Abstract

We show that λ/4-shifted distributed-feedback nonlinear devices can be used as an all-optical switch at relatively low input intensities. The λ/4 shift opens a narrow transmission window whose peak position within the stop band depends on the input intensity, a feature that can be used for low-power optical switching. The nonlinear coupled-mode approach is used to analyze the stationary operating regime of such a device and determine the transmittivity as a function of the input intensity. A closed-form solution, rather than a numerical one, is found for what we believe is the first time.

© 1994 Optical Society of America

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  1. H. G. Winful, J. H. Marburger, E. Garmire, Appl. Phys. Lett. 35, 379 (1979).
    [CrossRef]
  2. W. Chen, D. L. Mills, Phys. Rev. B 36,6269 (1987).
    [CrossRef]
  3. C. Martijn de Sterke, J. E. Sipe, Phys. Rev. A 39, 5163 (1989).
    [CrossRef]
  4. C. Martijn de Sterke, J. E. Sipe, Phys. Rev. A 42, 2858 (1990).
    [CrossRef]
  5. H. G. Winful, Appl. Phys. Lett. 46, 527 (1985).
    [CrossRef]
  6. M. Okuda, K. Onaka, Jpn. J. Appl. Phys. 16, 769 (1977).
    [CrossRef]
  7. J. He, M. Cada, Appl. Phys. Lett. 63, 866 (1993).
    [CrossRef]
  8. N. D. Sankey, D. F. Prelewitz, T. G. Brown, Appl. Phys. Lett. 60, 1427 (1992).
    [CrossRef]
  9. H. G. Winful, G. D. Cooperman, Appl. Phys. Lett. 40, 298 (1982).
    [CrossRef]
  10. C. Martijn de Sterke, J. E. Sipe, Opt. Lett. 18,269 (1993).
    [CrossRef]
  11. H. A. Haus, Opt. Lett. 15, 1134 (1992).
    [CrossRef]
  12. H. A. Haus, C. V. Shank, IEEE J. Quantum Electron. QE-12, 532 (1976).
    [CrossRef]
  13. S. Akiba, M. Usami, K. Utaka, J. Lightwave Technol. LT-5, 1564 (1987).
    [CrossRef]
  14. M. Yamada, K. Sakuda, Appl. Opt. 26,3474 (1987).
    [CrossRef] [PubMed]
  15. H. G. Winful, G. I. Stegeman, Proc. Soc. Photo-Opt. Instrum. Eng. 517, 214 (1984).
  16. A. Kogelnik, C. V. Shank, J. Appl. Phys. 43, 2327 (1972).
    [CrossRef]
  17. P. F. Byrd, M. D. Friedman, Handbook of ElliptiC Integrals for Engineers and Scientists (Springer-Verlag, Berlin, 1971).
  18. S. Radic, N. George, Opt. Lett. 19, 1064 (1994).
    [CrossRef] [PubMed]

1994 (1)

1993 (2)

1992 (2)

N. D. Sankey, D. F. Prelewitz, T. G. Brown, Appl. Phys. Lett. 60, 1427 (1992).
[CrossRef]

H. A. Haus, Opt. Lett. 15, 1134 (1992).
[CrossRef]

1990 (1)

C. Martijn de Sterke, J. E. Sipe, Phys. Rev. A 42, 2858 (1990).
[CrossRef]

1989 (1)

C. Martijn de Sterke, J. E. Sipe, Phys. Rev. A 39, 5163 (1989).
[CrossRef]

1987 (3)

S. Akiba, M. Usami, K. Utaka, J. Lightwave Technol. LT-5, 1564 (1987).
[CrossRef]

M. Yamada, K. Sakuda, Appl. Opt. 26,3474 (1987).
[CrossRef] [PubMed]

W. Chen, D. L. Mills, Phys. Rev. B 36,6269 (1987).
[CrossRef]

1985 (1)

H. G. Winful, Appl. Phys. Lett. 46, 527 (1985).
[CrossRef]

1984 (1)

H. G. Winful, G. I. Stegeman, Proc. Soc. Photo-Opt. Instrum. Eng. 517, 214 (1984).

1982 (1)

H. G. Winful, G. D. Cooperman, Appl. Phys. Lett. 40, 298 (1982).
[CrossRef]

1979 (1)

H. G. Winful, J. H. Marburger, E. Garmire, Appl. Phys. Lett. 35, 379 (1979).
[CrossRef]

1977 (1)

M. Okuda, K. Onaka, Jpn. J. Appl. Phys. 16, 769 (1977).
[CrossRef]

1976 (1)

H. A. Haus, C. V. Shank, IEEE J. Quantum Electron. QE-12, 532 (1976).
[CrossRef]

1972 (1)

A. Kogelnik, C. V. Shank, J. Appl. Phys. 43, 2327 (1972).
[CrossRef]

Akiba, S.

