Abstract

It is found that when a light beam is incident on a one-dimensional photonic crystal (1DPC) containing a defect layer, the lateral shifts of both the reflected and the transmitted beams are greatly enhanced near the defect mode of the 1DPC, whose location depends on the angles at a fixed frequency. The effect was studied by use of a Gaussian beam. The giant lateral displacement is due to the localization of the electromagnetic wave.

© 2006 Optical Society of America

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

2005 (1)

2004 (2)

D. Felbacq and R. Smaâli, Phys. Rev. Lett. 92, 193902 (2004).
[CrossRef] [PubMed]

L.-G. Wang, N.-H. Liu, Q. Lin, and S.-Y. Zhu, Phys. Rev. E 70, 016601 (2004).
[CrossRef]

2003 (3)

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

D. Felbacq, A. Moreau, and R. Smaâli, Opt. Lett. 28, 1633 (2003).
[CrossRef] [PubMed]

C. F. Li, Phys. Rev. Lett. 91, 133903 (2003).
[CrossRef] [PubMed]

2002 (1)

1998 (1)

B. M. Jost, A.-A. R. Al-Rashed and B. E. A. Saleh, Phys. Rev. Lett. 81, 2233 (1998).
[CrossRef]

1994 (1)

A. M. Steinberg and R. Y. Chiao, Phys. Rev. A 49, 3283 (1994).
[CrossRef] [PubMed]

1993 (1)

E. Pfleghaar, A. Marseille, and A. Weis, Phys. Rev. Lett. 70, 2281 (1993).
[CrossRef] [PubMed]

1992 (1)

F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
[CrossRef] [PubMed]

1987 (1)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

1982 (1)

W. J. Wild and C. L. Giles, Phys. Rev. A 25, 2099 (1982).
[CrossRef]

1977 (1)

1971 (1)

1964 (1)

1949 (1)

F. Goos and H. Hänchen, Ann. Phys. 5, 251 (1949).
[CrossRef]

1948 (1)

K. Artmann, Ann. Phys. 2, 87 (1948).
[CrossRef]

1947 (1)

F. Goos and H. Hänchen, Ann. Phys. 1, 333 (1947).
[CrossRef]

Al-Rashed, A.-A. R.

B. M. Jost, A.-A. R. Al-Rashed and B. E. A. Saleh, Phys. Rev. Lett. 81, 2233 (1998).
[CrossRef]

Anicin, B.

Artmann, K.

K. Artmann, Ann. Phys. 2, 87 (1948).
[CrossRef]

Bretenaker, F.

F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
[CrossRef] [PubMed]

Chan, S. W.

Chen, H.

Chiao, R. Y.

A. M. Steinberg and R. Y. Chiao, Phys. Rev. A 49, 3283 (1994).
[CrossRef] [PubMed]

Cowan, J. J.

Dutriaux, L.

F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
[CrossRef] [PubMed]

Felbacq, D.

Giles, C. L.

W. J. Wild and C. L. Giles, Phys. Rev. A 25, 2099 (1982).
[CrossRef]

Goos, F.

F. Goos and H. Hänchen, Ann. Phys. 5, 251 (1949).
[CrossRef]

F. Goos and H. Hänchen, Ann. Phys. 1, 333 (1947).
[CrossRef]

Hänchen, H.

F. Goos and H. Hänchen, Ann. Phys. 5, 251 (1949).
[CrossRef]

F. Goos and H. Hänchen, Ann. Phys. 1, 333 (1947).
[CrossRef]

Horowitz, B. R.

Jost, B. M.

B. M. Jost, A.-A. R. Al-Rashed and B. E. A. Saleh, Phys. Rev. Lett. 81, 2233 (1998).
[CrossRef]

Kivshar, Y. S.

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

Lai, H. M.

Le Floch, A.

F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
[CrossRef] [PubMed]

Li, C. F.

C. F. Li, Phys. Rev. Lett. 91, 133903 (2003).
[CrossRef] [PubMed]

Lin, Q.

L.-G. Wang, N.-H. Liu, Q. Lin, and S.-Y. Zhu, Phys. Rev. E 70, 016601 (2004).
[CrossRef]

Liu, N.-H.

L.-G. Wang, N.-H. Liu, Q. Lin, and S.-Y. Zhu, Phys. Rev. E 70, 016601 (2004).
[CrossRef]

Marseille, A.

E. Pfleghaar, A. Marseille, and A. Weis, Phys. Rev. Lett. 70, 2281 (1993).
[CrossRef] [PubMed]

Moreau, A.

Pfleghaar, E.

E. Pfleghaar, A. Marseille, and A. Weis, Phys. Rev. Lett. 70, 2281 (1993).
[CrossRef] [PubMed]

Renard, R. H.

Saleh, B. E.

B. M. Jost, A.-A. R. Al-Rashed and B. E. A. Saleh, Phys. Rev. Lett. 81, 2233 (1998).
[CrossRef]

Shadrivov, I. V.

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

Smaâli, R.

Steinberg, A. M.

A. M. Steinberg and R. Y. Chiao, Phys. Rev. A 49, 3283 (1994).
[CrossRef] [PubMed]

Tamir, T.

Wang, L. G.

Wang, L.-G.

