Abstract

We propose an analytical model for the grazing reflection of a narrow beam. For the special incidence condition, the output field is the superposition of the incidence and reflected fields, so the incidence cutoff frequency is defined in the angular spectrum. With the definition, we deduce the effective plane-wave-reflection coefficient, together with angular spectrum of the output field. The model is verified by numerical simulation. Calculation in ordinary linear, nonabsorbing media with this model reveals some remarkable characteristics of the output fields, such as negative lateral shift and a beam-width compression effect.

© 2006 Optical Society of America

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2006

H. Yu, X. Q. Jiang, J. Y. Yang, and M. H. Wang, Appl. Phys. Lett. 88, 011106 (2006).
[CrossRef]

2005

2004

D. K. Qing and G. Chen, Opt. Lett. 29, 872 (2004).
[CrossRef] [PubMed]

X. Q. Jiang, J. Y. Yang, H. Z. Zhan, K. J. Chen, Y. Tang, X. H. Li, and M. H. Wang, IEEE Photon. Technol. Lett. 16, 443 (2004).
[CrossRef]

2003

V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, Appl. Phys. Lett. 83, 2713 (2003).
[CrossRef]

2002

H. M. Lai and S. W. Chan, Opt. Lett. 27, 680 (2002).
[CrossRef]

J. Y. Yang, Q. J. Zhou, and R. T. Chen, Appl. Phys. Lett. 81, 2947 (2002).
[CrossRef]

2000

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, Phys. Rev. E 62, 7330 (2000).
[CrossRef]

1999

1985

1971

Bertoni, H. L.

Casperson, L. W.

Chan, S. W.

Chen, G.

Chen, K. J.

X. Q. Jiang, J. Y. Yang, H. Z. Zhan, K. J. Chen, Y. Tang, X. H. Li, and M. H. Wang, IEEE Photon. Technol. Lett. 16, 443 (2004).
[CrossRef]

Chen, R. T.

J. Y. Yang, Q. J. Zhou, and R. T. Chen, Appl. Phys. Lett. 81, 2947 (2002).
[CrossRef]

Jiang, X. Q.

H. Yu, X. Q. Jiang, J. Y. Yang, and M. H. Wang, Appl. Phys. Lett. 88, 011106 (2006).
[CrossRef]

X. Q. Jiang, J. Y. Yang, H. Z. Zhan, K. J. Chen, Y. Tang, X. H. Li, and M. H. Wang, IEEE Photon. Technol. Lett. 16, 443 (2004).
[CrossRef]

Kivshar, Y. S.

V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, Appl. Phys. Lett. 83, 2713 (2003).
[CrossRef]

Kwok, C. W.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, Phys. Rev. E 62, 7330 (2000).
[CrossRef]

Lai, H. M.

H. M. Lai and S. W. Chan, Opt. Lett. 27, 680 (2002).
[CrossRef]

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, Phys. Rev. E 62, 7330 (2000).
[CrossRef]

Li, X. H.

X. Q. Jiang, J. Y. Yang, H. Z. Zhan, K. J. Chen, Y. Tang, X. H. Li, and M. H. Wang, IEEE Photon. Technol. Lett. 16, 443 (2004).
[CrossRef]

Loo, Y. W.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, Phys. Rev. E 62, 7330 (2000).
[CrossRef]

Qing, D. K.

Riesz, R. P.

Shadrivov, V.

V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, Appl. Phys. Lett. 83, 2713 (2003).
[CrossRef]

Simon, R.

Tamir, T.

Tang, Y.

X. Q. Jiang, J. Y. Yang, H. Z. Zhan, K. J. Chen, Y. Tang, X. H. Li, and M. H. Wang, IEEE Photon. Technol. Lett. 16, 443 (2004).
[CrossRef]

Wang, L. G.

Wang, M. H.

H. Yu, X. Q. Jiang, J. Y. Yang, and M. H. Wang, Appl. Phys. Lett. 88, 011106 (2006).
[CrossRef]

X. Q. Jiang, J. Y. Yang, H. Z. Zhan, K. J. Chen, Y. Tang, X. H. Li, and M. H. Wang, IEEE Photon. Technol. Lett. 16, 443 (2004).
[CrossRef]

Xu, B. Y.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, Phys. Rev. E 62, 7330 (2000).
[CrossRef]

Yang, J. Y.

