Abstract

We numerically investigate the propagation characteristics of guided modes in a thin metal film V-groove embedded in a dielectric medium, with a particular emphasis on long-ranging channel plasmon polaritons (LR-CPPs). The LR-CPP shows several orders of magnitude larger propagation length than the previously studied short-range channel plasmon polariton (SR-CPP). Moreover, the LR-CPP possesses a peculiar mode cutoff mechanism when surrounding dielectric media are asymmetric and this makes its propagation characteristics very sensitive to index change of the surrounding dielectric media.

© 2011 OSA

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J. Chen, G. A. Smolyakov, S. R. Brueck, and K. J. Malloy, “Surface plasmon modes of finite, planar, metal-insulator-metal plasmonic waveguides,” Opt. Express 16(19), 14902–14909 (2008).
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R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

A. Boltasseva, V. S. Volkov, R. B. Nielsen, E. Moreno, S. G. Rodrigo, and S. I. Bozhevolnyi, “Triangular metal wedges for subwavelength plasmon-polariton guiding at telecom wavelengths,” Opt. Express 16(8), 5252–5260 (2008).
[CrossRef] [PubMed]

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100(2), 023901 (2008).
[CrossRef] [PubMed]

2007

P. Berini, R. Charbonneau, S. Jette-Charbonneau, N. Lahoud, and G. Mattiussi, “Long-range surface plasmon-polaritin waveguides and devices in lithium niobate,” J. Appl. Phys. 101(11), 113114 (2007).
[CrossRef]

2006

S. Park and S. H. Song, “Polymer variable optical attenuator based on long range surface plasmon polaritons,” Electron. Lett. 42(7), 402–404 (2006).
[CrossRef]

D. K. Gramotnev and K. C. Vernon, “Adiabatic nano-focusing of plasmons by sharp metallic wedges,” Appl. Phys. B 86(1), 7–17 (2006).
[CrossRef]

E. Moreno, F. J. Garcia-Vidal, S. G. Rodrigo, L. Martin-Moreno, and S. I. Bozhevolnyi, “Channel plasmon-polaritons: modal shape, dispersion, and losses,” Opt. Lett. 31(23), 3447–3449 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

2005

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95(4), 046802 (2005).
[CrossRef] [PubMed]

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]

A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljacić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95(6), 063901 (2005).
[CrossRef] [PubMed]

2004

R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A 21(12), 2442–2446 (2004).
[CrossRef]

D. K. Gramotnev and D. F. P. Pile, “Single-mode subwavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface,” Appl. Phys. Lett. 85(26), 6323–6325 (2004).
[CrossRef]

2003

K. Tanaka and M. Tanaka, “Simulation of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82(8), 1158–1160 (2003).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

2002

1998

1991

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B Condens. Matter 44(11), 5855–5872 (1991).
[CrossRef] [PubMed]

1969

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182(2), 539–554 (1969).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Berini, P.

P. Berini, R. Charbonneau, S. Jette-Charbonneau, N. Lahoud, and G. Mattiussi, “Long-range surface plasmon-polaritin waveguides and devices in lithium niobate,” J. Appl. Phys. 101(11), 113114 (2007).
[CrossRef]

Boltasseva, A.

Bozhevolnyi, S. I.

A. Boltasseva, V. S. Volkov, R. B. Nielsen, E. Moreno, S. G. Rodrigo, and S. I. Bozhevolnyi, “Triangular metal wedges for subwavelength plasmon-polariton guiding at telecom wavelengths,” Opt. Express 16(8), 5252–5260 (2008).
[CrossRef] [PubMed]

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100(2), 023901 (2008).
[CrossRef] [PubMed]

E. Moreno, F. J. Garcia-Vidal, S. G. Rodrigo, L. Martin-Moreno, and S. I. Bozhevolnyi, “Channel plasmon-polaritons: modal shape, dispersion, and losses,” Opt. Lett. 31(23), 3447–3449 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95(4), 046802 (2005).
[CrossRef] [PubMed]

Bradberry, G. W.

