Abstract

The numerical analysis of finite planar metal-insulator-metal waveguide structures using the transfer-matrix formalism reveals both bound and leaky surface plasmon (SP) modes. The dispersion relations, propagation lengths and confinement factors of these SP modes are presented. The highest energy SP mode consists of non-radiative (bound) and radiative (leaky) portions separated by a spectral gap. The leaky regime is further divided into antenna and reactive mode regions. The antenna mode may be used for both free-space coupling and beam steering devices.

© 2008 Optical Society of America

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  1. T. Goto, Y. Katagiri, H. Fukuda, H. Shinojima, Y. Nakano, I. Kobayashi, and Y. Mitsuoka, "Propagation loss measurement for surface plasmon-polariton modes at metal waveguides on semiconductor substrates," Appl. Phys. Lett. 84, 852-854 (2004).
    [CrossRef]
  2. R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, "Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons," Opt. Express 13, 977-984 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-3-977.
    [CrossRef] [PubMed]
  3. J. A. Dionne, L. A. Sweatlock, and H. A. Atwater, "Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization," Phys. Rev. B 73, 035407 (2006).
    [CrossRef]
  4. 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, 2442-2446 (2004).
    [CrossRef]
  5. P. Tournois and V. Laude, ??????Negative group velocities in metal-film optical waveguides,?????? Opt. Commun. 137, 41-45 (1997).
    [CrossRef]
  6. Y. Wang, ??????Wavelength selection with coupled surface plasmon waves,?????? Appl. Phys. Lett. 82, 4385-4387 (2003).
    [CrossRef]
  7. H. Shin, M. F. Yanik, S. Fan, R. Zia, and M. L. Brongersma, ??????Omnidirectional resonance in a metal-dielectric-metal geometry,?????? Appl. Phys. Lett. 84, 4421-4423 (2004).
    [CrossRef]
  8. J. S. Q. Liu and M. L. Brongersma, "Omnidirectional light emission via surface plasmon polaritons," Appl. Phys. Lett.  90, 091116 (2007).
    [CrossRef]
  9. H. T. Miyazaki and Y. Kurokawa, "Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity," Phys. Rev. Lett. 96,097401(2006).
    [CrossRef] [PubMed]
  10. Y. Kurokawa and H. T. Miyazaki, "Metal-insulator-metal plasmon nanocavities: Analysis of optical properties," Phys. Rev. B 75, 035411 (2007).
    [CrossRef]
  11. G. Veronis and S. Fan, "Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides," Appl. Phys. Lett. 87, 131102 (2005).
    [CrossRef]
  12. F. Villa, T. Lopez-Rios, and L. E. Regalado, "Electromagnetic modes in metal-insulator-metal structures," Phys. Rev. B 63, 165103 (2001).
    [CrossRef]
  13. E. N. Economou, ??????Surface plasmons in thin films,?????? Phys. Rev. 182, 539-554 (1969).
    [CrossRef]
  14. M. A. Gilmore and B. L. Johnson, J. Appl. Phys. 93, 4497 (2003).
    [CrossRef]
  15. 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, 075405 (2005).
    [CrossRef]
  16. J. Chilwell and I. Hodgkinson, "Thin-films field-transfer matrix theory of planar multilayer waveguides and reflection from prism-loaded waveguides," J. Opt. Soc. Am. A 1, 742-753 (1984).
    [CrossRef]
  17. J. J. Burke and G. I. Stegeman, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 33, 5186-5201 (1986).
    [CrossRef]
  18. A. D. Raki??, A. B. Djuriši??, J. M. Elazar, and M. L. Majewski, "Optical properties of metallic films for vertical-cavity optoelectronic devices," Appl. Opt. 37, 5271-5283 (1998).
    [CrossRef]
  19. G. W. Hanson and A. B. Yakovlev, "Investigation of mode interaction on planar dielectric waveguides with loss and gain," Radio Sci. 34, 1349-1359 (1999).
    [CrossRef]
  20. P. Berini, ??????Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of asymmetric structures,?????? Phys. Rev. B 63, 125417 (2001).
    [CrossRef]
  21. Y. D. Lin and J. W. Sheen, "Mode distinction and radiation-efficiency analysis of planar leaky-wave line source," IEEE Trans. Microwave Theory Tech. 45, 1672-1680 (1997).
    [CrossRef]

