Abstract

The elliptically polarized nonlinear beam propagation in a two-dimensional optical guided-wave system that contains isotropic Kerr media is solved numerically by using the finite-element method. Computed results for the nonlinear substrate exhibit novel transverse effects, such as spatial modulational instabilities for solitons emitted from the film. Since soliton emission can be interpreted in terms of self-induced Čerenkov radiation, these instabilities can be classified as Čerenkov instabilities. The sensitivity of the beam propagation to the initial state of polarization suggests the possibility of constructing new photonic devices.

© 1990 Optical Society of America

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    [CrossRef]
  3. G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanori, C. T. Seaton, “Third order nonlinear integrated optics,” IEEE J. Lightwave Technol. 6, 953–970 (1988).
    [CrossRef]
  4. Y. Silberberg, “Photonic switching devices,” Opt. News 15 (2), 7–12 (1989).
    [CrossRef]
  5. K. Ikeda, “Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system,” Opt. Commun. 30, 257–261 (1979).
    [CrossRef]
  6. K. Ikeda, H. Daido, O. Akimoto, “Optical turbulence: chaotic behavior of transmitted light from a ring cavity,” Phys. Rev. Lett. 45, 709–712 (1980).
    [CrossRef]
  7. K. Ikeda, O. Akimoto, “Instability leading to periodic and chaotic self-pulsations in a bistable optical cavity,” Phys. Rev. Lett. 48, 617–620 (1982).
    [CrossRef]
  8. H. G. Winful, “Self-induced polarization changes in birefringent optical fibers,” Appl. Phys. Lett. 47, 213–215 (1985).
    [CrossRef]
  9. H. G. Winful, “Polarization instabilities in birefringent nonlinear media: application to fiber-optic devices,” Opt. Lett. 11, 33–35 (1986).
    [CrossRef] [PubMed]
  10. B. Daino, G. Gregori, S. Wabnitz, “New all-optical devices based on third-order nonlinearity of birefringent fibers,” Opt. Lett. 11, 42–44 (1986).
    [CrossRef] [PubMed]
  11. A. Vatarescu, “Intensity discrimination through nonlinear power coupling in birefringent fibers,” Appl. Phys. Lett. 49, 61–63 (1986).
    [CrossRef]
  12. S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, G. I. Stegeman, “Experimental observations of polarization instability in a birefringent optical fiber,” Appl. Phys. Lett. 49, 1224–1226 (1986).
    [CrossRef]
  13. S. Wabnitz, “Spatial chaos in the polarization for a birefringent optical fiber with periodic coupling,” Phys. Rev. Lett. 58, 1415–1418 (1987).
    [CrossRef] [PubMed]
  14. A. Mecozzi, S. Trillo, S. Wabnitz, B. Daino, “All-optical switching and intensity discrimination by polarization instability in periodically twisted fiber filters,” Opt. Lett. 12, 275–277 (1987).
    [CrossRef] [PubMed]
  15. E. Caglioti, S. Trillo, S. Wabnitz, “Stochastic polarization instability: limitation to optical switching using fibers with modulated birefringence,” Opt. Lett. 12, 1044–1046 (1987).
    [CrossRef] [PubMed]
  16. Y. Silberberg, I. Bar-Joseph, “Instabilities, self-oscillation, and chaos in a simple nonlinear optical interaction,” Phys. Rev. Lett. 48, 1541–1543 (1982).
    [CrossRef]
  17. Y. Silberberg, I. Bar-Joseph, “Optical instabilities in a nonlinear Kerr medium,” J. Opt. Soc. Am. B 1, 662–670 (1984).
    [CrossRef]
  18. J. Yumoto, K. Otsuka, “Frustrated optical instability: self-induced periodic and chaotic spatial distribution of polarization in nonlinear optical media,” Phys. Rev. Lett. 54, 1806–1809 (1985).
    [CrossRef] [PubMed]
  19. A. E. Kaplan, C. T. Law, “Isolas in four-wave mixing optical bistability,” IEEE J. Quantum Electron. QE-21, 1529–1537 (1985).
    [CrossRef]
  20. A. L. Gaeta, R. W. Boyd, J. R. Ackerhalt, P. W. Milonni, “Instabilities and chaos in the polarizations of counterpropagating light fields,” Phys. Rev. Lett. 58, 2432–2435 (1987).
    [CrossRef] [PubMed]
  21. C. T. Law, A. E. Kaplan, “Dispersion-related multimode instabilities and self-sustained oscillations in nonlinear counterpropagating waves,” Opt. Lett. 14, 734–736 (1989).
    [CrossRef] [PubMed]
  22. A. E. Kaplan, “Multistable self-trapping of light and multi-stable soliton pulse propagation,” IEEE J. Quantum Electron. QE-21, 1538–1543 (1985).
    [CrossRef]
  23. K. J. Blow, N. J. Doran, D. Wood, “Polarization instabilities for solitons in birefringent fibers,” Opt. Lett. 12, 202–204 (1987).
    [CrossRef] [PubMed]
  24. R. H. Enns, S. S. Rangnekar, “Bistable solitons and optical switching,” IEEE J. Quantum Electron. QE-23, 1199–1204 (1987).
    [CrossRef]
  25. A. D. Boardman, G. S. Cooper, “Power-dependent polarization of optical pulses,” J. Opt. Soc. Am. B 5, 403–418 (1988).
    [CrossRef]
  26. S. Trillo, S. Wabnitz, “Ultrashort pulse train generation through induced modulational polarization instability in a birefringent Kerr-like medium,” J. Opt. Soc. Am. B 6, 238–249 (1989).
    [CrossRef]
  27. S. Trillo, S. Wabnitz, G. I. Stegeman, “Nonlinear propagation and self-switching of ultrashort optical pulses in fiber nonlinear directional couplers: the normal dispersion regime,” IEEE J. Quantum Electron. 25, 1907–1916 (1989).
    [CrossRef]
  28. J. V. Moloney, M. R. Belic, H. M. Gibbs, “Calculation of transverse effects in optical bistability using fast Fourier transform techniques,” Opt. Commun. 41, 379–382 (1982).
    [CrossRef]
  29. J. V. Moloney, “Self-focusing-induced optical turbulence,” Phys. Rev. Lett. 53, 556–559 (1984).
    [CrossRef]
  30. C. Flytzanis, “Instabilities and chaos in nonlinear optical beam interactions,” in Nonlinear Optics: Materials and Devices, C. Flytzanis, J. L. Oudar, eds. (Springer-Verlag, Berlin, 1986), pp. 231–248.
    [CrossRef]
  31. K. A. Shore, “Static and dynamic bifurcations in semiconductor lasers for device applications,” Opt. Quantum Electron. 19, S113–S119 (1987).
    [CrossRef]
  32. K. Hayata, M. Koshiba, “Symmetry breaking instabilities and bifurcation phenomena in dielectric slab waveguides containing saturable nonlinear media,” in Second Optoelectronic Conference Technical Digest (Institute of Electronics, Information, and Communication Engineers, Tokyo, 1988), pp. 224–225.
  33. B. D. Robert, J. E. Sipe, “Transverse instabilities in a thin nonlinear slab,” Phys. Rev. A 38, 5217–5226 (1988).
    [CrossRef] [PubMed]
  34. K. Hayata, M. Koshiba, “Self-focusing instability and chaotic behavior of nonlinear optical waves guided by dielectric slab structures,” Opt. Lett. 13, 1041–1043 (1988).
    [CrossRef] [PubMed]
  35. W. J. Firth, C. Paré, “Transverse modulational instabilities for counterpropagating beams in Kerr media,” Opt. Lett. 13, 1096–1098 (1988).
    [CrossRef] [PubMed]
  36. P. D. Maker, R. W. Terhune, C. M. Savage, “Intensity-dependent changes in the refractive index of liquids,” Phys. Rev. Lett. 12, 507–509 (1964).
    [CrossRef]
  37. P. D. Maker, R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137, A801–818 (1965).
    [CrossRef]
  38. T. A. B. Kennedy, S. Wabnitz, “Quantum propagation: squeezing via modulational polarization instabilities in a birefringent nonlinear medium,” Phys. Rev. A 38, 563–566 (1988).
    [CrossRef] [PubMed]
  39. A. Misawa, K. Hayata, M. Koshiba, “Self-induced Cerenkov radiation and polarization instabilities of the elliptically-polarized light propagating in an intensity-dependent nonlinear optical waveguide structure,” in Autumn National Convention Record (Institute of Electronics, Information, and Communication Engineers, Tokyo, 1989), pp. SC-5–SC-8.
  40. K. Hayata, A. Misawa, M. Koshiba, “Split-step finite-element method applied to nonlinear integrated optics,” J. Opt. Soc. Am. B 7, 1268–1280 (1990).
    [CrossRef]
  41. K. Hayata, M. Koshiba, “Numerical simulation of guided-wave SHG light sources utilising Cerenkov radiation scheme,” Electron. Lett. 25, 376–378 (1989).
    [CrossRef]
  42. K. Hayata, A. Misawa, M. Koshiba, “Nonlinear beam propagation in tapered waveguides,” Electron. Lett. 25, 661–662 (1989).
    [CrossRef]
  43. K. Hayata, A. Misawa, M. Koshiba, “Nonstationary behavior of nonlinearly coupled TE–TM waves propagating in dielectric slab structures,” in Seventh International Conference on Integrated Optics and Optical Fiber Communication Technical Digest (Institute of Electronics, Information, and Communication Engineers, Tokyo, 1989), pp. 20A1–20A5; K. Hayata, A. Misawa, M. Koshiba, “Nonstationary simulation of nonlinearly coupled TE–TM waves propagating down dielectric slab structures by the step-by-step finite-element method,” Opt. Lett. 15, 24–26 (1990).
    [CrossRef] [PubMed]
  44. M. Eguchi, K. Hayata, M. Koshiba, “Analysis of soliton pulse propagation in an optical fiber using the finite-element method,” Trans. Inst. Electron. Inform. Commun. Eng. J72-C-I, 329–337 (1989).
  45. M. Eguchi, K. Hayata, M. Koshiba, “Analysis of soliton pulse propagation in a birefringent optical fiber using the finite-element method,” Trans. Inst. Electron. Inform. Commun. Eng. J73-C-I, 113–120 (1990).
  46. P. E. Lagasse, R. Baets, “Application of propagating beam methods to electromagnetic and acoustic wave propagation problems,” Radio Sci. 22, 1225–1233 (1987), and references therein.
    [CrossRef]
  47. K. Hayata, M. Nagai, M. Koshiba, “Finite-element formalism for nonlinear slab-guided waves,” IEEE Trans. Microwave Theory Tech. 36, 1207–1215 (1988).
    [CrossRef]
  48. L. Leine, C. Wächter, U. Langbein, F. Lederer, “Evolution of nonlinear guided optical fields down a dielectric film with a nonlinear cladding,” J. Opt. Soc. Am. B 5, 547–558 (1988).
    [CrossRef]
  49. G. I. Stegeman, R. H. Stolen, “Waveguides and fibers for nonlinear optics,” J. Opt. Soc. Am. B 6, 652–662 (1989).
    [CrossRef]
  50. E. M. Wright, G. I. Stegeman, C. T. Seaton, J. V. Moloney, A. D. Boardman, “Multisoliton emission from a nonlinear waveguide,” Phys. Rev. A 34, 4442–4444 (1986).
    [CrossRef] [PubMed]
  51. M. A. Gubbels, E. M. Wright, G. I. Stegman, C. T. Seaton, J. V. Moloney, “Numerical study of soliton emission from a nonlinear waveguide,” J. Opt. Soc. Am. B 4, 1837–1842 (1987).
    [CrossRef]
  52. D. R. Heatley, E. M. Wright, G. I. Stegeman, “Soliton coupler,” Appl. Phys. Lett. 53, 172–174 (1988).
    [CrossRef]
  53. M. V. Tratnik, J. E. Sipe, “Nonlinear polarization dynamics. I. The single-pulse equations,” Phys. Rev. A 35, 2965–2975 (1987).
    [CrossRef] [PubMed]

