Abstract

Solutions of coupled-mode equations describing intensity-induced Bragg coupling of counterpropagating modes in a nonlinear distributed-feedback structure may become spatially unstable. Instability leads to nonpassing plateaus in the intensity transmission characteristics. This induces strong optical limiting action in the transmission mode and lower thresholding in the reflection mode.

© 1987 Optical Society of America

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References

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  1. For a review see G. I. Stegeman, C. T. Seaton, J. Appl. Phys. 58, R57 (1985).
    [Crossref]
  2. H. G. Winful, J. H. Marburger, E. Garmire, Appl. Phys. Lett. 35, 379 (1979).
    [Crossref]
  3. C. T. Seaton, G. I. Stegeman, H. G. Winful, Opt. Eng. 24, 593 (1985);G. I. Stegeman, C. Liao, H. G. Winful, in Optical Bistability IIC. M. Bowden, H. M. Gibbs, S. L. McCall, eds. (Plenum, New York, 1984), p. 389.
    [Crossref]
  4. F. Delyon, Y. E. Lévy, B. Souillard, Phys. Rev. Lett. 57, 2010 (1986).
    [Crossref] [PubMed]
  5. Define as a spatial eigensolution of the DFB structure a pair of counterpropagating waves that maintain their initial amplitude and relative phase constant throughout the medium.
  6. S. Wabnitz, G. Gregori, Opt. Commun. 59, 72 (1986).
    [Crossref]
  7. B. Daino, G. Gregori, S. Wabnitz, Opt. Lett. 11, 42 (1986);H. G. Winful, Opt. Lett. 11, 33 (1986);S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, G. I. Stegeman, Appl. Phys. Lett. 49, 1224 (1986).
    [Crossref] [PubMed]
  8. G. I. Stegeman, IEEE J. Quantum Electron. QE-18, 1610 (1982).
    [Crossref]
  9. P. F. Byrd, M. D. Friedman, Handbook of Elliptic Integrals for Engineers and Scientists (Springer-Verlag, Berlin, 1971).
    [Crossref]
  10. Note that once the rotating-wave approximation is removed, integrability of coupled mode equations is lost. This may lead to chaoticity in evolutions located in proximity to the separatrix of Eqs. (2); see S. Wabnitz, Phys. Rev. Lett. 58, 1415 (1987).
    [Crossref] [PubMed]

1987 (1)

Note that once the rotating-wave approximation is removed, integrability of coupled mode equations is lost. This may lead to chaoticity in evolutions located in proximity to the separatrix of Eqs. (2); see S. Wabnitz, Phys. Rev. Lett. 58, 1415 (1987).
[Crossref] [PubMed]

1986 (3)

1985 (2)

C. T. Seaton, G. I. Stegeman, H. G. Winful, Opt. Eng. 24, 593 (1985);G. I. Stegeman, C. Liao, H. G. Winful, in Optical Bistability IIC. M. Bowden, H. M. Gibbs, S. L. McCall, eds. (Plenum, New York, 1984), p. 389.
[Crossref]

For a review see G. I. Stegeman, C. T. Seaton, J. Appl. Phys. 58, R57 (1985).
[Crossref]

1982 (1)

G. I. Stegeman, IEEE J. Quantum Electron. QE-18, 1610 (1982).
[Crossref]

1979 (1)

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

Byrd, P. F.

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

Daino, B.

Delyon, F.

F. Delyon, Y. E. Lévy, B. Souillard, Phys. Rev. Lett. 57, 2010 (1986).
[Crossref] [PubMed]

Friedman, M. D.

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

Garmire, E.

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

Gregori, G.

Lévy, Y. E.

F. Delyon, Y. E. Lévy, B. Souillard, Phys. Rev. Lett. 57, 2010 (1986).
[Crossref] [PubMed]

Marburger, J. H.

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

Seaton, C. T.

For a review see G. I. Stegeman, C. T. Seaton, J. Appl. Phys. 58, R57 (1985).
[Crossref]

C. T. Seaton, G. I. Stegeman, H. G. Winful, Opt. Eng. 24, 593 (1985);G. I. Stegeman, C. Liao, H. G. Winful, in Optical Bistability IIC. M. Bowden, H. M. Gibbs, S. L. McCall, eds. (Plenum, New York, 1984), p. 389.
[Crossref]

Souillard, B.

F. Delyon, Y. E. Lévy, B. Souillard, Phys. Rev. Lett. 57, 2010 (1986).
[Crossref] [PubMed]

Stegeman, G. I.