2007

J. S. Q. Liu and M. L. Brongersma, "Omnidirectional light emission via surface plasmon polaritons," Appl. Phys. Lett.  90, 091116 (2007).
[CrossRef]

Y. Kurokawa and H. T. Miyazaki, "Metal-insulator-metal plasmon nanocavities: Analysis of optical properties," Phys. Rev. B 75, 035411 (2007).
[CrossRef]

2006

H. T. Miyazaki and Y. Kurokawa, "Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity," Phys. Rev. Lett. 96,097401(2006).
[CrossRef] [PubMed]

J. A. Dionne, L. A. Sweatlock, and H. A. Atwater, "Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization," Phys. Rev. B 73, 035407 (2006).
[CrossRef]

2005

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

G. Veronis and S. Fan, "Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides," Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

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, 075405 (2005).
[CrossRef]

2004

T. Goto, Y. Katagiri, H. Fukuda, H. Shinojima, Y. Nakano, I. Kobayashi, and Y. Mitsuoka, "Propagation loss measurement for surface plasmon-polariton modes at metal waveguides on semiconductor substrates," Appl. Phys. Lett. 84, 852-854 (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. A 21, 2442-2446 (2004).
[CrossRef]

H. Shin, M. F. Yanik, S. Fan, R. Zia, and M. L. Brongersma, ??????Omnidirectional resonance in a metal-dielectric-metal geometry,?????? Appl. Phys. Lett. 84, 4421-4423 (2004).
[CrossRef]

2003

Y. Wang, ??????Wavelength selection with coupled surface plasmon waves,?????? Appl. Phys. Lett. 82, 4385-4387 (2003).
[CrossRef]

M. A. Gilmore and B. L. Johnson, J. Appl. Phys. 93, 4497 (2003).
[CrossRef]

2001

F. Villa, T. Lopez-Rios, and L. E. Regalado, "Electromagnetic modes in metal-insulator-metal structures," Phys. Rev. B 63, 165103 (2001).
[CrossRef]

P. Berini, ??????Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of asymmetric structures,?????? Phys. Rev. B 63, 125417 (2001).
[CrossRef]

1999

G. W. Hanson and A. B. Yakovlev, "Investigation of mode interaction on planar dielectric waveguides with loss and gain," Radio Sci. 34, 1349-1359 (1999).
[CrossRef]

1998

1997

Y. D. Lin and J. W. Sheen, "Mode distinction and radiation-efficiency analysis of planar leaky-wave line source," IEEE Trans. Microwave Theory Tech. 45, 1672-1680 (1997).
[CrossRef]

P. Tournois and V. Laude, ??????Negative group velocities in metal-film optical waveguides,?????? Opt. Commun. 137, 41-45 (1997).
[CrossRef]

1986

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

1984

1969

E. N. Economou, ??????Surface plasmons in thin films,?????? Phys. Rev. 182, 539-554 (1969).
[CrossRef]

Atwater, H. A.

J. A. Dionne, L. A. Sweatlock, and H. A. Atwater, "Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization," Phys. Rev. B 73, 035407 (2006).
[CrossRef]

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, 075405 (2005).
[CrossRef]

Berini, P.

Brongersma, M. L.

J. S. Q. Liu and M. L. Brongersma, "Omnidirectional light emission via surface plasmon polaritons," Appl. Phys. Lett.  90, 091116 (2007).
[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. A 21, 2442-2446 (2004).
[CrossRef]

H. Shin, M. F. Yanik, S. Fan, R. Zia, and M. L. Brongersma, ??????Omnidirectional resonance in a metal-dielectric-metal geometry,?????? Appl. Phys. Lett. 84, 4421-4423 (2004).
[CrossRef]

Burke, J. J.

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

Catrysse, P. B.

Charbonneau, R.

Chilwell, J.

Dionne, J. A.

J. A. Dionne, L. A. Sweatlock, and H. A. Atwater, "Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization," Phys. Rev. B 73, 035407 (2006).
[CrossRef]

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, 075405 (2005).
[CrossRef]

Djuriši??, A. B.

Economou, E. N.

E. N. Economou, ??????Surface plasmons in thin films,?????? Phys. Rev. 182, 539-554 (1969).
[CrossRef]

Elazar, J. M.

Fan, S.