1990 (2)

K. Hayata, A. Misawa, M. Koshiba, “Split-step finite-element method applied to nonlinear integrated optics,” J. Opt. Soc. Am. B 7, 1268–1280 (1990).
[CrossRef]

M. Eguchi, K. Hayata, M. Koshiba, “Analysis of soliton pulse propagation in a birefringent optical fiber using the finite-element method,” Trans. Inst. Electron. Inform. Commun. Eng. J73-C-I, 113–120 (1990).

1989 (8)

K. Hayata, M. Koshiba, “Numerical simulation of guided-wave SHG light sources utilising Cerenkov radiation scheme,” Electron. Lett. 25, 376–378 (1989).
[CrossRef]

K. Hayata, A. Misawa, M. Koshiba, “Nonlinear beam propagation in tapered waveguides,” Electron. Lett. 25, 661–662 (1989).
[CrossRef]

M. Eguchi, K. Hayata, M. Koshiba, “Analysis of soliton pulse propagation in an optical fiber using the finite-element method,” Trans. Inst. Electron. Inform. Commun. Eng. J72-C-I, 329–337 (1989).

G. I. Stegeman, R. H. Stolen, “Waveguides and fibers for nonlinear optics,” J. Opt. Soc. Am. B 6, 652–662 (1989).
[CrossRef]

Y. Silberberg, “Photonic switching devices,” Opt. News 15 (2), 7–12 (1989).
[CrossRef]

C. T. Law, A. E. Kaplan, “Dispersion-related multimode instabilities and self-sustained oscillations in nonlinear counterpropagating waves,” Opt. Lett. 14, 734–736 (1989).
[CrossRef] [PubMed]

S. Trillo, S. Wabnitz, “Ultrashort pulse train generation through induced modulational polarization instability in a birefringent Kerr-like medium,” J. Opt. Soc. Am. B 6, 238–249 (1989).
[CrossRef]

S. Trillo, S. Wabnitz, G. I. Stegeman, “Nonlinear propagation and self-switching of ultrashort optical pulses in fiber nonlinear directional couplers: the normal dispersion regime,” IEEE J. Quantum Electron. 25, 1907–1916 (1989).
[CrossRef]

1988 (9)

B. D. Robert, J. E. Sipe, “Transverse instabilities in a thin nonlinear slab,” Phys. Rev. A 38, 5217–5226 (1988).
[CrossRef] [PubMed]

K. Hayata, M. Koshiba, “Self-focusing instability and chaotic behavior of nonlinear optical waves guided by dielectric slab structures,” Opt. Lett. 13, 1041–1043 (1988).
[CrossRef] [PubMed]

W. J. Firth, C. Paré, “Transverse modulational instabilities for counterpropagating beams in Kerr media,” Opt. Lett. 13, 1096–1098 (1988).
[CrossRef] [PubMed]

A. D. Boardman, G. S. Cooper, “Power-dependent polarization of optical pulses,” J. Opt. Soc. Am. B 5, 403–418 (1988).
[CrossRef]

