Abstract

We propose and implement a simple and accurate method to analyze a subwavelength rectangular hole in a real metal and obtain the modal characteristics of its fundamental mode. Our results are found to be in excellent agreement with those reported in the literature, obtained by the effective index method (EIM) and finite-element and finite-difference methods. Unlike the EIM, the present method has no ambiguity in its implementation and is able to predict the major field components also, which may be useful in understanding the extraordinary transmission characteristics of such structures.

© 2008 Optical Society of America

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References

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2007 (1)

2006 (2)

2005 (1)

2001 (1)

1998 (2)

T. W. Ebbessen, H. J. Lezac, H. F. Ghaemi, T. Thio, and P. A. Wolf, Nature 667, 391 (1998).

H. Renner, J. Opt. A 15, 1401 (1998).
[CrossRef]

1991 (1)

1989 (1)

1988 (1)

1986 (1)

I. Yokohama, K. Okamoto, and J. Noda, J. Lightwave Technol. LT-4, 1352 (1986).
[CrossRef]

1985 (1)

1984 (1)

A. Kumar, R. K. Varshney, and K. Thyagarajan, Electron. Lett. 20, 112 (1984).
[CrossRef]

1983 (1)

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Figures (4)

Fig. 1
Fig. 1

Schematic of (a) considered RCA and (b) equivalent pseudo-RCA.

Fig. 2
Fig. 2

Variation of (a) real ( n eff ) and (b) imaginary ( n eff ) and propagation length L for the fundamental y-polarized mode with wavelength λ, for a 300 nm × 200 nm air ( ε d = 1 ) hole in gold as obtained by the PM (solid curve) and the EIM (open squares)

Fig. 3
Fig. 3

Cutoff wavelength of the fundamental y-polarized mode as a function of width 2 b for an air ( ε d = 1 ) hole in silver of length 2 a = 270 nm , obtained by the PM (solid curve) and the EIM (asterisks).

Fig. 4
Fig. 4

Variation of the penetration depth along the x-direction ( γ r 1 ) and along the y-direction ( γ r 1 ) in the metal as a function of wavelength λ for a 300 nm × 200 nm air ( ε d = 1 ) hole in gold as obtained by the PM.

Equations (15)

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ε ( x , y ) = ε ( x ) + ε ( y ) ε d ,
d 2 ψ d x 2 + d 2 ψ d y 2 + [ k 0 2 ε ( x , y ) β 2 ] ψ = 0 ,
tan ( κ a ) = V 2 ( κ a ) 2 1 ,
tanh ( κ b ) = ( ε d ε m ) V 2 ( κ b ) 2 + 1 ,
V r 2 ( cos 2 x r cosh 2 x i + 1 ) V i 2 ( sin 2 x r sinh 2 x i ) = 2 ( x r 2 x i 2 ) ,
V i 2 ( cos 2 x r cosh 2 x i + 1 ) + V r 2 ( sin 2 x r sinh 2 x i ) = 4 x r x i .
μ cos 2 y i cosh 2 y r ξ ν sin 2 y i sinh 2 y r = 0 ,
ν cos 2 y i cosh 2 y r η + μ sin 2 y i sinh 2 y r = 0 ,
ξ = ( y r 2 y i 2 ) ( ε r 2 ε i 2 + ε d 2 ) + 4 ε r ε i y r y i + ε d 2 V r 2 ,
μ = ( y r 2 y i 2 ) ( ε r 2 ε i 2 + ε d 2 ) + 4 ε r ε i y r y i ε d 2 V r 2 ,
ν = 2 y r y i ( ε r 2 ε i 2 ε d 2 ) 2 ε r ε i ( y r 2 y i 2 ) + ε d 2 V i 2 ,
η = 2 y r y i ( ε r 2 ε i 2 + ε d 2 ) 2 ε r ε i ( y r 2 y i 2 ) ε d 2 V i 2 .
λ c = 2 π a β y k 0 tan 1 k 0 2 ( ε d + ε r ) β y 2 1 .
X ( x ) = A cos ( κ x ) x < a , = A cos ( κ a ) exp [ γ ( x a ) ] x > a ,
Y ( y ) = ( B ε d ) cosh ( κ y ) y < b , = ( B ε m ) cosh ( κ b ) exp [ γ ( y b ) ] y > b ,

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