S. Akiba, M. Usami, K. Utaka, J. Lightwave Technol. LT-5, 1564 (1987).
[CrossRef]

Brown, T. G.

N. D. Sankey, D. F. Prelewitz, T. G. Brown, Appl. Phys. Lett. 60, 1427 (1992).
[CrossRef]

Byrd, P. F.

P. F. Byrd, M. D. Friedman, Handbook of ElliptiC Integrals for Engineers and Scientists (Springer-Verlag, Berlin, 1971).

Cada, M.

J. He, M. Cada, Appl. Phys. Lett. 63, 866 (1993).
[CrossRef]

Chen, W.

W. Chen, D. L. Mills, Phys. Rev. B 36,6269 (1987).
[CrossRef]

Cooperman, G. D.

H. G. Winful, G. D. Cooperman, Appl. Phys. Lett. 40, 298 (1982).
[CrossRef]

Friedman, M. D.

P. F. Byrd, M. D. Friedman, Handbook of ElliptiC Integrals for Engineers and Scientists (Springer-Verlag, Berlin, 1971).

Garmire, E.

H. G. Winful, J. H. Marburger, E. Garmire, Appl. Phys. Lett. 35, 379 (1979).
[CrossRef]

George, N.

Haus, H. A.

H. A. Haus, Opt. Lett. 15, 1134 (1992).
[CrossRef]

H. A. Haus, C. V. Shank, IEEE J. Quantum Electron. QE-12, 532 (1976).
[CrossRef]

He, J.

J. He, M. Cada, Appl. Phys. Lett. 63, 866 (1993).
[CrossRef]

Kogelnik, A.

A. Kogelnik, C. V. Shank, J. Appl. Phys. 43, 2327 (1972).
[CrossRef]

Marburger, J. H.

H. G. Winful, J. H. Marburger, E. Garmire, Appl. Phys. Lett. 35, 379 (1979).
[CrossRef]

Martijn de Sterke, C.

C. Martijn de Sterke, J. E. Sipe, Opt. Lett. 18,269 (1993).
[CrossRef]

C. Martijn de Sterke, J. E. Sipe, Phys. Rev. A 42, 2858 (1990).
[CrossRef]

C. Martijn de Sterke, J. E. Sipe, Phys. Rev. A 39, 5163 (1989).
[CrossRef]

Mills, D. L.

W. Chen, D. L. Mills, Phys. Rev. B 36,6269 (1987).
[CrossRef]

Okuda, M.

M. Okuda, K. Onaka, Jpn. J. Appl. Phys. 16, 769 (1977).
[CrossRef]

Onaka, K.

M. Okuda, K. Onaka, Jpn. J. Appl. Phys. 16, 769 (1977).
[CrossRef]

Prelewitz, D. F.

N. D. Sankey, D. F. Prelewitz, T. G. Brown, Appl. Phys. Lett. 60, 1427 (1992).
[CrossRef]

Radic, S.

Sakuda, K.

Sankey, N. D.

N. D. Sankey, D. F. Prelewitz, T. G. Brown, Appl. Phys. Lett. 60, 1427 (1992).
[CrossRef]

Shank, C. V.

H. A. Haus, C. V. Shank, IEEE J. Quantum Electron. QE-12, 532 (1976).
[CrossRef]

A. Kogelnik, C. V. Shank, J. Appl. Phys. 43, 2327 (1972).
[CrossRef]

Sipe, J. E.

C. Martijn de Sterke, J. E. Sipe, Opt. Lett. 18,269 (1993).
[CrossRef]

C. Martijn de Sterke, J. E. Sipe, Phys. Rev. A 42, 2858 (1990).
[CrossRef]

C. Martijn de Sterke, J. E. Sipe, Phys. Rev. A 39, 5163 (1989).
[CrossRef]

Stegeman, G. I.

H. G. Winful, G. I. Stegeman, Proc. Soc. Photo-Opt. Instrum. Eng. 517, 214 (1984).

Usami, M.

S. Akiba, M. Usami, K. Utaka, J. Lightwave Technol. LT-5, 1564 (1987).
[CrossRef]

Utaka, K.

S. Akiba, M. Usami, K. Utaka, J. Lightwave Technol. LT-5, 1564 (1987).
[CrossRef]

Winful, H. G.

H. G. Winful, Appl. Phys. Lett. 46, 527 (1985).
[CrossRef]

H. G. Winful, G. I. Stegeman, Proc. Soc. Photo-Opt. Instrum. Eng. 517, 214 (1984).

H. G. Winful, G. D. Cooperman, Appl. Phys. Lett. 40, 298 (1982).
[CrossRef]

H. G. Winful, J. H. Marburger, E. Garmire, Appl. Phys. Lett. 35, 379 (1979).
[CrossRef]

Yamada, M.