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanori, C. T. Seaton, “Third order nonlinear integrated optics,” IEEE J. Lightwave Technol. 6, 953–970 (1988).
[CrossRef]

T. A. B. Kennedy, S. Wabnitz, “Quantum propagation: squeezing via modulational polarization instabilities in a birefringent nonlinear medium,” Phys. Rev. A 38, 563–566 (1988).
[CrossRef] [PubMed]

D. R. Heatley, E. M. Wright, G. I. Stegeman, “Soliton coupler,” Appl. Phys. Lett. 53, 172–174 (1988).
[CrossRef]

K. Hayata, M. Nagai, M. Koshiba, “Finite-element formalism for nonlinear slab-guided waves,” IEEE Trans. Microwave Theory Tech. 36, 1207–1215 (1988).
[CrossRef]

L. Leine, C. Wächter, U. Langbein, F. Lederer, “Evolution of nonlinear guided optical fields down a dielectric film with a nonlinear cladding,” J. Opt. Soc. Am. B 5, 547–558 (1988).
[CrossRef]

1987 (10)

P. E. Lagasse, R. Baets, “Application of propagating beam methods to electromagnetic and acoustic wave propagation problems,” Radio Sci. 22, 1225–1233 (1987), and references therein.
[CrossRef]

M. V. Tratnik, J. E. Sipe, “Nonlinear polarization dynamics. I. The single-pulse equations,” Phys. Rev. A 35, 2965–2975 (1987).
[CrossRef] [PubMed]

M. A. Gubbels, E. M. Wright, G. I. Stegman, C. T. Seaton, J. V. Moloney, “Numerical study of soliton emission from a nonlinear waveguide,” J. Opt. Soc. Am. B 4, 1837–1842 (1987).
[CrossRef]

S. Wabnitz, “Spatial chaos in the polarization for a birefringent optical fiber with periodic coupling,” Phys. Rev. Lett. 58, 1415–1418 (1987).
[CrossRef] [PubMed]

A. Mecozzi, S. Trillo, S. Wabnitz, B. Daino, “All-optical switching and intensity discrimination by polarization instability in periodically twisted fiber filters,” Opt. Lett. 12, 275–277 (1987).
[CrossRef] [PubMed]

E. Caglioti, S. Trillo, S. Wabnitz, “Stochastic polarization instability: limitation to optical switching using fibers with modulated birefringence,” Opt. Lett. 12, 1044–1046 (1987).
[CrossRef] [PubMed]

K. A. Shore, “Static and dynamic bifurcations in semiconductor lasers for device applications,” Opt. Quantum Electron. 19, S113–S119 (1987).
[CrossRef]

K. J. Blow, N. J. Doran, D. Wood, “Polarization instabilities for solitons in birefringent fibers,” Opt. Lett. 12, 202–204 (1987).
[CrossRef] [PubMed]

R. H. Enns, S. S. Rangnekar, “Bistable solitons and optical switching,” IEEE J. Quantum Electron. QE-23, 1199–1204 (1987).
[CrossRef]

A. L. Gaeta, R. W. Boyd, J. R. Ackerhalt, P. W. Milonni, “Instabilities and chaos in the polarizations of counterpropagating light fields,” Phys. Rev. Lett. 58, 2432–2435 (1987).
[CrossRef] [PubMed]

1986 (5)

H. G. Winful, “Polarization instabilities in birefringent nonlinear media: application to fiber-optic devices,” Opt. Lett. 11, 33–35 (1986).
[CrossRef] [PubMed]

B. Daino, G. Gregori, S. Wabnitz, “New all-optical devices based on third-order nonlinearity of birefringent fibers,” Opt. Lett. 11, 42–44 (1986).
[CrossRef] [PubMed]

A. Vatarescu, “Intensity discrimination through nonlinear power coupling in birefringent fibers,” Appl. Phys. Lett. 49, 61–63 (1986).
[CrossRef]

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, G. I. Stegeman, “Experimental observations of polarization instability in a birefringent optical fiber,” Appl. Phys. Lett. 49, 1224–1226 (1986).
[CrossRef]

E. M. Wright, G. I. Stegeman, C. T. Seaton, J. V. Moloney, A. D. Boardman, “Multisoliton emission from a nonlinear waveguide,” Phys. Rev. A 34, 4442–4444 (1986).
[CrossRef] [PubMed]

1985 (4)

H. G. Winful, “Self-induced polarization changes in birefringent optical fibers,” Appl. Phys. Lett. 47, 213–215 (1985).
[CrossRef]

J. Yumoto, K. Otsuka, “Frustrated optical instability: self-induced periodic and chaotic spatial distribution of polarization in nonlinear optical media,” Phys. Rev. Lett. 54, 1806–1809 (1985).
[CrossRef] [PubMed]

A. E. Kaplan, C. T. Law, “Isolas in four-wave mixing optical bistability,” IEEE J. Quantum Electron. QE-21, 1529–1537 (1985).
[CrossRef]

A. E. Kaplan, “Multistable self-trapping of light and multi-stable soliton pulse propagation,” IEEE J. Quantum Electron. QE-21, 1538–1543 (1985).
[CrossRef]

1984 (2)

Y. Silberberg, I. Bar-Joseph, “Optical instabilities in a nonlinear Kerr medium,” J. Opt. Soc. Am. B 1, 662–670 (1984).
[CrossRef]

J. V. Moloney, “Self-focusing-induced optical turbulence,” Phys. Rev. Lett. 53, 556–559 (1984).
[CrossRef]

1982 (3)

J. V. Moloney, M. R. Belic, H. M. Gibbs, “Calculation of transverse effects in optical bistability using fast Fourier transform techniques,” Opt. Commun. 41, 379–382 (1982).
[CrossRef]

K. Ikeda, O. Akimoto, “Instability leading to periodic and chaotic self-pulsations in a bistable optical cavity,” Phys. Rev. Lett. 48, 617–620 (1982).
[CrossRef]

Y. Silberberg, I. Bar-Joseph, “Instabilities, self-oscillation, and chaos in a simple nonlinear optical interaction,” Phys. Rev. Lett. 48, 1541–1543 (1982).
[CrossRef]

1980 (1)

K. Ikeda, H. Daido, O. Akimoto, “Optical turbulence: chaotic behavior of transmitted light from a ring cavity,” Phys. Rev. Lett. 45, 709–712 (1980).
[CrossRef]

1979 (1)

K. Ikeda, “Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system,” Opt. Commun. 30, 257–261 (1979).
[CrossRef]

1965 (1)

P. D. Maker, R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137, A801–818 (1965).
[CrossRef]

1964 (1)

P. D. Maker, R. W. Terhune, C. M. Savage, “Intensity-dependent changes in the refractive index of liquids,” Phys. Rev. Lett. 12, 507–509 (1964).
[CrossRef]

Ackerhalt, J. R.

A. L. Gaeta, R. W. Boyd, J. R. Ackerhalt, P. W. Milonni, “Instabilities and chaos in the polarizations of counterpropagating light fields,” Phys. Rev. Lett. 58, 2432–2435 (1987).
[CrossRef] [PubMed]

Akimoto, O.

K. Ikeda, O. Akimoto, “Instability leading to periodic and chaotic self-pulsations in a bistable optical cavity,” Phys. Rev. Lett. 48, 617–620 (1982).
[CrossRef]

K. Ikeda, H. Daido, O. Akimoto, “Optical turbulence: chaotic behavior of transmitted light from a ring cavity,” Phys. Rev. Lett. 45, 709–712 (1980).
[CrossRef]

Assanto, G.

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, G. I. Stegeman, “Experimental observations of polarization instability in a birefringent optical fiber,” Appl. Phys. Lett. 49, 1224–1226 (1986).
[CrossRef]

Baets, R.