H. Yu, X. Q. Jiang, J. Y. Yang, and M. H. Wang, Appl. Phys. Lett. 88, 011106 (2006).
[CrossRef]

X. Q. Jiang, J. Y. Yang, H. Z. Zhan, K. J. Chen, Y. Tang, X. H. Li, and M. H. Wang, IEEE Photon. Technol. Lett. 16, 443 (2004).
[CrossRef]

J. Y. Yang, Q. J. Zhou, and R. T. Chen, Appl. Phys. Lett. 81, 2947 (2002).
[CrossRef]

Yu, H.

H. Yu, X. Q. Jiang, J. Y. Yang, and M. H. Wang, Appl. Phys. Lett. 88, 011106 (2006).
[CrossRef]

Zhan, H. Z.

X. Q. Jiang, J. Y. Yang, H. Z. Zhan, K. J. Chen, Y. Tang, X. H. Li, and M. H. Wang, IEEE Photon. Technol. Lett. 16, 443 (2004).
[CrossRef]

Zharov, A. A.

V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, Appl. Phys. Lett. 83, 2713 (2003).
[CrossRef]

Zhou, Q. J.

J. Y. Yang, Q. J. Zhou, and R. T. Chen, Appl. Phys. Lett. 81, 2947 (2002).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

H. Yu, X. Q. Jiang, J. Y. Yang, and M. H. Wang, Appl. Phys. Lett. 88, 011106 (2006).
[CrossRef]

V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, Appl. Phys. Lett. 83, 2713 (2003).
[CrossRef]

J. Y. Yang, Q. J. Zhou, and R. T. Chen, Appl. Phys. Lett. 81, 2947 (2002).
[CrossRef]

IEEE Photon. Technol. Lett.

X. Q. Jiang, J. Y. Yang, H. Z. Zhan, K. J. Chen, Y. Tang, X. H. Li, and M. H. Wang, IEEE Photon. Technol. Lett. 16, 443 (2004).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Lett.

Phys. Rev. E

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, Phys. Rev. E 62, 7330 (2000).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of the reflection of a Gaussian beam on a dielectric interface.

Fig. 2
Fig. 2

Comparison of calculation results with numerical simulations at two different z planes in the incidence coordinates: (a) z = 300 μ m , (b) z = 1000 μ m . Other parameters in calculation are w = 2 μ m , θ 0 = 1 ° , n 1 = 3.3923 , n 2 = 3.3839 , λ = 1.31 μ m , h = 300 μ m .

Fig. 3
Fig. 3

Output optical fields in the TIR switch structure. In the TIR switch structure, h and H are determined by w. The other parameters are the same as in Fig. 2.

Equations (11)

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2 θ = 2 arctan ( λ π n 1 w ) 2 λ π n 1 w .
f ( k 0 n 1 sin θ 0 ) > f ( k 0 n 1 sin θ ) = π w e = f ( 0 ) e .
E ( A ) = E i ( x , y ) + E m ( x , y ) ,
E i ( x , y ) = 1 2 π + f ( k x ) exp { i [ k x x + ( k 0 2 n 1 2 k x 2 ) 1 2 z ] } d k x ,
E m ( x , y ) = 1 2 π + f ( k x ) r ( k x ) exp { i [ k x x + ( k 0 2 n 1 2 k x 2 ) 1 2 z ] } d k x .
x = x cos 2 θ 0 ( h z ) sin 2 θ 0 ,
z = z cos 2 θ 0 + ( x + h tan θ 0 ) sin 2 θ 0 .
E ( A S ) = 1 2 π + f ( k x ) [ 1 + r ( k x ) ] exp { i [ k x x + ( k 0 2 n 1 2 k x 2 ) 1 2 z ] } d k x .
E ( A ) = 1 2 π + f ( k x ) R ( k x ) exp { i [ k x x + ( k 0 2 n 1 2 k x 2 ) 1 2 z ] } d k x ,
R ( k x ) = r ( k x ) + exp { i k x [ 2 x cos 2 θ 0 ( h z ) sin 2 θ 0 ] + i ( k 0 2 n 1 2 k x 2 ) 1 2 ( 2 z sin 2 θ 0 + x sin 2 θ 0 + 2 h sin 2 θ 0 ) } .
g ( k x ) = 1 cos 2 θ 0 f ( k 0 n 1 sin 2 θ 0 k x cos 2 θ 0 ) exp [ i k 0 n 1 sin 2 θ 0 k x cos 2 θ 0 ( z h ) sin 2 θ 0 ] × exp { i [ k 0 2 n 1 2 ( k 0 n 1 sin 2 θ 0 k x cos 2 θ 0 ) 2 ] 1 2 ( z cos 2 θ 0 + 2 h sin 2 θ 0 ) } + f ( k x ) × r ( k x ) exp [ i ( k 0 2 n 1 2 k x 2 ) 1 2 z ] .

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