Abstract

A detailed mathematical analysis along with a theoretical model for the modes supported at the interface of a metal and periodically stratified medium (Bragg structure) is presented. The modes that are supported at the interface of a plasmon active metal (such as gold) and a Bragg structure are commonly known as surface plasmon–Bragg modes. We found that these modes have effective indices lower than any of the material indices of the layers comprising the Bragg structure, and they are highly dispersive when compared to the conventional surface plasmon modes that are supported at the metal and dielectric interface. The plausible physical explanation behind the strong dispersive behavior of the surface plasmon–Bragg mode is provided. Finally, the comparison of dissipation loss for the surface plasmon–Bragg modes is investigated and it has been shown that there is more than fivefold enhancement in the magnitude of propagation lengths as compared to the conventional surface plasmon mode.

© 2009 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2006

2005

A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated optical components utilizing long-range surface plasmon polaritons,” J. Lightwave Technol. 23, 413-422 (2005).
[CrossRef]

X. Hu, Q. Gong, S. Feng, B. Cheng, and D. Zhang, “Tunable multi channel filter in nonlinear ferroelectric photonic crystal,” Opt. Commun. 253, 138-144 (2005).
[CrossRef]

2004

A. Mizrahi and L. Schachter, “Optical Bragg accelerators,” Phys. Rev. E 70, 016505-016521 (2004).
[CrossRef]

2003

2000

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

1998

R. M. de Ridder, K. Worhoff, A. Driessen, P. V. Lambeck, and H. Albers, “Silicon oxynitride planar waveguiding structures for applications in optical communications,” IEEE J. Sel. Top. Quantum Electron. 4, 930-937 (1998).
[CrossRef]

1991

1990

F. A. Burton and S. A. Cassidy, “A complete description of the dispersion relation for thin metal film plasmon-polariton,” J. Lightwave Technol. 8, 1843-1849 (1990).
[CrossRef]

1986

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

1977

1976

P. Yeh and A. Yariv, “Bragg reflection waveguides,” Opt. Commun. 19, 427-430 (1976).
[CrossRef]

Albers, H.

R. M. de Ridder, K. Worhoff, A. Driessen, P. V. Lambeck, and H. Albers, “Silicon oxynitride planar waveguiding structures for applications in optical communications,” IEEE J. Sel. Top. Quantum Electron. 4, 930-937 (1998).
[CrossRef]

Berini, P.

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

Boltasseva, A.

Bozhevolnyi, S. I.

Burke, J. J.

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

Burton, F. A.

F. A. Burton and S. A. Cassidy, “A complete description of the dispersion relation for thin metal film plasmon-polariton,” J. Lightwave Technol. 8, 1843-1849 (1990).
[CrossRef]

Cassidy, S. A.

F. A. Burton and S. A. Cassidy, “A complete description of the dispersion relation for thin metal film plasmon-polariton,” J. Lightwave Technol. 8, 1843-1849 (1990).
[CrossRef]

Cheng, B.

X. Hu, Q. Gong, S. Feng, B. Cheng, and D. Zhang, “Tunable multi channel filter in nonlinear ferroelectric photonic crystal,” Opt. Commun. 253, 138-144 (2005).
[CrossRef]

de Ridder, R. M.

R. M. de Ridder, K. Worhoff, A. Driessen, P. V. Lambeck, and H. Albers, “Silicon oxynitride planar waveguiding structures for applications in optical communications,” IEEE J. Sel. Top. Quantum Electron. 4, 930-937 (1998).
[CrossRef]

Driessen, A.

R. M. de Ridder, K. Worhoff, A. Driessen, P. V. Lambeck, and H. Albers, “Silicon oxynitride planar waveguiding structures for applications in optical communications,” IEEE J. Sel. Top. Quantum Electron. 4, 930-937 (1998).
[CrossRef]

Feng, S.

X. Hu, Q. Gong, S. Feng, B. Cheng, and D. Zhang, “Tunable multi channel filter in nonlinear ferroelectric photonic crystal,” Opt. Commun. 253, 138-144 (2005).
[CrossRef]

Golub, I.

Gong, Q.

X. Hu, Q. Gong, S. Feng, B. Cheng, and D. Zhang, “Tunable multi channel filter in nonlinear ferroelectric photonic crystal,” Opt. Commun. 253, 138-144 (2005).
[CrossRef]

Helmy, A. S.

Hong, C.

Hu, X.

X. Hu, Q. Gong, S. Feng, B. Cheng, and D. Zhang, “Tunable multi channel filter in nonlinear ferroelectric photonic crystal,” Opt. Commun. 253, 138-144 (2005).
[CrossRef]

Kjaer, K.

Lambeck, P. V.

