be observed. On the other hand, sa0 mode propagates along the slab edge and is focused at the tip with high energy; this phenomenon can be considered as plasmon nanofocusing in a metal nano-slab waveguide. Strong field confinement in the tip is observed as shown in the field profile of Fig. 5. This result can be understood by the extremely large effective index of sa0 mode in a small slab width [Fig. 3(a)], and also presents one of the unique functions of a metal slab waveguide.

3.2 Sample and measurement

3.3 Experimental results

The measured optical images for the Δϕ = 0 and Δϕ = π are shown in Fig. 7
Fig. 7 Observed images of the selective excitation method. The experimentally observed scattering from the tip (shown by the dashed circle) for the case of (a) Δϕ = 0 and (b) Δϕ = π. Arrows indicate polarization direction of the incident beams.
. A clear difference is noticeable between Δϕ = 0 and Δϕ = π in the experiments. For the Δϕ = 0, the strong scattering from the tip can be observed [Fig. 7(a)]. In contrast, for the Δϕ = π, the scattering from the tip is very weak [Fig. 7(b)].

The dependence of the output signals on the phase difference can be explained through a variation in the excitation efficiency of SPP modes. In the case of Δϕ = 0, the excitation efficiency of ss0 (LRSP-like) mode is significantly higher than that of sa0 (SRSP-like) mode, because of the field symmetry formed by the two incident beams. Because the length between the edge and the tip (21 μm) is significantly longer than the propagation length of the sa0 mode (propagation length~1μm), only ss0 mode (propagation length~42μm) can reach the tip and be observed. This is confirmed by numerical simulations. Therefore, only the selectively excited ss0 mode reaches the tip [Fig. 5(a)], without loss, and is observed as a strong output signal as shown in Fig. 7(a).

On the other hand, for the Δϕ = π, only sa0 mode show high excitation efficiency by forming an antisymmetric field and they cannot reach the tip and never contribute to the scattering at the tip due to the dissipation. Thus, in such actual lossy case, it is difficult to directly observe nanofocusing of the sa0 mode as shown in the lossless simulation of Fig. 5(b).

4. Mutual mode conversion

As shown in Fig. 8(a), the symmetry of electric field Ey clearly shows the mode conversion from symmetric mode (LRSP) to antisymmetric mode (SRSP) by the phase shift of π. The mode conversion from SRSP to LRSP also can be done as shown in Fig. 8(b), where antisymmetric mode (SRSP) converts to symmetric mode (LRSP). Note that scattering caused by the phase shifter slightly disturbs the electric fields of converted modes. Graded index or tapered structure of the phase shifter expects to reduce the disturbance. Further theoretical investigations are needed to optimize the structure as well as experimental demonstrations in future.

5. Conclusion

We have proposed theoretically selective mode excitation and mutual mode conversion of SRSP-like and LRSP-like mode supported in a symmetric metal slab. We have demonstrated experimentally that the excitation of these modes can be controlled by the symmetry of two incident beams. We have shown numerically that the mode conversion between SRSP and LRSP can be achieved by a phase shifter. We expect that our studies will highlight NOICs based on plasmonic waveguide mediated by LRSP.

Acknowledgments

This work was supported by a Grant-in-Aid for Scientific Research B (25286007) from the Ministry of Education, Culture, Sports, Science and Technology, Japan (MEXT). A part of this work was supported by the Nanotechnology Platform Project (Nanotechnology Open Facilities in Osaka University) of MEXT (Nos. F-12-OS-0003, S-12-OS-0012). The work of the second author was supported by a Grant-in-Aid for the Japan Society for the Promotion of Science (JSPS) Fellows.

References and links

1.

J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22(7), 475–477 (1997). [CrossRef] [PubMed]

2.

J. Takahara and T. Kobayash, “Low-dimensional optical waves and nano-optical circuits,” Optics & Photonics News 15(10), 54–59 (2004). [CrossRef]

3.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010). [CrossRef]

4.

S. I. Bozhevolnyi, Plasmonic Nanoguides and Circuits (Pan Stanford Publishing, 2009).

5.

F. Kusunoki, T. Yotsuya, J. Takahara, and T. Kobayashi, “Propagation properties of guided waves in index-guided two-dimensional optical waveguides,” Appl. Phys. Lett. 86(21), 211101 (2005). [CrossRef]

6.

J. Takahara and F. Kusunoki, “Guiding and nanofocusing of two-dimensional optical beam for nanooptical integrated circuits,” IEICE Trans. Electron. E90–C(1), 87–94 (2007). [CrossRef]

7.

M. Fukui, V. So, and R. Normandin, “Lifetimes of surface plasmons in thin silver films,” Phys. Status Solidi 91(1), 61–64 (1979). [CrossRef]

8.

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47(26), 1927–1930 (1981). [CrossRef]

9.

P. Berini, “Long-range surface plasmon polaritons,” Adv. in Opt. and Photon. 1(3), 484–588 (2009). [CrossRef]

10.

K. Yamamoto, K. Kurihara, J. Takahara, and A. Otomo, “Effective excitation of superfocusing surface plasmons using phase controlled waveguide modes,” Mater. Res. Soc. Symp. Proc. 1182–EE13–05, 55 (2009).

11.

M. Miyata and J. Takahara, “Excitation control of long-range surface plasmons by two incident beams,” Opt. Express 20(9), 9493–9500 (2012). [CrossRef] [PubMed]

12.

R. Zia, A. Chandran, and M. L. Brongersma, “Dielectric waveguide model for guided surface polaritons,” Opt. Lett. 30(12), 1473–1475 (2005). [CrossRef] [PubMed]

13.