G. Veronis and S. Fan, "Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides," Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

H. Shin, M. F. Yanik, S. Fan, R. Zia, and M. L. Brongersma, ??????Omnidirectional resonance in a metal-dielectric-metal geometry,?????? Appl. Phys. Lett. 84, 4421-4423 (2004).
[CrossRef]

Fukuda, H.

T. Goto, Y. Katagiri, H. Fukuda, H. Shinojima, Y. Nakano, I. Kobayashi, and Y. Mitsuoka, "Propagation loss measurement for surface plasmon-polariton modes at metal waveguides on semiconductor substrates," Appl. Phys. Lett. 84, 852-854 (2004).
[CrossRef]

Gilmore, M. A.

M. A. Gilmore and B. L. Johnson, J. Appl. Phys. 93, 4497 (2003).
[CrossRef]

Goto, T.

T. Goto, Y. Katagiri, H. Fukuda, H. Shinojima, Y. Nakano, I. Kobayashi, and Y. Mitsuoka, "Propagation loss measurement for surface plasmon-polariton modes at metal waveguides on semiconductor substrates," Appl. Phys. Lett. 84, 852-854 (2004).
[CrossRef]

Hanson, G. W.

G. W. Hanson and A. B. Yakovlev, "Investigation of mode interaction on planar dielectric waveguides with loss and gain," Radio Sci. 34, 1349-1359 (1999).
[CrossRef]

Hodgkinson, I.

Johnson, B. L.

M. A. Gilmore and B. L. Johnson, J. Appl. Phys. 93, 4497 (2003).
[CrossRef]

Katagiri, Y.

T. Goto, Y. Katagiri, H. Fukuda, H. Shinojima, Y. Nakano, I. Kobayashi, and Y. Mitsuoka, "Propagation loss measurement for surface plasmon-polariton modes at metal waveguides on semiconductor substrates," Appl. Phys. Lett. 84, 852-854 (2004).
[CrossRef]

Kobayashi, I.

T. Goto, Y. Katagiri, H. Fukuda, H. Shinojima, Y. Nakano, I. Kobayashi, and Y. Mitsuoka, "Propagation loss measurement for surface plasmon-polariton modes at metal waveguides on semiconductor substrates," Appl. Phys. Lett. 84, 852-854 (2004).
[CrossRef]

Kurokawa, Y.

Y. Kurokawa and H. T. Miyazaki, "Metal-insulator-metal plasmon nanocavities: Analysis of optical properties," Phys. Rev. B 75, 035411 (2007).
[CrossRef]

H. T. Miyazaki and Y. Kurokawa, "Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity," Phys. Rev. Lett. 96,097401(2006).
[CrossRef] [PubMed]

Lahoud, N.

Laude, V.

P. Tournois and V. Laude, ??????Negative group velocities in metal-film optical waveguides,?????? Opt. Commun. 137, 41-45 (1997).
[CrossRef]

Lin, Y. D.

Y. D. Lin and J. W. Sheen, "Mode distinction and radiation-efficiency analysis of planar leaky-wave line source," IEEE Trans. Microwave Theory Tech. 45, 1672-1680 (1997).
[CrossRef]

Liu, J. S. Q.

J. S. Q. Liu and M. L. Brongersma, "Omnidirectional light emission via surface plasmon polaritons," Appl. Phys. Lett.  90, 091116 (2007).
[CrossRef]

Lopez-Rios, T.

F. Villa, T. Lopez-Rios, and L. E. Regalado, "Electromagnetic modes in metal-insulator-metal structures," Phys. Rev. B 63, 165103 (2001).
[CrossRef]

Majewski, M. L.

Mattiussi, G.

Mitsuoka, Y.

T. Goto, Y. Katagiri, H. Fukuda, H. Shinojima, Y. Nakano, I. Kobayashi, and Y. Mitsuoka, "Propagation loss measurement for surface plasmon-polariton modes at metal waveguides on semiconductor substrates," Appl. Phys. Lett. 84, 852-854 (2004).
[CrossRef]

Miyazaki, H. T.

Y. Kurokawa and H. T. Miyazaki, "Metal-insulator-metal plasmon nanocavities: Analysis of optical properties," Phys. Rev. B 75, 035411 (2007).
[CrossRef]

H. T. Miyazaki and Y. Kurokawa, "Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity," Phys. Rev. Lett. 96,097401(2006).
[CrossRef] [PubMed]

Nakano, Y.