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B Condens. Matter 44(11), 5855–5872 (1991).
[CrossRef] [PubMed]

Brongersma, M. L.

Brueck, S. R.

Catrysse, P. B.

Charbonneau, R.

P. Berini, R. Charbonneau, S. Jette-Charbonneau, N. Lahoud, and G. Mattiussi, “Long-range surface plasmon-polaritin waveguides and devices in lithium niobate,” J. Appl. Phys. 101(11), 113114 (2007).
[CrossRef]

Chen, J.

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Devaux, E.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95(4), 046802 (2005).
[CrossRef] [PubMed]

Dintinger, J.

Djurisic, A. B.

Ebbesen, T. W.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95(4), 046802 (2005).
[CrossRef] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Economou, E. N.

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182(2), 539–554 (1969).
[CrossRef]

Elazar, J. M.

Garcia-Vidal, F. J.

García-Vidal, F. J.

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100(2), 023901 (2008).
[CrossRef] [PubMed]

Genov, D. A.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

Gramotnev, D. K.

D. K. Gramotnev and K. C. Vernon, “Adiabatic nano-focusing of plasmons by sharp metallic wedges,” Appl. Phys. B 86(1), 7–17 (2006).
[CrossRef]

D. K. Gramotnev and D. F. P. Pile, “Single-mode subwavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface,” Appl. Phys. Lett. 85(26), 6323–6325 (2004).
[CrossRef]

Ibanescu, M.

A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljacić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95(6), 063901 (2005).
[CrossRef] [PubMed]

Jette-Charbonneau, S.

P. Berini, R. Charbonneau, S. Jette-Charbonneau, N. Lahoud, and G. Mattiussi, “Long-range surface plasmon-polaritin waveguides and devices in lithium niobate,” J. Appl. Phys. 101(11), 113114 (2007).
[CrossRef]

Joannopoulos, J. D.

A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljacić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95(6), 063901 (2005).
[CrossRef] [PubMed]

Karalis, A.

A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljacić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95(6), 063901 (2005).
[CrossRef] [PubMed]

Kim, S.

Kobayashi, T.

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]

Koshiba, M.

Kusunoki, F.

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]

Lahoud, N.

P. Berini, R. Charbonneau, S. Jette-Charbonneau, N. Lahoud, and G. Mattiussi, “Long-range surface plasmon-polaritin waveguides and devices in lithium niobate,” J. Appl. Phys. 101(11), 113114 (2007).
[CrossRef]

Laluet, J. Y.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

Lee, S.

Lidorikis, E.

A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljacić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95(6), 063901 (2005).
[CrossRef] [PubMed]

Majewski, M. L.

Malloy, K. J.

Maradudin, A. A.

I. V. Novikov and A. A. Maradudin, “Channel polaritons,” Phys. Rev. B 66(3), 035403 (2002).
[CrossRef]

Martin, O. J. F.

Martin-Moreno, L.

Martín-Moreno, L.

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100(2), 023901 (2008).
[CrossRef] [PubMed]

Mattiussi, G.

P. Berini, R. Charbonneau, S. Jette-Charbonneau, N. Lahoud, and G. Mattiussi, “Long-range surface plasmon-polaritin waveguides and devices in lithium niobate,” J. Appl. Phys. 101(11), 113114 (2007).
[CrossRef]

Moreno, E.

Nielsen, R. B.

Novikov, I. V.

I. V. Novikov and A. A. Maradudin, “Channel polaritons,” Phys. Rev. B 66(3), 035403 (2002).
[CrossRef]

Oulton, R. F.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

Park, S.

S. Park and S. H. Song, “Polymer variable optical attenuator based on long range surface plasmon polaritons,” Electron. Lett. 42(7), 402–404 (2006).
[CrossRef]

Pile, D. F. P.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

D. K. Gramotnev and D. F. P. Pile, “Single-mode subwavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface,” Appl. Phys. Lett. 85(26), 6323–6325 (2004).
[CrossRef]

Rakic, A. D.

Rodrigo, S. G.

Sambles, J. R.