P. E. Lagasse, R. Baets, “Application of propagating beam methods to electromagnetic and acoustic wave propagation problems,” Radio Sci. 22, 1225–1233 (1987), and references therein.
[CrossRef]

Bar-Joseph, I.

Y. Silberberg, I. Bar-Joseph, “Optical instabilities in a nonlinear Kerr medium,” J. Opt. Soc. Am. B 1, 662–670 (1984).
[CrossRef]

Y. Silberberg, I. Bar-Joseph, “Instabilities, self-oscillation, and chaos in a simple nonlinear optical interaction,” Phys. Rev. Lett. 48, 1541–1543 (1982).
[CrossRef]

Belic, M. R.

J. V. Moloney, M. R. Belic, H. M. Gibbs, “Calculation of transverse effects in optical bistability using fast Fourier transform techniques,” Opt. Commun. 41, 379–382 (1982).
[CrossRef]

Blow, K. J.

Boardman, A. D.

A. D. Boardman, G. S. Cooper, “Power-dependent polarization of optical pulses,” J. Opt. Soc. Am. B 5, 403–418 (1988).
[CrossRef]

E. M. Wright, G. I. Stegeman, C. T. Seaton, J. V. Moloney, A. D. Boardman, “Multisoliton emission from a nonlinear waveguide,” Phys. Rev. A 34, 4442–4444 (1986).
[CrossRef] [PubMed]

Boyd, R. W.

A. L. Gaeta, R. W. Boyd, J. R. Ackerhalt, P. W. Milonni, “Instabilities and chaos in the polarizations of counterpropagating light fields,” Phys. Rev. Lett. 58, 2432–2435 (1987).
[CrossRef] [PubMed]

Caglioti, E.

Cooper, G. S.

Daido, H.

K. Ikeda, H. Daido, O. Akimoto, “Optical turbulence: chaotic behavior of transmitted light from a ring cavity,” Phys. Rev. Lett. 45, 709–712 (1980).
[CrossRef]

Daino, B.

Doran, N. J.

Eguchi, M.

M. Eguchi, K. Hayata, M. Koshiba, “Analysis of soliton pulse propagation in a birefringent optical fiber using the finite-element method,” Trans. Inst. Electron. Inform. Commun. Eng. J73-C-I, 113–120 (1990).

M. Eguchi, K. Hayata, M. Koshiba, “Analysis of soliton pulse propagation in an optical fiber using the finite-element method,” Trans. Inst. Electron. Inform. Commun. Eng. J72-C-I, 329–337 (1989).

Enns, R. H.

R. H. Enns, S. S. Rangnekar, “Bistable solitons and optical switching,” IEEE J. Quantum Electron. QE-23, 1199–1204 (1987).
[CrossRef]

Finlayson, N.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanori, C. T. Seaton, “Third order nonlinear integrated optics,” IEEE J. Lightwave Technol. 6, 953–970 (1988).
[CrossRef]

Firth, W. J.

Flytzanis, C.

C. Flytzanis, “Instabilities and chaos in nonlinear optical beam interactions,” in Nonlinear Optics: Materials and Devices, C. Flytzanis, J. L. Oudar, eds. (Springer-Verlag, Berlin, 1986), pp. 231–248.
[CrossRef]

Gaeta, A. L.

A. L. Gaeta, R. W. Boyd, J. R. Ackerhalt, P. W. Milonni, “Instabilities and chaos in the polarizations of counterpropagating light fields,” Phys. Rev. Lett. 58, 2432–2435 (1987).
[CrossRef] [PubMed]

Gibbs, H. M.

J. V. Moloney, M. R. Belic, H. M. Gibbs, “Calculation of transverse effects in optical bistability using fast Fourier transform techniques,” Opt. Commun. 41, 379–382 (1982).
[CrossRef]

Gregori, G.

Gubbels, M. A.

Hayata, K.

K. Hayata, A. Misawa, M. Koshiba, “Split-step finite-element method applied to nonlinear integrated optics,” J. Opt. Soc. Am. B 7, 1268–1280 (1990).
[CrossRef]

M. Eguchi, K. Hayata, M. Koshiba, “Analysis of soliton pulse propagation in a birefringent optical fiber using the finite-element method,” Trans. Inst. Electron. Inform. Commun. Eng. J73-C-I, 113–120 (1990).

K. Hayata, M. Koshiba, “Numerical simulation of guided-wave SHG light sources utilising Cerenkov radiation scheme,” Electron. Lett. 25, 376–378 (1989).
[CrossRef]

K. Hayata, A. Misawa, M. Koshiba, “Nonlinear beam propagation in tapered waveguides,” Electron. Lett. 25, 661–662 (1989).
[CrossRef]

M. Eguchi, K. Hayata, M. Koshiba, “Analysis of soliton pulse propagation in an optical fiber using the finite-element method,” Trans. Inst. Electron. Inform. Commun. Eng. J72-C-I, 329–337 (1989).

K. Hayata, M. Nagai, M. Koshiba, “Finite-element formalism for nonlinear slab-guided waves,” IEEE Trans. Microwave Theory Tech. 36, 1207–1215 (1988).
[CrossRef]

K. Hayata, M. Koshiba, “Self-focusing instability and chaotic behavior of nonlinear optical waves guided by dielectric slab structures,” Opt. Lett. 13, 1041–1043 (1988).
[CrossRef] [PubMed]

A. Misawa, K. Hayata, M. Koshiba, “Self-induced Cerenkov radiation and polarization instabilities of the elliptically-polarized light propagating in an intensity-dependent nonlinear optical waveguide structure,” in Autumn National Convention Record (Institute of Electronics, Information, and Communication Engineers, Tokyo, 1989), pp. SC-5–SC-8.

K. Hayata, A. Misawa, M. Koshiba, “Nonstationary behavior of nonlinearly coupled TE–TM waves propagating in dielectric slab structures,” in Seventh International Conference on Integrated Optics and Optical Fiber Communication Technical Digest (Institute of Electronics, Information, and Communication Engineers, Tokyo, 1989), pp. 20A1–20A5; K. Hayata, A. Misawa, M. Koshiba, “Nonstationary simulation of nonlinearly coupled TE–TM waves propagating down dielectric slab structures by the step-by-step finite-element method,” Opt. Lett. 15, 24–26 (1990).
[CrossRef] [PubMed]

K. Hayata, M. Koshiba, “Symmetry breaking instabilities and bifurcation phenomena in dielectric slab waveguides containing saturable nonlinear media,” in Second Optoelectronic Conference Technical Digest (Institute of Electronics, Information, and Communication Engineers, Tokyo, 1988), pp. 224–225.

Heatley, D. R.

D. R. Heatley, E. M. Wright, G. I. Stegeman, “Soliton coupler,” Appl. Phys. Lett. 53, 172–174 (1988).
[CrossRef]

Ikeda, K.

K. Ikeda, O. Akimoto, “Instability leading to periodic and chaotic self-pulsations in a bistable optical cavity,” Phys. Rev. Lett. 48, 617–620 (1982).
[CrossRef]

K. Ikeda, H. Daido, O. Akimoto, “Optical turbulence: chaotic behavior of transmitted light from a ring cavity,” Phys. Rev. Lett. 45, 709–712 (1980).
[CrossRef]

K. Ikeda, “Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system,” Opt. Commun. 30, 257–261 (1979).
[CrossRef]

Kaplan, A. E.

