Abstract

An analysis of the switching properties of nonlinear waveguide arrays with longitudinally decreasing coupling coefficients is presented. It is shown that one can achieve both phase- and amplitude-controlled optical switching with a high extinction ratio by providing axially decreasing mutual coupling, which induces adiabatic narrowing of spatial light-wave distributions in the waveguide arrays.

© 1995 Optical Society of America

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References

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1994 (4)

1993 (1)

Ch. Claude, Yu. S. Kivshar, O. Kluth, K. H. Spatschek, Phys. Rev. B 47, 14228 (1993).
[CrossRef]

1992 (1)

C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, F. Lederer, Opt. Commun. 89, 473 (1992).
[CrossRef]

1991 (2)

1990 (2)

Y. Chen, A. W. Snyder, D. J. Mitchell, Electron. Lett. 26, 77 (1990).
[CrossRef]

N. Finlayson, G. I. Stegeman, Appl. Phys. Lett. 56, 2276 (1990).
[CrossRef]

1989 (1)

1988 (2)

1987 (1)

1982 (1)

S. M. Jensen, IEEE J. Quantum Electron. QE-18, 1580 (1982).
[CrossRef]

Aceves, A. B.

Chen, Y.

Y. Chen, A. W. Snyder, D. J. Mitchell, Electron. Lett. 26, 77 (1990).
[CrossRef]

Chernikov, S. V.

Christodoulides, D. N.

Claude, Ch.

Ch. Claude, Yu. S. Kivshar, O. Kluth, K. H. Spatschek, Phys. Rev. B 47, 14228 (1993).
[CrossRef]

Cronin-Golomb, M.

De Angelis, C.

Dianov, E. M.

Finlayson, N.

N. Finlayson, G. I. Stegeman, Appl. Phys. Lett. 56, 2276 (1990).
[CrossRef]

Jensen, S. M.

S. M. Jensen, IEEE J. Quantum Electron. QE-18, 1580 (1982).
[CrossRef]

Joseph, R. I.

Kivshar, Yu. S.

Ch. Claude, Yu. S. Kivshar, O. Kluth, K. H. Spatschek, Phys. Rev. B 47, 14228 (1993).
[CrossRef]

Kluth, O.

Ch. Claude, Yu. S. Kivshar, O. Kluth, K. H. Spatschek, Phys. Rev. B 47, 14228 (1993).
[CrossRef]

Królikowski, W.

Kuehl, H. H.

Lederer, F.

Mamyshev, P. V.

Marcuse, D.

D. Marcuse, Light Transmission Optics, 2nd ed. (Van Nostrand Reinhold, New York, 1982), pp. 429–434.

Mitchell, D. J.

Y. Chen, A. W. Snyder, D. J. Mitchell, Electron. Lett. 26, 77 (1990).
[CrossRef]

Muschall, R.

R. Muschall, C. Schmidt-Hattenberger, F. Lederer, Opt. Lett. 19, 323 (1994).
[CrossRef] [PubMed]

C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, F. Lederer, Opt. Commun. 89, 473 (1992).
[CrossRef]

Prokhorov, A. M.

Rubenchik, A. M.

Schmidt-Hattenberger, C.

Snyder, A. W.

Y. Chen, A. W. Snyder, D. J. Mitchell, Electron. Lett. 26, 77 (1990).
[CrossRef]

Soto-Crespo, J. M.

J. M. Soto-Crespo, E. M. Wright, J. Appl. Phys. 70, 7240 (1991).
[CrossRef]

Spatschek, K. H.

Ch. Claude, Yu. S. Kivshar, O. Kluth, K. H. Spatschek, Phys. Rev. B 47, 14228 (1993).
[CrossRef]

Stegeman, G. I.

N. Finlayson, G. I. Stegeman, Appl. Phys. Lett. 56, 2276 (1990).
[CrossRef]

Tajima, K.

Trillo, S.

Trutschel, U.

Turitsyn, S. K.

Wabnitz, S.

Wright, E. M.

J. M. Soto-Crespo, E. M. Wright, J. Appl. Phys. 70, 7240 (1991).
[CrossRef]

Appl. Phys. Lett. (1)

N. Finlayson, G. I. Stegeman, Appl. Phys. Lett. 56, 2276 (1990).
[CrossRef]

Electron. Lett. (1)

Y. Chen, A. W. Snyder, D. J. Mitchell, Electron. Lett. 26, 77 (1990).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. M. Jensen, IEEE J. Quantum Electron. QE-18, 1580 (1982).
[CrossRef]

J. Appl. Phys. (1)

J. M. Soto-Crespo, E. M. Wright, J. Appl. Phys. 70, 7240 (1991).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, F. Lederer, Opt. Commun. 89, 473 (1992).
[CrossRef]

Opt. Lett. (8)

Phys. Rev. B (1)

Ch. Claude, Yu. S. Kivshar, O. Kluth, K. H. Spatschek, Phys. Rev. B 47, 14228 (1993).
[CrossRef]

Other (1)

D. Marcuse, Light Transmission Optics, 2nd ed. (Van Nostrand Reinhold, New York, 1982), pp. 429–434.

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Figures (4)

Fig. 1
Fig. 1

Compression of a spatial solitary wave in a waveguide array with a longitudinally decreasing coupling coefficient. The dotted curve is an approximate solution given by Eq. (4).

Fig. 2
Fig. 2

Amplitude distributions at Z = 20 for three different initial phases; three cores (n = 0, ±1) are excited at Z = 0. (a) The coupling coefficient is constant, K(Z) = 1; (b) the coupling coefficient is longitudinally decreasing, K(Z) = exp(−0.05Z).

Fig. 3
Fig. 3

Normalized output power (Z = 20) at each core versus the initial phase; three cores (n = 0, ±1) are excited at Z = 0. (a) The coupling coefficient is constant, K(Z) = 1; (b) the coupling coefficient is longitudinally decreasing, K(Z) = exp(−0.05Z).

Fig. 4
Fig. 4

Output power (Z = 30) at each core versus the initial amplitude A; two cores are excited at Z = 0. (a) The coupling coefficient is constant, K(Z) = 1; (b) the coupling coefficient is longitudinally decreasing, K(Z) = exp(−0.05Z).

Equations (7)

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d a n d z = i γ a n 2 a n + i k ( z ) ( a n - 1 + a n + 1 ) , n = 0 , ± 1 , ± 2 , ,
d b n d Z = i b n 2 b n + i K ( Z ) ( b n - 1 + b n + 1 ) ,
i q Z + K ( Z ) Δ 2 2 q X 2 + q 2 q = 0
b n ( Z ) = q ( X = n Δ , Z ) exp [ 2 i 0 z K ( Z ) d Z ] .
b n ( Z ) = A K ( Z ) sech [ A n 2 K ( Z ) ] × exp { i 0 Z [ A 2 2 K ( Z ) + 2 K ( Z ) ] d Z }
b 0 ( 0 ) = A ,             b 1 ( 0 ) = b - 1 * ( 0 ) = A sech ( A / 2 ) exp ( i ϕ ) , b n ( 0 ) = 0 ( n 0 , ± 1 ) ,
b 1 ( 0 ) = B ,             b 0 ( 0 ) = A ,             b n ( 0 ) = 0 ( n 0 , 1 ) ,

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