Abstract

We propose a novel waveguide structure using a hetero-metal film which is composed of two metals of different plasma frequencies. In the proposed waveguide, a long-range surface plasmon-polariton (LR-SPP) mode in the central metal film of a higher plasma frequency are horizontally confined since no propagation mode is allowed in the outer films of a lower plasma frequency for a certain frequency range which is dubbed a plasmonic mode-gap (PMG). The propagation characteristics of the proposed PMG waveguide are numerically analyzed. The proposed waveguide shows tight horizontal confinement close to the diffraction limit and notable suppression of radiation loss in bendings due to the PMG effect. It seems that the PMG guiding can improve integration densities of optical devices based on the LR-SPPs without exacerbating their propagation losses.

© 2010 OSA

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  8. 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).
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    [CrossRef]
  22. A. Hosseini, A. Nieuwoudt, and Y. Massoud, “Optimizing dielectric strips over a metallic substrate for subwavelength light confinement,” IEEE Photon. Technol. Lett. 19(7), 522–524 (2007).
    [CrossRef]
  23. S. Lee, S. Kim, and H. Lim, “Improved bending loss characteristics of asymmetric surface plasmonic waveguides for flexible optical wiring,” Opt. Express 17(22), 19435–19443 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-22-19435 .
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2009 (1)

S. Lee, S. Kim, and H. Lim, “Improved bending loss characteristics of asymmetric surface plasmonic waveguides for flexible optical wiring,” Opt. Express 17(22), 19435–19443 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-22-19435 .
[CrossRef] [PubMed]

2007 (1)

A. Hosseini, A. Nieuwoudt, and Y. Massoud, “Optimizing dielectric strips over a metallic substrate for subwavelength light confinement,” IEEE Photon. Technol. Lett. 19(7), 522–524 (2007).
[CrossRef]

2006 (2)

F. Kusunoki, T. Yotsuya, and J. Takahara, “Confinement and guiding of two-dimensional optical waves by low-refractive-index cores,” Opt. Express 14(12), 5651–5656 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-12-5651 .
[CrossRef] [PubMed]

P. Berini and J. Lu, “Curved long-range surface plasmon-polariton waveguides,” Opt. Express 14(6), 2365–2371 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-6-2365 .
[CrossRef] [PubMed]

2005 (4)

R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13(3), 977–984 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-3-977 .
[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]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model,” Phys. Rev. B 72(7), 075405 (2005).
[CrossRef]

2004 (3)

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

B. Wang and G. P. Wang, “Metal hterowaveguides for nanometric focusing of light,” Appl. Phys. Lett. 85(16), 3599–3601 (2004).
[CrossRef]

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

2003 (3)

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

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]

R. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, “Polymer-based surface-plasmon polariton stripe waveguides at telecommunication wavelengths,” Appl. Phys. Lett. 82(5), 668–670 (2003).
[CrossRef]

2002 (1)

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

1998 (1)

S. J. Al-Bader and H. A. Jamid, “Perfectly matched layer absorbing boundary conditions for the method of lines modeling scheme,” IEEE Microw. Guid. Wave Lett. 8(11), 357–359 (1998).
[CrossRef]

1996 (1)

S. Kim and A. Gopinath, “Vector analysis of optical dielectric waveguide bends using finite-difference method,” J. Lightwave Technol. 14(9), 2085–2092 (1996).
[CrossRef]

1995 (1)

R. Mittra and U. Pekel, “A new look at the perfectly matched layer (PML) concept for the reflectionless absorption of electromagnetic waves,” IEEE Microw. Guid Wave Lett. 5(3), 84–86 (1995).
[CrossRef]

1994 (1)

G. L. Xu, W. P. Huang, M. S. Stern, and S. K. Chaudhuri, “Full-vectorial mode calculations by finite difference method,” IEE Proc., Optoelectron. 141(5), 281–286 (1994).
[CrossRef]

1986 (1)

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33(8), 5186–5201 (1986).
[CrossRef]

1969 (1)

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

Al-Bader, S. J.

