Abstract

We show that, in vectorial intracavity second-harmonic generation, symmetry breaking occurs if the input amplitude exceeds a critical value. The resulting asymmetric stationary solutions are characterized by a second harmonic that is independent of the input amplitude. The solutions can destabilize through Hopf bifurcations, leading to self-oscillations with pronounced antiphase dynamics. We demonstrate that symmetry breaking can be exploited for flip-flop operation.

© 1998 Optical Society of America

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References

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    [CrossRef]

1997 (3)

C. Etrich, U. Peschel, and F. Lederer, Phys. Rev. E 56, 4803 (1997).
[CrossRef]

C. Etrich, U. Peschel, and F. Lederer, Phys. Rev. Lett. 79, 2454 (1997).
[CrossRef]

M. Haelterman, S. Trillo, and S. Wabnitz, J. Opt. Soc. Am. B 11, 447 (1997).

1996 (2)

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

A. Kobyakov and F. Lederer, Phys. Rev. A 54, 3455 (1996).
[CrossRef] [PubMed]

1995 (2)

W. E. Toruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef]

R. Reinisch, E. Popov, and M. Nevière, Opt. Lett. 20, 854 (1995).
[CrossRef] [PubMed]

1994 (1)

1992 (2)

H. Kawaguchi and T. Irie, Electron. Lett. 28, 1645 (1992).
[CrossRef]

T. Peschel and F. Lederer, Phys. Rev. B 46, 7632 (1992).
[CrossRef]

1990 (1)

1989 (1)

1988 (1)

Etrich, C.

C. Etrich, U. Peschel, and F. Lederer, Phys. Rev. Lett. 79, 2454 (1997).
[CrossRef]

C. Etrich, U. Peschel, and F. Lederer, Phys. Rev. E 56, 4803 (1997).
[CrossRef]

Haelterman, M.

M. Haelterman, S. Trillo, and S. Wabnitz, J. Opt. Soc. Am. B 11, 447 (1997).

M. Haelterman and P. Mandel, Opt. Lett. 15, 1412 (1990).
[CrossRef] [PubMed]

Hagan, D. J.

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

W. E. Toruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef]

Henking, R.

Irie, T.

H. Kawaguchi and T. Irie, Electron. Lett. 28, 1645 (1992).
[CrossRef]

Kawaguchi, H.

H. Kawaguchi and T. Irie, Electron. Lett. 28, 1645 (1992).
[CrossRef]

Kobyakov, A.

A. Kobyakov and F. Lederer, Phys. Rev. A 54, 3455 (1996).
[CrossRef] [PubMed]

Kürz, P.

Lederer, F.

C. Etrich, U. Peschel, and F. Lederer, Phys. Rev. Lett. 79, 2454 (1997).
[CrossRef]

C. Etrich, U. Peschel, and F. Lederer, Phys. Rev. E 56, 4803 (1997).
[CrossRef]

A. Kobyakov and F. Lederer, Phys. Rev. A 54, 3455 (1996).
[CrossRef] [PubMed]

T. Peschel and F. Lederer, Phys. Rev. B 46, 7632 (1992).
[CrossRef]

Mandel, P.

Menyuk, C. R.

W. E. Toruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef]

Mlynek, J.

Nevière, M.

Otsuka, K.

Paschotta, R.

Peschel, T.

T. Peschel and F. Lederer, Phys. Rev. B 46, 7632 (1992).
[CrossRef]

Peschel, U.

C. Etrich, U. Peschel, and F. Lederer, Phys. Rev. Lett. 79, 2454 (1997).
[CrossRef]

C. Etrich, U. Peschel, and F. Lederer, Phys. Rev. E 56, 4803 (1997).
[CrossRef]

Popov, E.

Regener, R.

Reinisch, R.

Schiller, S.

Sohler, W.

Stegeman, G. I.

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

W. E. Toruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef]

Torner, L.

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

W. E. Toruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef]

Toruellas, W. E.

W. E. Toruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef]

Trillo, S.

M. Haelterman, S. Trillo, and S. Wabnitz, J. Opt. Soc. Am. B 11, 447 (1997).

Van Stryland, E. W.

W. E. Toruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef]

Wabnitz, S.

M. Haelterman, S. Trillo, and S. Wabnitz, J. Opt. Soc. Am. B 11, 447 (1997).

Wang, Z.

W. E. Toruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef]

Electron. Lett. (1)

H. Kawaguchi and T. Irie, Electron. Lett. 28, 1645 (1992).
[CrossRef]

J. Opt. Soc. Am. B (2)

M. Haelterman, S. Trillo, and S. Wabnitz, J. Opt. Soc. Am. B 11, 447 (1997).

R. Regener and W. Sohler, J. Opt. Soc. Am. B 5, 267 (1988).
[CrossRef]

Opt. Lett. (4)

Opt. Quantum Electron. (1)

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

Phys. Rev. A (1)

A. Kobyakov and F. Lederer, Phys. Rev. A 54, 3455 (1996).
[CrossRef] [PubMed]

Phys. Rev. B (1)

T. Peschel and F. Lederer, Phys. Rev. B 46, 7632 (1992).
[CrossRef]

Phys. Rev. E (1)

C. Etrich, U. Peschel, and F. Lederer, Phys. Rev. E 56, 4803 (1997).
[CrossRef]

Phys. Rev. Lett. (2)

C. Etrich, U. Peschel, and F. Lederer, Phys. Rev. Lett. 79, 2454 (1997).
[CrossRef]

W. E. Toruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Symmetry-breaking and Hopf bifurcations of the transmitted amplitudes versus the incident field E for the balanced case ΔA=2, ΔB=1.5, γ=1. Solid (dashed) curves, stable (unstable) plane-wave solutions; filled (open) circles, maximum amplitude of stable (unstable) periodic solutions; open squares, symmetry-breaking bifurcations; filled squares, Hopf bifurcations.

Fig. 2
Fig. 2

Self-oscillations with antiphase dynamics and flip-flop operation for the balanced case ΔA=2, ΔB=1.5, γ=1, E=7.5, δE=0. A switching pulse was added to E2 at T=0. Thin curve, A1; thick curve, A2.

Fig. 3
Fig. 3

Hopf bifurcations of the transmitted amplitude (one of the FH's) versus the incident field E for a small imbalance (δE=0.05; the other parameters and graphical conventions are as in Fig.  1).

Equations (7)

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

τFHω=τFH0ωFH+i/TFH-ω, τSHω=τSH0ωSH+i/TSH-ω.
iddt+ωFH-ωin+iTFHaj+χFHeffa3-j*b=τFH0ej, j=1, 2, iddt+ωSH-2ωin+iTSHb+χSHeffa1a2=0,
T=t/TFH, Aj=χFHeffχSHeffaj, Ej=τFH0χFHeffχSHeffej, B=χFHeffb, j=1, 2,
iddT+ΔA+iAj+A3-j*B=Ej, iddT+ΔB+iγB+A1A2=0, j=1, 2,
ΔA+i-A202ΔB+iγA10=E1, ΔA+i-A102ΔB+iγA20=E2.
ΔA2+1-I1I2ΔB2+γ2I1-I2=0.
I1/2=E22ΔA2+1+ΔAΔB-γ±E22ΔA2+1+ΔAΔB-γ2-ΔA2+1ΔB2+γ21/2,

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