P. Berini and I. De Leon, “Surface plasmon–polariton amplifiers and lasers,” Nat. Photonics 6(1), 16–24 (2011). [CrossRef]

14.

M. L. Brongersma and V. M. Shalaev, “Applied physics. The case for plasmonics,” Science 328(5977), 440–441 (2010). [CrossRef] [PubMed]

15.

M. Miyata and J. Takahara, “Colloidal quantum dot-based plasmon emitters with planar integration and long-range guiding,” Opt. Express 21(7), 7882–7890 (2013). [CrossRef] [PubMed]

16.

P. Berini, “Plasmon polariton modes guided by a metal film of finite width,” Opt. Lett. 24(15), 1011–1013 (1999). [CrossRef] [PubMed]

17.

P. Berini, “Plasmon-polariton modes guided by a metal film of finite width bounded by different dielectrics,” Opt. Express 7(10), 329–335 (2000). [CrossRef] [PubMed]

18.

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B 61(15), 10484–10503 (2000). [CrossRef]

19.

R. Charbonneau, P. Berini, E. Berolo, and E. Lisicka-Shrzek, “Experimental observation of plasmon polariton waves supported by a thin metal film of finite width,” Opt. Lett. 25(11), 844–846 (2000). [CrossRef] [PubMed]

20.

J. C. Weeber, J. R. Krenn, A. Dereux, B. Lamprecht, Y. Lacroute, and J. P. Goudonnet, “Near-field observation of surface plasmon polariton propagation on thin metal stripes,” Phys. Rev. B 64(4), 045411 (2001). [CrossRef]

21.

E. Verhagen, M. Spasenović, A. Polman, and L. K. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett. 102(20), 203904 (2009). [CrossRef] [PubMed]

22.

A. J. Babadjanyan, N. L. Margaryan, and Kh. V. Nerkararyan, “Superfocusing of surface polaritons in the conical structure,” J. Appl. Phys. 87(8), 3785–3788 (2000). [CrossRef]

23.

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93(13), 137404 (2004). [CrossRef] [PubMed]

24.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: a nanoconfined light source,” Nano Lett. 7(9), 2784–2788 (2007). [CrossRef] [PubMed]

25.

F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, “Nanoscale chemical mapping using three-dimensional adiabatic compression of surface plasmon polaritons,” Nat. Nanotechnol. 5(1), 67–72 (2010). [CrossRef] [PubMed]

26.

M. Durach, A. Rusina, M. I. Stockman, and K. Nelson, “Toward full spatiotemporal control on the nanoscale,” Nano Lett. 7(10), 3145–3149 (2007). [CrossRef] [PubMed]

27.

H. Choi, D. F. P. Pile, S. Nam, G. Bartal, and X. Zhang, “Compressing surface plasmons for nano-scale optical focusing,” Opt. Express 17(9), 7519–7524 (2009). [CrossRef] [PubMed]

28.

E. Verhagen, L. Kuipers, and A. Polman, “Enhanced nonlinear optical effects with a tapered plasmonic waveguide,” Nano Lett. 7(2), 334–337 (2007). [CrossRef] [PubMed]

29.

E. Verhagen, A. Polman, and L. K. Kuipers, “Nanofocusing in laterally tapered plasmonic waveguides,” Opt. Express 16(1), 45–57 (2008). [CrossRef] [PubMed]

30.

A. Wiener, A. I. Fernández-Domínguez, A. P. Horsfield, J. B. Pendry, and S. A. Maier, “Nonlocal effects in the nanofocusing performance of plasmonic tips,” Nano Lett. 12(6), 3308–3314 (2012). [CrossRef] [PubMed]

OCIS Codes
(230.7370) Optical devices : Waveguides
(240.6680) Optics at surfaces : Surface plasmons
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Plasmonics

History
Original Manuscript: July 31, 2013
Revised Manuscript: September 27, 2013
Manuscript Accepted: September 29, 2013
Published: November 4, 2013

Virtual Issues
Surface Plasmon Photonics (2013) Optics Express

Citation
Junichi Takahara and Masashi Miyata, "Mutual mode control of short- and long-range surface plasmons," Opt. Express 21, 27402-27410 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-22-27402


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References

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  25. F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, “Nanoscale chemical mapping using three-dimensional adiabatic compression of surface plasmon polaritons,” Nat. Nanotechnol.5(1), 67–72 (2010). [CrossRef] [PubMed]
  26. M. Durach, A. Rusina, M. I. Stockman, and K. Nelson, “Toward full spatiotemporal control on the nanoscale,” Nano Lett.7(10), 3145–3149 (2007). [CrossRef] [PubMed]
  27. H. Choi, D. F. P. Pile, S. Nam, G. Bartal, and X. Zhang, “Compressing surface plasmons for nano-scale optical focusing,” Opt. Express17(9), 7519–7524 (2009). [CrossRef] [PubMed]
  28. E. Verhagen, L. Kuipers, and A. Polman, “Enhanced nonlinear optical effects with a tapered plasmonic waveguide,” Nano Lett.7(2), 334–337 (2007). [CrossRef] [PubMed]
  29. E. Verhagen, A. Polman, and L. K. Kuipers, “Nanofocusing in laterally tapered plasmonic waveguides,” Opt. Express16(1), 45–57 (2008). [CrossRef] [PubMed]
  30. A. Wiener, A. I. Fernández-Domínguez, A. P. Horsfield, J. B. Pendry, and S. A. Maier, “Nonlocal effects in the nanofocusing performance of plasmonic tips,” Nano Lett.12(6), 3308–3314 (2012). [CrossRef] [PubMed]

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