T. Goto, Y. Katagiri, H. Fukuda, H. Shinojima, Y. Nakano, I. Kobayashi, and Y. Mitsuoka, "Propagation loss measurement for surface plasmon-polariton modes at metal waveguides on semiconductor substrates," Appl. Phys. Lett. 84, 852-854 (2004).
[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, 075405 (2005).
[CrossRef]

Raki??, A. D.

Regalado, L. E.

F. Villa, T. Lopez-Rios, and L. E. Regalado, "Electromagnetic modes in metal-insulator-metal structures," Phys. Rev. B 63, 165103 (2001).
[CrossRef]

Selker, M. D.

Sheen, J. W.

Y. D. Lin and J. W. Sheen, "Mode distinction and radiation-efficiency analysis of planar leaky-wave line source," IEEE Trans. Microwave Theory Tech. 45, 1672-1680 (1997).
[CrossRef]

Shin, H.

H. Shin, M. F. Yanik, S. Fan, R. Zia, and M. L. Brongersma, ??????Omnidirectional resonance in a metal-dielectric-metal geometry,?????? Appl. Phys. Lett. 84, 4421-4423 (2004).
[CrossRef]

Shinojima, H.

T. Goto, Y. Katagiri, H. Fukuda, H. Shinojima, Y. Nakano, I. Kobayashi, and Y. Mitsuoka, "Propagation loss measurement for surface plasmon-polariton modes at metal waveguides on semiconductor substrates," Appl. Phys. Lett. 84, 852-854 (2004).
[CrossRef]

Stegeman, G. I.

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

Sweatlock, L. A.

J. A. Dionne, L. A. Sweatlock, and H. A. Atwater, "Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization," Phys. Rev. B 73, 035407 (2006).
[CrossRef]

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, 075405 (2005).
[CrossRef]

Tournois, P.

P. Tournois and V. Laude, ??????Negative group velocities in metal-film optical waveguides,?????? Opt. Commun. 137, 41-45 (1997).
[CrossRef]

Veronis, G.

G. Veronis and S. Fan, "Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides," Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

Villa, F.

F. Villa, T. Lopez-Rios, and L. E. Regalado, "Electromagnetic modes in metal-insulator-metal structures," Phys. Rev. B 63, 165103 (2001).
[CrossRef]

Wang, Y.

Y. Wang, ??????Wavelength selection with coupled surface plasmon waves,?????? Appl. Phys. Lett. 82, 4385-4387 (2003).
[CrossRef]

Yakovlev, A. B.

G. W. Hanson and A. B. Yakovlev, "Investigation of mode interaction on planar dielectric waveguides with loss and gain," Radio Sci. 34, 1349-1359 (1999).
[CrossRef]

Yanik, M. F.

H. Shin, M. F. Yanik, S. Fan, R. Zia, and M. L. Brongersma, ??????Omnidirectional resonance in a metal-dielectric-metal geometry,?????? Appl. Phys. Lett. 84, 4421-4423 (2004).
[CrossRef]

Zia, R.

H. Shin, M. F. Yanik, S. Fan, R. Zia, and M. L. Brongersma, ??????Omnidirectional resonance in a metal-dielectric-metal geometry,?????? Appl. Phys. Lett. 84, 4421-4423 (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. A 21, 2442-2446 (2004).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett

J. S. Q. Liu and M. L. Brongersma, "Omnidirectional light emission via surface plasmon polaritons," Appl. Phys. Lett.  90, 091116 (2007).
[CrossRef]

Appl. Phys. Lett.

Y. Wang, ??????Wavelength selection with coupled surface plasmon waves,?????? Appl. Phys. Lett. 82, 4385-4387 (2003).
[CrossRef]

H. Shin, M. F. Yanik, S. Fan, R. Zia, and M. L. Brongersma, ??????Omnidirectional resonance in a metal-dielectric-metal geometry,?????? Appl. Phys. Lett. 84, 4421-4423 (2004).
[CrossRef]

G. Veronis and S. Fan, "Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides," Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

T. Goto, Y. Katagiri, H. Fukuda, H. Shinojima, Y. Nakano, I. Kobayashi, and Y. Mitsuoka, "Propagation loss measurement for surface plasmon-polariton modes at metal waveguides on semiconductor substrates," Appl. Phys. Lett. 84, 852-854 (2004).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