C. T. Law, A. E. Kaplan, “Dispersion-related multimode instabilities and self-sustained oscillations in nonlinear counterpropagating waves,” Opt. Lett. 14, 734–736 (1989).
[CrossRef] [PubMed]

A. E. Kaplan, C. T. Law, “Isolas in four-wave mixing optical bistability,” IEEE J. Quantum Electron. QE-21, 1529–1537 (1985).
[CrossRef]

A. E. Kaplan, “Multistable self-trapping of light and multi-stable soliton pulse propagation,” IEEE J. Quantum Electron. QE-21, 1538–1543 (1985).
[CrossRef]

Kennedy, T. A. B.

T. A. B. Kennedy, S. Wabnitz, “Quantum propagation: squeezing via modulational polarization instabilities in a birefringent nonlinear medium,” Phys. Rev. A 38, 563–566 (1988).
[CrossRef] [PubMed]

Koshiba, M.

M. Eguchi, K. Hayata, M. Koshiba, “Analysis of soliton pulse propagation in a birefringent optical fiber using the finite-element method,” Trans. Inst. Electron. Inform. Commun. Eng. J73-C-I, 113–120 (1990).

K. Hayata, A. Misawa, M. Koshiba, “Split-step finite-element method applied to nonlinear integrated optics,” J. Opt. Soc. Am. B 7, 1268–1280 (1990).
[CrossRef]

M. Eguchi, K. Hayata, M. Koshiba, “Analysis of soliton pulse propagation in an optical fiber using the finite-element method,” Trans. Inst. Electron. Inform. Commun. Eng. J72-C-I, 329–337 (1989).

K. Hayata, A. Misawa, M. Koshiba, “Nonlinear beam propagation in tapered waveguides,” Electron. Lett. 25, 661–662 (1989).
[CrossRef]

K. Hayata, M. Koshiba, “Numerical simulation of guided-wave SHG light sources utilising Cerenkov radiation scheme,” Electron. Lett. 25, 376–378 (1989).
[CrossRef]

K. Hayata, M. Nagai, M. Koshiba, “Finite-element formalism for nonlinear slab-guided waves,” IEEE Trans. Microwave Theory Tech. 36, 1207–1215 (1988).
[CrossRef]

K. Hayata, M. Koshiba, “Self-focusing instability and chaotic behavior of nonlinear optical waves guided by dielectric slab structures,” Opt. Lett. 13, 1041–1043 (1988).
[CrossRef] [PubMed]

K. Hayata, A. Misawa, M. Koshiba, “Nonstationary behavior of nonlinearly coupled TE–TM waves propagating in dielectric slab structures,” in Seventh International Conference on Integrated Optics and Optical Fiber Communication Technical Digest (Institute of Electronics, Information, and Communication Engineers, Tokyo, 1989), pp. 20A1–20A5; K. Hayata, A. Misawa, M. Koshiba, “Nonstationary simulation of nonlinearly coupled TE–TM waves propagating down dielectric slab structures by the step-by-step finite-element method,” Opt. Lett. 15, 24–26 (1990).
[CrossRef] [PubMed]

A. Misawa, K. Hayata, M. Koshiba, “Self-induced Cerenkov radiation and polarization instabilities of the elliptically-polarized light propagating in an intensity-dependent nonlinear optical waveguide structure,” in Autumn National Convention Record (Institute of Electronics, Information, and Communication Engineers, Tokyo, 1989), pp. SC-5–SC-8.

K. Hayata, M. Koshiba, “Symmetry breaking instabilities and bifurcation phenomena in dielectric slab waveguides containing saturable nonlinear media,” in Second Optoelectronic Conference Technical Digest (Institute of Electronics, Information, and Communication Engineers, Tokyo, 1988), pp. 224–225.

Lagasse, P. E.

P. E. Lagasse, R. Baets, “Application of propagating beam methods to electromagnetic and acoustic wave propagation problems,” Radio Sci. 22, 1225–1233 (1987), and references therein.
[CrossRef]

Langbein, U.

Law, C. T.

Lederer, F.

Leine, L.

Maker, P. D.

P. D. Maker, R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137, A801–818 (1965).
[CrossRef]

P. D. Maker, R. W. Terhune, C. M. Savage, “Intensity-dependent changes in the refractive index of liquids,” Phys. Rev. Lett. 12, 507–509 (1964).
[CrossRef]

Mecozzi, A.

Milonni, P. W.

A. L. Gaeta, R. W. Boyd, J. R. Ackerhalt, P. W. Milonni, “Instabilities and chaos in the polarizations of counterpropagating light fields,” Phys. Rev. Lett. 58, 2432–2435 (1987).
[CrossRef] [PubMed]

Misawa, A.

K. Hayata, A. Misawa, M. Koshiba, “Split-step finite-element method applied to nonlinear integrated optics,” J. Opt. Soc. Am. B 7, 1268–1280 (1990).
[CrossRef]

K. Hayata, A. Misawa, M. Koshiba, “Nonlinear beam propagation in tapered waveguides,” Electron. Lett. 25, 661–662 (1989).
[CrossRef]

A. Misawa, K. Hayata, M. Koshiba, “Self-induced Cerenkov radiation and polarization instabilities of the elliptically-polarized light propagating in an intensity-dependent nonlinear optical waveguide structure,” in Autumn National Convention Record (Institute of Electronics, Information, and Communication Engineers, Tokyo, 1989), pp. SC-5–SC-8.

K. Hayata, A. Misawa, M. Koshiba, “Nonstationary behavior of nonlinearly coupled TE–TM waves propagating in dielectric slab structures,” in Seventh International Conference on Integrated Optics and Optical Fiber Communication Technical Digest (Institute of Electronics, Information, and Communication Engineers, Tokyo, 1989), pp. 20A1–20A5; K. Hayata, A. Misawa, M. Koshiba, “Nonstationary simulation of nonlinearly coupled TE–TM waves propagating down dielectric slab structures by the step-by-step finite-element method,” Opt. Lett. 15, 24–26 (1990).
[CrossRef] [PubMed]

Moloney, J. V.

M. A. Gubbels, E. M. Wright, G. I. Stegman, C. T. Seaton, J. V. Moloney, “Numerical study of soliton emission from a nonlinear waveguide,” J. Opt. Soc. Am. B 4, 1837–1842 (1987).
[CrossRef]

E. M. Wright, G. I. Stegeman, C. T. Seaton, J. V. Moloney, A. D. Boardman, “Multisoliton emission from a nonlinear waveguide,” Phys. Rev. A 34, 4442–4444 (1986).
[CrossRef] [PubMed]

J. V. Moloney, “Self-focusing-induced optical turbulence,” Phys. Rev. Lett. 53, 556–559 (1984).
[CrossRef]

J. V. Moloney, M. R. Belic, H. M. Gibbs, “Calculation of transverse effects in optical bistability using fast Fourier transform techniques,” Opt. Commun. 41, 379–382 (1982).
[CrossRef]

Nagai, M.

K. Hayata, M. Nagai, M. Koshiba, “Finite-element formalism for nonlinear slab-guided waves,” IEEE Trans. Microwave Theory Tech. 36, 1207–1215 (1988).
[CrossRef]

Otsuka, K.

J. Yumoto, K. Otsuka, “Frustrated optical instability: self-induced periodic and chaotic spatial distribution of polarization in nonlinear optical media,” Phys. Rev. Lett. 54, 1806–1809 (1985).
[CrossRef] [PubMed]

Paré, C.

Rangnekar, S. S.

R. H. Enns, S. S. Rangnekar, “Bistable solitons and optical switching,” IEEE J. Quantum Electron. QE-23, 1199–1204 (1987).
[CrossRef]

Robert, B. D.