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B Condens. Matter 44(11), 5855–5872 (1991).
[CrossRef] [PubMed]

Selker, M. D.

Smolyakov, G. A.

Soljacic, M.

A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljacić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95(6), 063901 (2005).
[CrossRef] [PubMed]

Song, S. H.

S. Park and S. H. Song, “Polymer variable optical attenuator based on long range surface plasmon polaritons,” Electron. Lett. 42(7), 402–404 (2006).
[CrossRef]

Sorger, V. J.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

Takahara, J.

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]

Tanaka, K.

K. Tanaka and M. Tanaka, “Simulation of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82(8), 1158–1160 (2003).
[CrossRef]

Tanaka, M.

K. Tanaka and M. Tanaka, “Simulation of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82(8), 1158–1160 (2003).
[CrossRef]

Tsuji, Y.

Vernon, K. C.

D. K. Gramotnev and K. C. Vernon, “Adiabatic nano-focusing of plasmons by sharp metallic wedges,” Appl. Phys. B 86(1), 7–17 (2006).
[CrossRef]

Volkov, V. S.

A. Boltasseva, V. S. Volkov, R. B. Nielsen, E. Moreno, S. G. Rodrigo, and S. I. Bozhevolnyi, “Triangular metal wedges for subwavelength plasmon-polariton guiding at telecom wavelengths,” Opt. Express 16(8), 5252–5260 (2008).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95(4), 046802 (2005).
[CrossRef] [PubMed]

Yang, F.

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B Condens. Matter 44(11), 5855–5872 (1991).
[CrossRef] [PubMed]

Yotsuya, T.

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]

Zhang, X.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

Zia, R.

Appl. Opt.

Appl. Phys. B

D. K. Gramotnev and K. C. Vernon, “Adiabatic nano-focusing of plasmons by sharp metallic wedges,” Appl. Phys. B 86(1), 7–17 (2006).
[CrossRef]

Appl. Phys. Lett.

D. K. Gramotnev and D. F. P. Pile, “Single-mode subwavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface,” Appl. Phys. Lett. 85(26), 6323–6325 (2004).
[CrossRef]

K. Tanaka and M. Tanaka, “Simulation of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82(8), 1158–1160 (2003).
[CrossRef]

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]

Electron. Lett.

S. Park and S. H. Song, “Polymer variable optical attenuator based on long range surface plasmon polaritons,” Electron. Lett. 42(7), 402–404 (2006).
[CrossRef]

J. Appl. Phys.

P. Berini, R. Charbonneau, S. Jette-Charbonneau, N. Lahoud, and G. Mattiussi, “Long-range surface plasmon-polaritin waveguides and devices in lithium niobate,” J. Appl. Phys. 101(11), 113114 (2007).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. A

Nat. Photonics

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

Nature

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev.

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182(2), 539–554 (1969).
[CrossRef]

Phys. Rev. B

I. V. Novikov and A. A. Maradudin, “Channel polaritons,” Phys. Rev. B 66(3), 035403 (2002).
[CrossRef]

Phys. Rev. B Condens. Matter

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B Condens. Matter 44(11), 5855–5872 (1991).
[CrossRef] [PubMed]

Phys. Rev. Lett.

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100(2), 023901 (2008).
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Figures (8)

Fig. 1
Fig. 1

(a) Geometry of thin metal film V-groove waveguide. Electric field profiles, Ex for (b) Symmetrically-coupled LR-SPPs, (c) Symmetrically-coupled SR-SPPs, (d) Antisymmetrically-coupled LR-SPPs, and (e) Antisymmetrically-coupled SR-SPPs in one-dimensional dielectric/metal/dielectric/metal/dielectric (D/M/D/M/D) structure. Also, (f) and (g) shows the complex effective index as functions of gap distance for (b) and (c) cases, respectively: t = 10nm, n1 = n2 = 2.38, and λ = 1.55μm.