Y. D. Lin and J. W. Sheen, "Mode distinction and radiation-efficiency analysis of planar leaky-wave line source," IEEE Trans. Microwave Theory Tech. 45, 1672-1680 (1997).
[CrossRef]

J. Appl. Phys.

M. A. Gilmore and B. L. Johnson, J. Appl. Phys. 93, 4497 (2003).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

P. Tournois and V. Laude, ??????Negative group velocities in metal-film optical waveguides,?????? Opt. Commun. 137, 41-45 (1997).
[CrossRef]

Opt. Express

Phys. Rev.

E. N. Economou, ??????Surface plasmons in thin films,?????? Phys. Rev. 182, 539-554 (1969).
[CrossRef]

Phys. Rev. B

P. Berini, ??????Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of asymmetric structures,?????? Phys. Rev. B 63, 125417 (2001).
[CrossRef]

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, 075405 (2005).
[CrossRef]

J. A. Dionne, L. A. Sweatlock, and H. A. Atwater, "Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization," Phys. Rev. B 73, 035407 (2006).
[CrossRef]

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

Y. Kurokawa and H. T. Miyazaki, "Metal-insulator-metal plasmon nanocavities: Analysis of optical properties," Phys. Rev. B 75, 035411 (2007).
[CrossRef]

F. Villa, T. Lopez-Rios, and L. E. Regalado, "Electromagnetic modes in metal-insulator-metal structures," Phys. Rev. B 63, 165103 (2001).
[CrossRef]

Phys. Rev. Lett.

H. T. Miyazaki and Y. Kurokawa, "Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity," Phys. Rev. Lett. 96,097401(2006).
[CrossRef] [PubMed]

Radio Sci.

G. W. Hanson and A. B. Yakovlev, "Investigation of mode interaction on planar dielectric waveguides with loss and gain," Radio Sci. 34, 1349-1359 (1999).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

TM dispersion relations (a) and characteristic tangential field profiles (B) for a symmetric Ag/air/Ag planar MIM structure bounded by free space with insulator thickness dI = 300 nm and metal thickness dM = 50 nm. (b) illustrates fields at vacuum wavelengths of 400 nm (black) and 600 nm (gray). Panels (a)–(e) plot the tangential magnetic field (Hy) for the conventional metal-clad waveguide mode, and modes SL, AL, SH, and AH respectively. Panel (f) shows the tangential electric fields (Ez) of mode AH.

Fig. 2.
Fig. 2.

MIM dispersion as a function of insulator thickness (a) and metal film thickness (b). The arrow indicates increasing thickness. The y-axis ranges of above panels are various. (a): MIM geometry with metal thickness dM = 50 nm and insulator thickness dI = 20, 50, 100 and 200 nm (for modes SL, AL and SH) and dI = 100, 200 and 300 nm (for mode AH). Dispersion relations for air/Ag (50 nm)/air IMI waveguide, low energy antisymmetric modes (top two panels) and high energy symmetric modes (bottom two panels), are plotted in solid black lines as reference. (b): MIM geometry with insulator thickness dI = 300 nm and metal thickness dM = 20, 35, and 50 nm. Dispersion relations for semi-infinite MIM waveguide, low energy symmetric modes (left two panels) and high energy antisymmetric modes (right two panels) are also plotted in solid black lines as reference.

Fig. 3.
Fig. 3.

Wavelength-dependent propagation length and confinement factor for a MIM structure of dI = 300 nm and dM = 50 nm. It is the same waveguide structure as that in Fig. 1.

Fig. 4.
Fig. 4.

Propagation length L (black lines and symbols) and confinement factor Γ (gray lines and symbols) for the MIM plasmonic waveguide at a free-space wavelength of 500 nm as a function of (A) metal ((B) insulator) thickness with fixed (A) insulator thickness dI = 100 nm ((B) metal thickness, dM = 20 nm).

Fig. 5.
Fig. 5.

MIM leaky wave-front tilt θ (A) and radiation free-space coupling pattern at a free-space wavelength of 633nm (B) as a function of insulator and metal thickness (d I,M ). In (A), the transition from black to gray in the plot curves occurs at the wavelength where the MIM waveguide modal propagation constant has equal real and imaginary values.

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