B. D. Robert, J. E. Sipe, “Transverse instabilities in a thin nonlinear slab,” Phys. Rev. A 38, 5217–5226 (1988).
[CrossRef] [PubMed]

Savage, C. M.

P. D. Maker, R. W. Terhune, C. M. Savage, “Intensity-dependent changes in the refractive index of liquids,” Phys. Rev. Lett. 12, 507–509 (1964).
[CrossRef]

Seaton, C. T.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanori, C. T. Seaton, “Third order nonlinear integrated optics,” IEEE J. Lightwave Technol. 6, 953–970 (1988).
[CrossRef]

M. A. Gubbels, E. M. Wright, G. I. Stegman, C. T. Seaton, J. V. Moloney, “Numerical study of soliton emission from a nonlinear waveguide,” J. Opt. Soc. Am. B 4, 1837–1842 (1987).
[CrossRef]

E. M. Wright, G. I. Stegeman, C. T. Seaton, J. V. Moloney, A. D. Boardman, “Multisoliton emission from a nonlinear waveguide,” Phys. Rev. A 34, 4442–4444 (1986).
[CrossRef] [PubMed]

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, G. I. Stegeman, “Experimental observations of polarization instability in a birefringent optical fiber,” Appl. Phys. Lett. 49, 1224–1226 (1986).
[CrossRef]

Shore, K. A.

K. A. Shore, “Static and dynamic bifurcations in semiconductor lasers for device applications,” Opt. Quantum Electron. 19, S113–S119 (1987).
[CrossRef]

Silberberg, Y.

Y. Silberberg, “Photonic switching devices,” Opt. News 15 (2), 7–12 (1989).
[CrossRef]

Y. Silberberg, I. Bar-Joseph, “Optical instabilities in a nonlinear Kerr medium,” J. Opt. Soc. Am. B 1, 662–670 (1984).
[CrossRef]

Y. Silberberg, I. Bar-Joseph, “Instabilities, self-oscillation, and chaos in a simple nonlinear optical interaction,” Phys. Rev. Lett. 48, 1541–1543 (1982).
[CrossRef]

Sipe, J. E.

B. D. Robert, J. E. Sipe, “Transverse instabilities in a thin nonlinear slab,” Phys. Rev. A 38, 5217–5226 (1988).
[CrossRef] [PubMed]

M. V. Tratnik, J. E. Sipe, “Nonlinear polarization dynamics. I. The single-pulse equations,” Phys. Rev. A 35, 2965–2975 (1987).
[CrossRef] [PubMed]

Stegeman, G. I.

G. I. Stegeman, R. H. Stolen, “Waveguides and fibers for nonlinear optics,” J. Opt. Soc. Am. B 6, 652–662 (1989).
[CrossRef]

S. Trillo, S. Wabnitz, G. I. Stegeman, “Nonlinear propagation and self-switching of ultrashort optical pulses in fiber nonlinear directional couplers: the normal dispersion regime,” IEEE J. Quantum Electron. 25, 1907–1916 (1989).
[CrossRef]

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanori, C. T. Seaton, “Third order nonlinear integrated optics,” IEEE J. Lightwave Technol. 6, 953–970 (1988).
[CrossRef]

D. R. Heatley, E. M. Wright, G. I. Stegeman, “Soliton coupler,” Appl. Phys. Lett. 53, 172–174 (1988).
[CrossRef]

E. M. Wright, G. I. Stegeman, C. T. Seaton, J. V. Moloney, A. D. Boardman, “Multisoliton emission from a nonlinear waveguide,” Phys. Rev. A 34, 4442–4444 (1986).
[CrossRef] [PubMed]

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, G. I. Stegeman, “Experimental observations of polarization instability in a birefringent optical fiber,” Appl. Phys. Lett. 49, 1224–1226 (1986).
[CrossRef]

Stegman, G. I.

Stolen, R. H.

G. I. Stegeman, R. H. Stolen, “Waveguides and fibers for nonlinear optics,” J. Opt. Soc. Am. B 6, 652–662 (1989).
[CrossRef]

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, G. I. Stegeman, “Experimental observations of polarization instability in a birefringent optical fiber,” Appl. Phys. Lett. 49, 1224–1226 (1986).
[CrossRef]

Terhune, R. W.

P. D. Maker, R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137, A801–818 (1965).
[CrossRef]

P. D. Maker, R. W. Terhune, C. M. Savage, “Intensity-dependent changes in the refractive index of liquids,” Phys. Rev. Lett. 12, 507–509 (1964).
[CrossRef]

Tratnik, M. V.

M. V. Tratnik, J. E. Sipe, “Nonlinear polarization dynamics. I. The single-pulse equations,” Phys. Rev. A 35, 2965–2975 (1987).
[CrossRef] [PubMed]

Trillo, S.

S. Trillo, S. Wabnitz, “Ultrashort pulse train generation through induced modulational polarization instability in a birefringent Kerr-like medium,” J. Opt. Soc. Am. B 6, 238–249 (1989).
[CrossRef]

S. Trillo, S. Wabnitz, G. I. Stegeman, “Nonlinear propagation and self-switching of ultrashort optical pulses in fiber nonlinear directional couplers: the normal dispersion regime,” IEEE J. Quantum Electron. 25, 1907–1916 (1989).
[CrossRef]

A. Mecozzi, S. Trillo, S. Wabnitz, B. Daino, “All-optical switching and intensity discrimination by polarization instability in periodically twisted fiber filters,” Opt. Lett. 12, 275–277 (1987).
[CrossRef] [PubMed]

E. Caglioti, S. Trillo, S. Wabnitz, “Stochastic polarization instability: limitation to optical switching using fibers with modulated birefringence,” Opt. Lett. 12, 1044–1046 (1987).
[CrossRef] [PubMed]

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, G. I. Stegeman, “Experimental observations of polarization instability in a birefringent optical fiber,” Appl. Phys. Lett. 49, 1224–1226 (1986).
[CrossRef]

Vatarescu, A.

A. Vatarescu, “Intensity discrimination through nonlinear power coupling in birefringent fibers,” Appl. Phys. Lett. 49, 61–63 (1986).
[CrossRef]

Wabnitz, S.

S. Trillo, S. Wabnitz, G. I. Stegeman, “Nonlinear propagation and self-switching of ultrashort optical pulses in fiber nonlinear directional couplers: the normal dispersion regime,” IEEE J. Quantum Electron. 25, 1907–1916 (1989).
[CrossRef]

S. Trillo, S. Wabnitz, “Ultrashort pulse train generation through induced modulational polarization instability in a birefringent Kerr-like medium,” J. Opt. Soc. Am. B 6, 238–249 (1989).
[CrossRef]

T. A. B. Kennedy, S. Wabnitz, “Quantum propagation: squeezing via modulational polarization instabilities in a birefringent nonlinear medium,” Phys. Rev. A 38, 563–566 (1988).
[CrossRef] [PubMed]

S. Wabnitz, “Spatial chaos in the polarization for a birefringent optical fiber with periodic coupling,” Phys. Rev. Lett. 58, 1415–1418 (1987).
[CrossRef] [PubMed]

E. Caglioti, S. Trillo, S. Wabnitz, “Stochastic polarization instability: limitation to optical switching using fibers with modulated birefringence,” Opt. Lett. 12, 1044–1046 (1987).
[CrossRef] [PubMed]

A. Mecozzi, S. Trillo, S. Wabnitz, B. Daino, “All-optical switching and intensity discrimination by polarization instability in periodically twisted fiber filters,” Opt. Lett. 12, 275–277 (1987).
[CrossRef] [PubMed]

B. Daino, G. Gregori, S. Wabnitz, “New all-optical devices based on third-order nonlinearity of birefringent fibers,” Opt. Lett. 11, 42–44 (1986).
[CrossRef] [PubMed]

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, G. I. Stegeman, “Experimental observations of polarization instability in a birefringent optical fiber,” Appl. Phys. Lett. 49, 1224–1226 (1986).
[CrossRef]

Wächter, C.