Fig. 2
Fig. 2

(a) Effective index and (b) propagation length with metal thickness for LR-CPP and SR-CPP modes for various metal thickness. Dominant electric field profiles, Ex for (c) LR-CPP with t = 10nm, (d) SR-CPP with t = 10nm, (e) LR-CPP with t = 100nm, and (f) SR-CPP with t = 100nm. (h = 4μm, θ = 30°, λ = 1.55μm, n1 = n2 = 2.38in all calculations.)

Fig. 3
Fig. 3

Effective index and propagation length for LR-CPP as functions of (a) groove angle (h = 5μm, λ = 1.55μm), (b) groove depth (θ = 30°, λ = 1.55μm), and (c) wavelength (h = 5μm, θ = 30°). Dominant electric field profiles, Ex for LR-CPP with different compositions: (d) θ = 10°, h = 5μm, λ = 1.55μm, (e) θ = 30°, h = 5μm, λ = 1.55μm, (f) θ = 60°, h = 5μm, λ = 1.55μm, (g) θ = 30°, h = 8μm, λ = 1.55μm, (h) θ = 30°, h = 5μm, λ = 0.729μm. (t = 10nm, n1 = n2 = 2.38 in all calculations.)

Fig. 4
Fig. 4

Dispersion curves for LR-CPP, SR-CPP, and WPP modes with (a) t = 10nm and (b) t = 20nm in a uniform medium of n1 = n2 = 2.38. The dashed line represents the light line of n = 2.38. (c) The propagation length of the modes for t = 10nm. (θ = 30°, h = 5μm in all calculations.)

Fig. 5
Fig. 5

Dispersion curves for two CPP modes with various index asymmetries; (a) LR-CPP and (b) SR-CPP with n1 >n2 = 2.38, (c) LR-CPP and (d) SR-CPP with n2 >n1 = 2.38. The dashed line represents the light line of n = 2.38. The number in each legend denotes the index in the higher-index region. Dispersion curves for symmetric environment are also plotted for reference. (t = 10nm, θ = 30°, h = 5μm in all calculations.)

Fig. 6
Fig. 6

Dependence of complex effective indices on gap distance in two coupled metal films with different core indices, n1 : (a) real and (b) imaginary part of effective index for symmetrically-coupled LR-SPP, (c) real (d) imaginary part of effective index for symmetrically-coupled SR-SPP. The insets show corresponding mode shapes. The operating wavelengths are chosen close to the cutoff wavelengths of the LR-CPP and the SR-CPP: λ = 1.55μm in (a) and (b), and λ = 11.8 μm in (c) and (d). (t = 10nm, and n2 = 2.38 in all calculations.)

Fig. 7
Fig. 7

Dispersion curves for the WPP modes with index asymmetries of (a) n1 >n2 = 2.38 and (b) n2 >n1 = 2.38. (t = 10nm, θ = 30°, h = 5μm) The dashed line represents the light line of n = 2.38. The number in each legend denotes the index in the higher-index region. Dispersion curves for symmetric environment are also plotted for reference. (c) Dominant electric field profiles, Ex for the WPP of n1 = 2.39, n2 = 2.38, t = 10nm θ = 30°, h = 5μm, λ = 14μm (0.089 eV).

Fig. 8
Fig. 8

Propagation characteristics of LR-CPP in asymmetric environment. (a) Effective index and (b) propagation length for LR-CPP as functions of index asymmetry. Dominant electric field profiles, Ex for LR-CPP with different index compositions: (c) n1 = 2.38, n2 = 2.38, (d) n1 = 2.384, n2 = 2.38, (e) n1 = 2.385, n2 = 2.38, (f) n1 = 2.38, n2 = 2.392. Because of even symmetry, in x direction, only the half of the mode profile is plotted. (t = 10nm, h = 5μm, θ = 30°, λ = 1.55μm and calculation domain is 15μm x 60μm in all calculations.)

Equations (2)

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A m = W m max { W ( r ) } = 1 max { W ( r ) } W ( r ) d 2 r ,
W ( r ) = 1 2 ( d ( ε ( r ) w ) d w | E ( r ) | 2 + μ 0 | H ( r ) | 2 ) .

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