S. J. Al-Bader and H. A. Jamid, “Perfectly matched layer absorbing boundary conditions for the method of lines modeling scheme,” IEEE Microw. Guid. Wave Lett. 8(11), 357–359 (1998).
[CrossRef]

Atwater, H. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model,” Phys. Rev. B 72(7), 075405 (2005).
[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 and J. Lu, “Curved long-range surface plasmon-polariton waveguides,” Opt. Express 14(6), 2365–2371 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-6-2365 .
[CrossRef] [PubMed]

R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13(3), 977–984 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-3-977 .
[CrossRef] [PubMed]

Bozhevolnyi, S. I.

R. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, “Polymer-based surface-plasmon polariton stripe waveguides at telecommunication wavelengths,” Appl. Phys. Lett. 82(5), 668–670 (2003).
[CrossRef]

Brongersma, M. L.

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

Burke, J. J.

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33(8), 5186–5201 (1986).
[CrossRef]

Catrysse, P. B.

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

Charbonneau, R.

R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13(3), 977–984 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-3-977 .
[CrossRef] [PubMed]

Chaudhuri, S. K.

G. L. Xu, W. P. Huang, M. S. Stern, and S. K. Chaudhuri, “Full-vectorial mode calculations by finite difference method,” IEE Proc., Optoelectron. 141(5), 281–286 (1994).
[CrossRef]

Dereux, A.

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

Dionne, J. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model,” Phys. Rev. B 72(7), 075405 (2005).
[CrossRef]

Ebbesen, T. W.

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]

Enkrich, C.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

Gopinath, A.

S. Kim and A. Gopinath, “Vector analysis of optical dielectric waveguide bends using finite-difference method,” J. Lightwave Technol. 14(9), 2085–2092 (1996).
[CrossRef]

Hosseini, A.

A. Hosseini, A. Nieuwoudt, and Y. Massoud, “Optimizing dielectric strips over a metallic substrate for subwavelength light confinement,” IEEE Photon. Technol. Lett. 19(7), 522–524 (2007).
[CrossRef]

Huang, W. P.

G. L. Xu, W. P. Huang, M. S. Stern, and S. K. Chaudhuri, “Full-vectorial mode calculations by finite difference method,” IEE Proc., Optoelectron. 141(5), 281–286 (1994).
[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]

Jamid, H. A.

S. J. Al-Bader and H. A. Jamid, “Perfectly matched layer absorbing boundary conditions for the method of lines modeling scheme,” IEEE Microw. Guid. Wave Lett. 8(11), 357–359 (1998).
[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.

S. Lee, S. Kim, and H. Lim, “Improved bending loss characteristics of asymmetric surface plasmonic waveguides for flexible optical wiring,” Opt. Express 17(22), 19435–19443 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-22-19435 .
[CrossRef] [PubMed]

S. Kim and A. Gopinath, “Vector analysis of optical dielectric waveguide bends using finite-difference method,” J. Lightwave Technol. 14(9), 2085–2092 (1996).
[CrossRef]

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]

Koschny, T.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

Kusunoki, F.

F. Kusunoki, T. Yotsuya, and J. Takahara, “Confinement and guiding of two-dimensional optical waves by low-refractive-index cores,” Opt. Express 14(12), 5651–5656 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-12-5651 .
[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]

Lahoud, N.

R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13(3), 977–984 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-3-977 .
[CrossRef] [PubMed]

Lee, S.

S. Lee, S. Kim, and H. Lim, “Improved bending loss characteristics of asymmetric surface plasmonic waveguides for flexible optical wiring,” Opt. Express 17(22), 19435–19443 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-22-19435 .
[CrossRef] [PubMed]

Leosson, K.

R. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, “Polymer-based surface-plasmon polariton stripe waveguides at telecommunication wavelengths,” Appl. Phys. Lett. 82(5), 668–670 (2003).
[CrossRef]

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]

Lim, H.

S. Lee, S. Kim, and H. Lim, “Improved bending loss characteristics of asymmetric surface plasmonic waveguides for flexible optical wiring,” Opt. Express 17(22), 19435–19443 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-22-19435 .
[CrossRef] [PubMed]

Linden, S.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

Lu, J.

P. Berini and J. Lu, “Curved long-range surface plasmon-polariton waveguides,” Opt. Express 14(6), 2365–2371 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-6-2365 .
[CrossRef] [PubMed]

Maradudin, A. A.

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

Massoud, Y.

A. Hosseini, A. Nieuwoudt, and Y. Massoud, “Optimizing dielectric strips over a metallic substrate for subwavelength light confinement,” IEEE Photon. Technol. Lett. 19(7), 522–524 (2007).
[CrossRef]

Mattiussi, G.

R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13(3), 977–984 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-3-977 .
[CrossRef] [PubMed]

Mittra, R.

R. Mittra and U. Pekel, “A new look at the perfectly matched layer (PML) concept for the reflectionless absorption of electromagnetic waves,” IEEE Microw. Guid Wave Lett. 5(3), 84–86 (1995).
[CrossRef]

Nieuwoudt, A.

A. Hosseini, A. Nieuwoudt, and Y. Massoud, “Optimizing dielectric strips over a metallic substrate for subwavelength light confinement,” IEEE Photon. Technol. Lett. 19(7), 522–524 (2007).
[CrossRef]

Nikolajsen, R.

R. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, “Polymer-based surface-plasmon polariton stripe waveguides at telecommunication wavelengths,” Appl. Phys. Lett. 82(5), 668–670 (2003).
[CrossRef]

Novikov, I. V.

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

Pekel, U.

R. Mittra and U. Pekel, “A new look at the perfectly matched layer (PML) concept for the reflectionless absorption of electromagnetic waves,” IEEE Microw. Guid Wave Lett. 5(3), 84–86 (1995).
[CrossRef]

Polman, A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model,” Phys. Rev. B 72(7), 075405 (2005).
[CrossRef]

Salakhutdinov, I.

R. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, “Polymer-based surface-plasmon polariton stripe waveguides at telecommunication wavelengths,” Appl. Phys. Lett. 82(5), 668–670 (2003).
[CrossRef]

Selker, M. D.

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

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]

Soukoulis, C. M.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

Stegeman, G. I.

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33(8), 5186–5201 (1986).
[CrossRef]

Stern, M. S.

G. L. Xu, W. P. Huang, M. S. Stern, and S. K. Chaudhuri, “Full-vectorial mode calculations by finite difference method,” IEE Proc., Optoelectron. 141(5), 281–286 (1994).
[CrossRef]

Sweatlock, L. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model,” Phys. Rev. B 72(7), 075405 (2005).
[CrossRef]

Takahara, J.

F. Kusunoki, T. Yotsuya, and J. Takahara, “Confinement and guiding of two-dimensional optical waves by low-refractive-index cores,” Opt. Express 14(12), 5651–5656 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-12-5651 .
[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]

Tamir, T.

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33(8), 5186–5201 (1986).
[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]

Wang, B.

B. Wang and G. P. Wang, “Metal hterowaveguides for nanometric focusing of light,” Appl. Phys. Lett. 85(16), 3599–3601 (2004).
[CrossRef]

Wang, G. P.

B. Wang and G. P. Wang, “Metal hterowaveguides for nanometric focusing of light,” Appl. Phys. Lett. 85(16), 3599–3601 (2004).
[CrossRef]

Wegener, M.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

Xu, G. L.