R. M. de Ridder, K. Worhoff, A. Driessen, P. V. Lambeck, and H. Albers, “Silicon oxynitride planar waveguiding structures for applications in optical communications,” IEEE J. Sel. Top. Quantum Electron. 4, 930-937 (1998).
[CrossRef]

Larsen, M. S.

Leosson, K.

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

Mizrahi, A.

A. Mizrahi and L. Schachter, “Optical Bragg accelerators,” Phys. Rev. E 70, 016505-016521 (2004).
[CrossRef]

Nikolajsen, T.

Schachter, L.

A. Mizrahi and L. Schachter, “Optical Bragg accelerators,” Phys. Rev. E 70, 016505-016521 (2004).
[CrossRef]

Simova, E.

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

Stegeman, G. I.

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

Tamir, T.

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

Worhoff, K.

R. M. de Ridder, K. Worhoff, A. Driessen, P. V. Lambeck, and H. Albers, “Silicon oxynitride planar waveguiding structures for applications in optical communications,” IEEE J. Sel. Top. Quantum Electron. 4, 930-937 (1998).
[CrossRef]

Yariv, A.

Yeh, P.

Zervas, M. N.

Zhang, D.

X. Hu, Q. Gong, S. Feng, B. Cheng, and D. Zhang, “Tunable multi channel filter in nonlinear ferroelectric photonic crystal,” Opt. Commun. 253, 138-144 (2005).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

R. M. de Ridder, K. Worhoff, A. Driessen, P. V. Lambeck, and H. Albers, “Silicon oxynitride planar waveguiding structures for applications in optical communications,” IEEE J. Sel. Top. Quantum Electron. 4, 930-937 (1998).
[CrossRef]

J. Lightwave Technol.

F. A. Burton and S. A. Cassidy, “A complete description of the dispersion relation for thin metal film plasmon-polariton,” J. Lightwave Technol. 8, 1843-1849 (1990).
[CrossRef]

A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated optical components utilizing long-range surface plasmon polaritons,” J. Lightwave Technol. 23, 413-422 (2005).
[CrossRef]

J. Opt. Soc. Am.

Opt. Commun.

X. Hu, Q. Gong, S. Feng, B. Cheng, and D. Zhang, “Tunable multi channel filter in nonlinear ferroelectric photonic crystal,” Opt. Commun. 253, 138-144 (2005).
[CrossRef]

P. Yeh and A. Yariv, “Bragg reflection waveguides,” Opt. Commun. 19, 427-430 (1976).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

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

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

Phys. Rev. E

A. Mizrahi and L. Schachter, “Optical Bragg accelerators,” Phys. Rev. E 70, 016505-016521 (2004).
[CrossRef]

Other

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

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Figures (5)

Fig. 1
Fig. 1

Schematic of the planar geometry showing the interface of a semi-infinite metal and Bragg structure (periodically stratified region).

Fig. 2
Fig. 2

Modal field of SP–Bragg mode supported at the interface of a metal and Bragg structure interface for λ = 1.55 μm .

Fig. 3
Fig. 3

Plot of n eff as a function of wavelength for a SP–Bragg mode and conventional SP mode.

Fig. 4
Fig. 4

Plot for variation of fractional power in the metal as a function of wavelength for SP–Bragg mode and conventional SP mode.

Fig. 5
Fig. 5

Plot of propagation length ( L p ) as a function of wavelength for SP–Bragg mode and conventional SP mode.

Equations (7)

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H y ( metal ) ( x ) = C 1 e k M x , for x < 0 ; H y ( periodic ) ( x ) = C 2 [ ( a 0 e i k 1 x ( x n Λ ) + b 0 e i k 1 x ( x n Λ ) ) ] e i n ( K Λ ) , where   n Λ x n Λ + d 1 ; H y ( periodic ) ( x ) = C 2 [ ( c 0 e i k 2 x ( x n Λ d 1 ) + d 0 e i k 2 x ( x n Λ d 1 ) ) ] e i n ( K Λ ) , where   n Λ + d 1 x ( n + 1 ) d 1 ;
β 2 μ 0 ω | H y | 2 d x = 1.
K ( β , ω ) = 1 Λ cos - 1 [ Re ( P ) ] ,
P = e i k 1 x d 1 [ cos ( k 2 x d 2 ) 1 2 i ( n 1 2 n 2 2 k 2 x k 1 x + n 2 2 n 1 2 k 1 x k 2 x ) sin ( k 2 x d 2 ) ] .
k m ε m = i k 1 x n 1 2 e i K Λ P Q e i K Λ P + Q ,
Q = e i k 1 x d 1 [ 1 2 i ( n 1 2 n 2 2 k 2 x k 1 x n 2 2 n 1 2 k 1 x k 2 x ) sin ( k 2 x d 2 ) ] .
γ = 2 ω c n eff 0 n r n i | H y | 2 d x | H y | 2 d x ,

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