Winful, H. G.

H. G. Winful, “Polarization instabilities in birefringent nonlinear media: application to fiber-optic devices,” Opt. Lett. 11, 33–35 (1986).
[CrossRef] [PubMed]

H. G. Winful, “Self-induced polarization changes in birefringent optical fibers,” Appl. Phys. Lett. 47, 213–215 (1985).
[CrossRef]

Wood, D.

Wright, E. M.

D. R. Heatley, E. M. Wright, G. I. Stegeman, “Soliton coupler,” Appl. Phys. Lett. 53, 172–174 (1988).
[CrossRef]

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanori, C. T. Seaton, “Third order nonlinear integrated optics,” IEEE J. Lightwave Technol. 6, 953–970 (1988).
[CrossRef]

M. A. Gubbels, E. M. Wright, G. I. Stegman, C. T. Seaton, J. V. Moloney, “Numerical study of soliton emission from a nonlinear waveguide,” J. Opt. Soc. Am. B 4, 1837–1842 (1987).
[CrossRef]

E. M. Wright, G. I. Stegeman, C. T. Seaton, J. V. Moloney, A. D. Boardman, “Multisoliton emission from a nonlinear waveguide,” Phys. Rev. A 34, 4442–4444 (1986).
[CrossRef] [PubMed]

Yumoto, J.

J. Yumoto, K. Otsuka, “Frustrated optical instability: self-induced periodic and chaotic spatial distribution of polarization in nonlinear optical media,” Phys. Rev. Lett. 54, 1806–1809 (1985).
[CrossRef] [PubMed]

Zanori, R.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanori, C. T. Seaton, “Third order nonlinear integrated optics,” IEEE J. Lightwave Technol. 6, 953–970 (1988).
[CrossRef]

Appl. Phys. Lett. (4)

H. G. Winful, “Self-induced polarization changes in birefringent optical fibers,” Appl. Phys. Lett. 47, 213–215 (1985).
[CrossRef]

A. Vatarescu, “Intensity discrimination through nonlinear power coupling in birefringent fibers,” Appl. Phys. Lett. 49, 61–63 (1986).
[CrossRef]

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, G. I. Stegeman, “Experimental observations of polarization instability in a birefringent optical fiber,” Appl. Phys. Lett. 49, 1224–1226 (1986).
[CrossRef]

D. R. Heatley, E. M. Wright, G. I. Stegeman, “Soliton coupler,” Appl. Phys. Lett. 53, 172–174 (1988).
[CrossRef]

Electron. Lett. (2)

K. Hayata, M. Koshiba, “Numerical simulation of guided-wave SHG light sources utilising Cerenkov radiation scheme,” Electron. Lett. 25, 376–378 (1989).
[CrossRef]

K. Hayata, A. Misawa, M. Koshiba, “Nonlinear beam propagation in tapered waveguides,” Electron. Lett. 25, 661–662 (1989).
[CrossRef]

IEEE J. Lightwave Technol. (1)

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanori, C. T. Seaton, “Third order nonlinear integrated optics,” IEEE J. Lightwave Technol. 6, 953–970 (1988).
[CrossRef]

IEEE J. Quantum Electron. (4)

A. E. Kaplan, C. T. Law, “Isolas in four-wave mixing optical bistability,” IEEE J. Quantum Electron. QE-21, 1529–1537 (1985).
[CrossRef]

A. E. Kaplan, “Multistable self-trapping of light and multi-stable soliton pulse propagation,” IEEE J. Quantum Electron. QE-21, 1538–1543 (1985).
[CrossRef]

R. H. Enns, S. S. Rangnekar, “Bistable solitons and optical switching,” IEEE J. Quantum Electron. QE-23, 1199–1204 (1987).
[CrossRef]

S. Trillo, S. Wabnitz, G. I. Stegeman, “Nonlinear propagation and self-switching of ultrashort optical pulses in fiber nonlinear directional couplers: the normal dispersion regime,” IEEE J. Quantum Electron. 25, 1907–1916 (1989).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

K. Hayata, M. Nagai, M. Koshiba, “Finite-element formalism for nonlinear slab-guided waves,” IEEE Trans. Microwave Theory Tech. 36, 1207–1215 (1988).
[CrossRef]

J. Opt. Soc. Am. B (7)

Opt. Commun. (2)

K. Ikeda, “Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system,” Opt. Commun. 30, 257–261 (1979).
[CrossRef]

J. V. Moloney, M. R. Belic, H. M. Gibbs, “Calculation of transverse effects in optical bistability using fast Fourier transform techniques,” Opt. Commun. 41, 379–382 (1982).
[CrossRef]

Opt. Lett. (8)

Opt. News (1)

Y. Silberberg, “Photonic switching devices,” Opt. News 15 (2), 7–12 (1989).
[CrossRef]

Opt. Quantum Electron. (1)

K. A. Shore, “Static and dynamic bifurcations in semiconductor lasers for device applications,” Opt. Quantum Electron. 19, S113–S119 (1987).
[CrossRef]

Phys. Rev. (1)

P. D. Maker, R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137, A801–818 (1965).
[CrossRef]

Phys. Rev. A (4)

T. A. B. Kennedy, S. Wabnitz, “Quantum propagation: squeezing via modulational polarization instabilities in a birefringent nonlinear medium,” Phys. Rev. A 38, 563–566 (1988).
[CrossRef] [PubMed]

B. D. Robert, J. E. Sipe, “Transverse instabilities in a thin nonlinear slab,” Phys. Rev. A 38, 5217–5226 (1988).
[CrossRef] [PubMed]

M. V. Tratnik, J. E. Sipe, “Nonlinear polarization dynamics. I. The single-pulse equations,” Phys. Rev. A 35, 2965–2975 (1987).
[CrossRef] [PubMed]

E. M. Wright, G. I. Stegeman, C. T. Seaton, J. V. Moloney, A. D. Boardman, “Multisoliton emission from a nonlinear waveguide,” Phys. Rev. A 34, 4442–4444 (1986).
[CrossRef] [PubMed]

Phys. Rev. Lett. (8)

P. D. Maker, R. W. Terhune, C. M. Savage, “Intensity-dependent changes in the refractive index of liquids,” Phys. Rev. Lett. 12, 507–509 (1964).
[CrossRef]

J. V. Moloney, “Self-focusing-induced optical turbulence,” Phys. Rev. Lett. 53, 556–559 (1984).
[CrossRef]

K. Ikeda, H. Daido, O. Akimoto, “Optical turbulence: chaotic behavior of transmitted light from a ring cavity,” Phys. Rev. Lett. 45, 709–712 (1980).
[CrossRef]

K. Ikeda, O. Akimoto, “Instability leading to periodic and chaotic self-pulsations in a bistable optical cavity,” Phys. Rev. Lett. 48, 617–620 (1982).
[CrossRef]

Y. Silberberg, I. Bar-Joseph, “Instabilities, self-oscillation, and chaos in a simple nonlinear optical interaction,” Phys. Rev. Lett. 48, 1541–1543 (1982).
[CrossRef]

S. Wabnitz, “Spatial chaos in the polarization for a birefringent optical fiber with periodic coupling,” Phys. Rev. Lett. 58, 1415–1418 (1987).
[CrossRef] [PubMed]

J. Yumoto, K. Otsuka, “Frustrated optical instability: self-induced periodic and chaotic spatial distribution of polarization in nonlinear optical media,” Phys. Rev. Lett. 54, 1806–1809 (1985).
[CrossRef] [PubMed]

A. L. Gaeta, R. W. Boyd, J. R. Ackerhalt, P. W. Milonni, “Instabilities and chaos in the polarizations of counterpropagating light fields,” Phys. Rev. Lett. 58, 2432–2435 (1987).
[CrossRef] [PubMed]

Radio Sci. (1)

P. E. Lagasse, R. Baets, “Application of propagating beam methods to electromagnetic and acoustic wave propagation problems,” Radio Sci. 22, 1225–1233 (1987), and references therein.
[CrossRef]

Trans. Inst. Electron. Inform. Commun. Eng. (2)

M. Eguchi, K. Hayata, M. Koshiba, “Analysis of soliton pulse propagation in an optical fiber using the finite-element method,” Trans. Inst. Electron. Inform. Commun. Eng. J72-C-I, 329–337 (1989).