G. L. Xu, W. P. Huang, M. S. Stern, and S. K. Chaudhuri, “Full-vectorial mode calculations by finite difference method,” IEE Proc., Optoelectron. 141(5), 281–286 (1994).
[CrossRef]

Yotsuya, T.

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Figures (13)

Fig. 1
Fig. 1

(a) Cross-sectional view of a plasmonic mode-gap waveguide using a hetero-metal film. (b) Cross-sectional view of a metal stripe waveguide. (c) Dispersion curves for fundamental modes of infinite metal films. Blue and red curves are for films of gold and copper, respectively. The dashed and the solid curves are for the films of t = 10 nm and 20 nm, respectively. The dotted curves are dispersion curves of SPPs guided by semi-infinite metals for references.

Fig. 2
Fig. 2

(a) Effective refractive index and (b) propagation loss [dB/μm] vs. wavelength for two types of straight waveguides (W = 0.4μm).

Fig. 3
Fig. 3

Electric field (Ey ) distributions in the two types of straight waveguides of t = 20nm, W = 0.4μm. Mode-gap waveguide for (a) λ = 0.633μm and (b) λ = 0.8μm. Metal-stripe waveguide for (c) λ = 0.633μm and (d) λ = 0.8μm.

Fig. 4
Fig. 4

(a) Effective refractive index and (b) propagation loss [dB/μm] of vs. width of core metal (Au) for two types of straight waveguides (t = 20nm, λ = 0.633, 0.8, and 0.9 μm)

Fig. 5
Fig. 5

Electric field (Ey ) distributions in mode-gap waveguides of (a) W = 0.2μm and (b) W = 0.085μm. Electric field (Ey ) distributions in metal-stripe waveguides of (c) W = 0.2μm and (d) W = 0.03μm. In all the cases, the metal film thickness is t = 20nm and the excitation wavelength is λ = 0.633 μm.

Fig. 6
Fig. 6

(a) Modal sizes and (b) figures of merit of plasmonic mode-gap and metal-stripe waveguides as functions of W for λ = 0.633 μm.

Fig. 7
Fig. 7

Structures of two types of curved waveguides: (a) plasmonic mode-gap waveguide and (b) metal-strip waveguide. For analysis of the curved waveguides, a cylindrical coordinate system is used.

Fig. 8
Fig. 8

(a) Effective refractive index and (b) bending loss [dB/90°] vs. radius of curvature for two types of curved waveguides (t = 20nm, W = 0.4μm, λ = 0.633, 0.8, and 0.9μm)

Fig. 9
Fig. 9

Electric field (Ez ) distributions of two types of curved waveguides of t = 20nm, W = 0.4μm for λ = 0.633μm; Mode-gap waveguides of (a) Ropt = 1μm and (b) R = 0.5μm. Metal-stripe waveguides of (c) Ropt = 2μm and (d) R = 0.5μm.

Fig. 10
Fig. 10

(a) Effective refractive index and (b) bending loss [dB/90°] vs. radius of curvature for two types of curved waveguides of different core widths (W = 0.1, 0.2, and 0.4μm, t = 20nm, λ = 0.633μm)

Fig. 11
Fig. 11

Electric field (Ez ) distributions in two types of curved waveguides of t = 20nm, W = 0.1μm, and R = 1μm for λ = 0.633μm. (a) Mode-gap waveguide and (b) metal-stripe waveguide.

Fig. 12
Fig. 12

(a) Effective refractive index, and (b) bending loss [dB/90°] vs. radius of curvature for two types of curved waveguides of different metal thicknesses (t = 10 and 20nm, W = 0.4μm, λ = 0.633μm)

Fig. 13
Fig. 13

Electric field (Ez ) distributions in two types of curved waveguides of t = 10nm, W = 0.4μm, and R = 10μm for λ = 0.633μm; (a) Mode-gap waveguide and (b) metal-stripe waveguide.

Equations (1)

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ε m = 1 ω p 2 ω ( ω + i ω c o l ) ,

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