L.-G. Wang, N.-H. Liu, Q. Lin, and S.-Y. Zhu, Phys. Rev. E 70, 016601 (2004).
[CrossRef]

Weis, A.

E. Pfleghaar, A. Marseille, and A. Weis, Phys. Rev. Lett. 70, 2281 (1993).
[CrossRef] [PubMed]

Wild, W. J.

W. J. Wild and C. L. Giles, Phys. Rev. A 25, 2099 (1982).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Zharov, A. A

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

Zhu, S. Y.

Zhu, S.-Y.

L.-G. Wang, N.-H. Liu, Q. Lin, and S.-Y. Zhu, Phys. Rev. E 70, 016601 (2004).
[CrossRef]

Ann. Phys. (3)

F. Goos and H. Hänchen, Ann. Phys. 1, 333 (1947).
[CrossRef]

F. Goos and H. Hänchen, Ann. Phys. 5, 251 (1949).
[CrossRef]

K. Artmann, Ann. Phys. 2, 87 (1948).
[CrossRef]

Appl. Phys. Lett. (1)

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

J. Opt. Soc. Am. (3)

Opt. Lett. (3)

Phys. Rev. A (2)

A. M. Steinberg and R. Y. Chiao, Phys. Rev. A 49, 3283 (1994).
[CrossRef] [PubMed]

W. J. Wild and C. L. Giles, Phys. Rev. A 25, 2099 (1982).
[CrossRef]

Phys. Rev. E (1)

L.-G. Wang, N.-H. Liu, Q. Lin, and S.-Y. Zhu, Phys. Rev. E 70, 016601 (2004).
[CrossRef]

Phys. Rev. Lett. (6)

C. F. Li, Phys. Rev. Lett. 91, 133903 (2003).
[CrossRef] [PubMed]

D. Felbacq and R. Smaâli, Phys. Rev. Lett. 92, 193902 (2004).
[CrossRef] [PubMed]

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
[CrossRef] [PubMed]

E. Pfleghaar, A. Marseille, and A. Weis, Phys. Rev. Lett. 70, 2281 (1993).
[CrossRef] [PubMed]

B. M. Jost, A.-A. R. Al-Rashed and B. E. A. Saleh, Phys. Rev. Lett. 81, 2233 (1998).
[CrossRef]

Other (1)

C.M.Soukoulis, ed., Photonic Band Gaps and Localization (Plenum, 1993).

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Figures (4)

Fig. 1
Fig. 1

Schematic of a 1DPC with a defect layer.

Fig. 2
Fig. 2

Lateral shift Δ at an incident angle of 20° for a wide beam at different frequencies. Solid curve, m = 5 ; dashed curve, m = 4 ; dotted curve, m = 3 . Left-hand inset, transmissivity t 2 ; right-hand inset, lateral shift near the defect mode.

Fig. 3
Fig. 3

Relative lateral shift δ λ and relative half-width W ¯ W for an incident beam of ω 2 π = 103.5 GHz with half-widths (a), (d) W = 24 mm ; (b), (e) W = 60 mm ; (c), (f) W = 200 mm . (a)–(f) Solid curves, reflected beam; dashed curves, transmitted beam; dotted curves, result of using Eq. (4). (g) Dependence of the value of r and t on θ; inset, relative phases ( ϕ r , t ϕ r , t 0 ) , where ϕ r , t 0 are the constant phases of r ( k y ) and t ( k y ) at normal incidence. Note that the curve of ( ϕ r ϕ r 0 ) overlaps that of ( ϕ t ϕ t 0 ) . m = 4 .

Fig. 4
Fig. 4

Distribution of the energy flow inside and outside the 1DPC. The incident beam has angle 24.2°, with W = 60 mm . Other parameters are the same as in Fig. 3.

Equations (9)

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M j ( Δ z , k y ) = [ cos ( k z j Δ z ) i 1 q j sin ( k z j Δ z ) i q j sin ( k z j Δ z ) cos ( k z j Δ z ) ] ,
r ( k y ) = [ q 0 X 22 ( k y ) q s X 11 ( k y ) ] [ q 0 q s X 12 ( k y ) X 21 ( k y ) ] [ q 0 X 22 ( k y ) + q s X 11 ( k y ) ] [ q 0 q s X 12 ( k y ) + X 21 ( k y ) ] ,
t ( k y ) = 2 q 0 [ q 0 X 22 ( k y ) + q s X 11 ( k y ) ] [ q 0 q s X 12 ( k y ) + X 21 ( k y ) ] ,
Δ r , t = d ϕ r , t d k y ,
E x ( i ) ( z , y ) = 1 2 π E ̃ ( k y ) exp [ i ( k z z + k y y ) ] d k y
E x ( r ) ( z , y ) = 1 2 π r ( k y ) E ̃ ( k y ) exp ( i k z z + i k y y ) d k y ( z < 0 ) ,
E x ( t ) ( z , y ) = 1 2 π t ( k y ) E ̃ ( k y ) exp [ i k z ( z d r ) + i k y y ] d k y ( z > d T ) .
δ r , t = y E x ( r , t ) ( y ) 2 d y E x ( r , t ) ( y ) 2 d y .
β r , t = 4 ( y δ r , t ) 2 E x ( r , t ) ( y ) 2 d y E x ( r , t ) ( y ) 2 d y ,

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