C. T. Seaton, G. I. Stegeman, H. G. Winful, Opt. Eng. 24, 593 (1985);G. I. Stegeman, C. Liao, H. G. Winful, in Optical Bistability IIC. M. Bowden, H. M. Gibbs, S. L. McCall, eds. (Plenum, New York, 1984), p. 389.
[Crossref]

For a review see G. I. Stegeman, C. T. Seaton, J. Appl. Phys. 58, R57 (1985).
[Crossref]

G. I. Stegeman, IEEE J. Quantum Electron. QE-18, 1610 (1982).
[Crossref]

Wabnitz, S.

Note that once the rotating-wave approximation is removed, integrability of coupled mode equations is lost. This may lead to chaoticity in evolutions located in proximity to the separatrix of Eqs. (2); see S. Wabnitz, Phys. Rev. Lett. 58, 1415 (1987).
[Crossref] [PubMed]

S. Wabnitz, G. Gregori, Opt. Commun. 59, 72 (1986).
[Crossref]

B. Daino, G. Gregori, S. Wabnitz, Opt. Lett. 11, 42 (1986);H. G. Winful, Opt. Lett. 11, 33 (1986);S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, G. I. Stegeman, Appl. Phys. Lett. 49, 1224 (1986).
[Crossref] [PubMed]

Winful, H. G.

C. T. Seaton, G. I. Stegeman, H. G. Winful, Opt. Eng. 24, 593 (1985);G. I. Stegeman, C. Liao, H. G. Winful, in Optical Bistability IIC. M. Bowden, H. M. Gibbs, S. L. McCall, eds. (Plenum, New York, 1984), p. 389.
[Crossref]

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

Appl. Phys. Lett. (1)

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

IEEE J. Quantum Electron. (1)

G. I. Stegeman, IEEE J. Quantum Electron. QE-18, 1610 (1982).
[Crossref]

J. Appl. Phys. (1)

For a review see G. I. Stegeman, C. T. Seaton, J. Appl. Phys. 58, R57 (1985).
[Crossref]

Opt. Commun. (1)

S. Wabnitz, G. Gregori, Opt. Commun. 59, 72 (1986).
[Crossref]

Opt. Eng. (1)

C. T. Seaton, G. I. Stegeman, H. G. Winful, Opt. Eng. 24, 593 (1985);G. I. Stegeman, C. Liao, H. G. Winful, in Optical Bistability IIC. M. Bowden, H. M. Gibbs, S. L. McCall, eds. (Plenum, New York, 1984), p. 389.
[Crossref]

Opt. Lett. (1)

Phys. Rev. Lett. (2)

F. Delyon, Y. E. Lévy, B. Souillard, Phys. Rev. Lett. 57, 2010 (1986).
[Crossref] [PubMed]

Note that once the rotating-wave approximation is removed, integrability of coupled mode equations is lost. This may lead to chaoticity in evolutions located in proximity to the separatrix of Eqs. (2); see S. Wabnitz, Phys. Rev. Lett. 58, 1415 (1987).
[Crossref] [PubMed]

Other (2)

Define as a spatial eigensolution of the DFB structure a pair of counterpropagating waves that maintain their initial amplitude and relative phase constant throughout the medium.

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

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Figures (4)

Fig. 1
Fig. 1

Projection onto the (s3, s0) plane of the trajectories representing the field distributions along a DFB structure for ΔβL = −10, KL = 2: (a) s1 = 2.95; (b) s1 = 3.1 [solid lines indicate that s0(1) = s1].

Fig. 2
Fig. 2

Transmitted versus incident normalized powers QL|a+|2 for different detunings δ.

Fig. 3
Fig. 3

Normalized cutoff power QPc/(−Δβ) behavior versus detuning −δ.

Fig. 4
Fig. 4

Same as in Fig. 2, with ΔβL = −10 and KL = 4.

Equations (6)

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i d a + / d z = K exp ( 2 i Δ β z ) a + Q ( | a + | 2 + 2 | a | 2 ) a + , i d a / d z = K exp ( 2 i Δ β z ) a + + Q ( 2 | a + | 2 + | a | 2 ) a ,
S 0 = | a + | 2 + | a | 2 , S 1 = | a + | 2 | a | 2 , S 2 = 2 Re [ a + a * exp ( i Δ β z ) ] , S 3 = 2 Im [ a + a * exp ( i Δ β z ) ] .
s 0 = 2 K L s 3 , s 1 = 0 , s 2 = 2 Δ β L s 3 3 s 0 s 3 , s 3 = 2 K L s 0 + 2 Δ β L s 2 + 3 s 0 s 2 ,
s 0 + ( 9 / 2 ) s 0 3 + 9 Δ β L s 0 2 [ 3 Γ / 2 + 4 L 2 ( K 2 Δ β 2 ) ] s 0 Δ β L Γ = 0 .
s 3 = 0 , 2 L ( K s 0 + Δ β s 2 ) + 3 s 0 s 2 = 0 .
P b ( 2 K / 3 Q ) ( δ 2 / 3 1 ) 3 / 2 ,

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