Appl. Opt. (1)

Appl. Phys. Lett. (5)

H. G. Winful, J. H. Marburger, E. Garmire, Appl. Phys. Lett. 35, 379 (1979).
[CrossRef]

J. He, M. Cada, Appl. Phys. Lett. 63, 866 (1993).
[CrossRef]

N. D. Sankey, D. F. Prelewitz, T. G. Brown, Appl. Phys. Lett. 60, 1427 (1992).
[CrossRef]

H. G. Winful, G. D. Cooperman, Appl. Phys. Lett. 40, 298 (1982).
[CrossRef]

H. G. Winful, Appl. Phys. Lett. 46, 527 (1985).
[CrossRef]

IEEE J. Quantum Electron. (1)

H. A. Haus, C. V. Shank, IEEE J. Quantum Electron. QE-12, 532 (1976).
[CrossRef]

J. Appl. Phys. (1)

A. Kogelnik, C. V. Shank, J. Appl. Phys. 43, 2327 (1972).
[CrossRef]

J. Lightwave Technol. (1)

S. Akiba, M. Usami, K. Utaka, J. Lightwave Technol. LT-5, 1564 (1987).
[CrossRef]

Jpn. J. Appl. Phys. (1)

M. Okuda, K. Onaka, Jpn. J. Appl. Phys. 16, 769 (1977).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (2)

C. Martijn de Sterke, J. E. Sipe, Phys. Rev. A 39, 5163 (1989).
[CrossRef]

C. Martijn de Sterke, J. E. Sipe, Phys. Rev. A 42, 2858 (1990).
[CrossRef]

Phys. Rev. B (1)

W. Chen, D. L. Mills, Phys. Rev. B 36,6269 (1987).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

H. G. Winful, G. I. Stegeman, Proc. Soc. Photo-Opt. Instrum. Eng. 517, 214 (1984).

Other (1)

P. F. Byrd, M. D. Friedman, Handbook of ElliptiC Integrals for Engineers and Scientists (Springer-Verlag, Berlin, 1971).

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Figures (3)

Fig. 1
Fig. 1

DFB structure with the phase shift ΔΩ at the center located at z = 0. The sinusoidal curve represents the periodic linear refractive index nL(z). Normalized intensities I, M and T are defined in the text.

Fig. 2
Fig. 2

Transmittivity (T/I0) versus I0 for the structure of Fig. 1 when ΔΩ = π and Δβ = 0. Each curve corresponds to a different coupling parameter κL, varied between 1.5 and 3.

Fig. 3
Fig. 3

(a) Variation of T/I0 with the Bragg detuning ΔβL for three values of the normalized output flux T and for κL = 2. (b) Variation of T/I0 with ΔβL for four values of the normalized input I0 and κL = 2.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

n L ( z ) = n 0 + Δ n cos ( 2 β B z + Ω ) , Ω = { Ω 1 , z < 0 Ω 2 , z 0 ,
E ( z ) = E + ( z ) exp ( i β z ) + E - ( z ) exp ( - i β z ) .
d E + d z = i κ E - exp [ - i ( 2 Δ β z - Ω ) ] + i γ ( E + 2 + 2 E - 2 ) E + ,
d E - d z = - i κ E + exp [ i ( 2 Δ β z - Ω ) ] - i γ ( 2 E + 2 + E - 2 ) E - ,
Γ i = E + E - cos Ψ i + ( 2 Δ β + 3 γ E - 2 ) E + 2 / ( 2 κ ) ,
E i T 2 = E + 2 - E - 2 ,
E 1 T 2 = E 2 T 2 = E T 2 = E + ( L ) 2 .
cos Ψ 2 ( 0 ) = - 1 κ L ( M - T M ) 1 / 2 ( 2 M + Δ β L ) .
Γ 1 = I c [ 4 M ( M - T ) + ( Δ β L ) ( 2 M - T ) ] / κ L .
( L 2 d I d z ) 2 = ( κ L ) 2 I ( I - T ) - [ 4 M ( M - T ) + ( Δ β L ) ( 2 M - T ) - I ( Δ β L ) - 2 I ( I - T ) ] 2 .
M = T [ 1 + n d ( u , k ) ] / 2 ,
I i = T 2 [ 1 ± k k ( x ± x + k 2 ) 1 / 2 ] , i = 1 , 2 , 3 , 4 ,
I 0 = I 3 + ( I 2 - I 3 ) ( I 1 - I 3 ) ( I 1 - I 3 ) - ( I 1 - I 2 ) s n 2 [ F ( φ 0 , k 0 ) - 4 / g 0 , k 0 ] ,

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