M. Eguchi, K. Hayata, M. Koshiba, “Analysis of soliton pulse propagation in a birefringent optical fiber using the finite-element method,” Trans. Inst. Electron. Inform. Commun. Eng. J73-C-I, 113–120 (1990).

Other (6)

K. Hayata, A. Misawa, M. Koshiba, “Nonstationary behavior of nonlinearly coupled TE–TM waves propagating in dielectric slab structures,” in Seventh International Conference on Integrated Optics and Optical Fiber Communication Technical Digest (Institute of Electronics, Information, and Communication Engineers, Tokyo, 1989), pp. 20A1–20A5; K. Hayata, A. Misawa, M. Koshiba, “Nonstationary simulation of nonlinearly coupled TE–TM waves propagating down dielectric slab structures by the step-by-step finite-element method,” Opt. Lett. 15, 24–26 (1990).
[CrossRef] [PubMed]

R. W. Boyd, M. G. Raymer, L. M. Narducci, eds., Optical Instabilities (Cambridge U. Press, Cambridge, 1986).

N. B. Abraham, F. T. Arecchi, L. A. Lugiato, eds., Instabilities and Chaos in Quantum Optics II (Plenum, New York, 1988).
[CrossRef]

C. Flytzanis, “Instabilities and chaos in nonlinear optical beam interactions,” in Nonlinear Optics: Materials and Devices, C. Flytzanis, J. L. Oudar, eds. (Springer-Verlag, Berlin, 1986), pp. 231–248.
[CrossRef]

A. Misawa, K. Hayata, M. Koshiba, “Self-induced Cerenkov radiation and polarization instabilities of the elliptically-polarized light propagating in an intensity-dependent nonlinear optical waveguide structure,” in Autumn National Convention Record (Institute of Electronics, Information, and Communication Engineers, Tokyo, 1989), pp. SC-5–SC-8.

K. Hayata, M. Koshiba, “Symmetry breaking instabilities and bifurcation phenomena in dielectric slab waveguides containing saturable nonlinear media,” in Second Optoelectronic Conference Technical Digest (Institute of Electronics, Information, and Communication Engineers, Tokyo, 1988), pp. 224–225.

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Figures (10)

Fig. 1
Fig. 1

Dielectric slab waveguide made of Kerr self-focusing nonlinear media; d is the film thickness.

Fig. 2
Fig. 2

Elemental unit with three nodal points. Within the element, electromagnetic field components are interpolated by piecewise quadratic polynominals (Le is the length of a line element).

Fig. 3
Fig. 3

Dependence of nonlinear beam evolution on the optically induced anisotropy η. Only the substrate is nonlinear i.e., αc = αf = 0 and αs = α. The linearly polarized linear eigenmodes (TE0, TM0) with equal power are incident onto the entrance (z = 0) of the waveguide i.e., P TM = P TE = P / 2 ( α ¯ = 14 ) and ϕ = 0. Note that the behavior of the TM component hx is unstable and sensitive to η, in contrast to the stability of the TE component ex. The evolution of ey is the same as that of hx. The electric and magnetic field strengths are plotted in volts per meter and amperes per meter, respectively. (a) η = 1, (b) η = 1/3, (c) η = −1/2.

Fig. 4
Fig. 4

Dependence of elliptically polarized beam evolution on η. P TE = P TM = P / 2 ( α ¯ = 14 ); ϕ = π/4. Results for η = 1 are not shown because they exhibited the same behavior as those shown in Fig. 3(a). (a) η = 1/3, (b) η = −1/2.

Fig. 5
Fig. 5

Same as Fig. 3(b) but for PTEPTM, with P TE + P TM = P ( α ¯ = 14 ). (a) PTE/PTM = 4/1, (b) PTE/PTM = 1/4.

Fig. 6
Fig. 6

Same as Fig. 5 but for P TE + P TM = P / 2 ( α ¯ = 7 ). (a) PTE/PTM = 4/1, (b) PTE/PTM = 1/4.

Fig. 7
Fig. 7

Dependence of nonlinear beam evolution on the initial phase difference ϕ. The whole region of the waveguide is uniformly nonlinear i e αc = αf = αs = α. The linearly polarized linear eigenmodes (TE0, TM0) with equal power are incident onto the entrance (z = 0) of the waveguide, i.e., P TE + P TM = P / 2 ( α ¯ = 14 ) and η = 1/3. Note again that the behavior of the TM component (ey) is unstable and sensitive to ϕ, in contrast to the stability of the TE component (ex). (a) ϕ = 0, (b) ϕ = π/4, (c) ϕ = π/2.

Fig. 8
Fig. 8

Same as Fig. 7 but for η = −1/2. (a) ϕ = 0, (b) ϕ = π/4, (c) ϕ = π/2.

Fig. 9
Fig. 9

Same as Fig. 7 but for PTE = PTM = P/4. (a) ϕ = 0, (b) ϕ = π/4, (c) ϕ = π/2.

Fig. 10
Fig. 10

Same as Fig. 7 but for η = −1/2 and PTE = PTM = P/4. (a) ϕ = 0, (b) ϕ = π/4, (c) ϕ = π/2.

Equations (75)

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D = ε L E + α [ η E ( E · E * ) + ( 1 η ) E * ( E · E ) ] ,
[ ε ] = [ ε x x ε x y ε x z ε y x ε y y ε y z ε z x ε z y ε z z ] ,
ε x x = ε L + α ( | E x | 2 + η | E y | 2 + η | E z | 2 ) ,
ε x y = α ( 1 η ) E x * E y ,
ε x z = α ( 1 η ) E x * E z ,
ε y x = α ( 1 η ) E x E y * ,
ε y y = ε L + α ( η | E x | 2 + | E y | 2 + η | E z | 2 ) ,
ε y z = α ( 1 η ) E y * E z ,
ε z x = α ( 1 η ) E x E z * ,
ε z y = α ( 1 η ) E y E z * ,
ε z z = ε L + α ( η | E x | 2 + η | E y | 2 + | E z | 2 ) .
2 γ ¯ e x z ¯ + b a g x z ¯ = 2 e x y ¯ 2 + ( γ ¯ 2 + ε x x ε x y b a ε x z c a ) e x + c a g x y ¯ + b a γ ¯ g x ,
[ ( b / a ) e x ] z ¯ + γ ¯ [ ( ε z z / a ) g x ] z ¯ + γ ¯ ε z z a g x z ¯ [ ( ε z y / a ) g x / z ¯ ] y ¯ [ ( ε y z / a ) g x / y ¯ ] z ¯ = [ ( c / a ) e x ] y ¯ γ ¯ b a e x + [ ( ε y y / a ) g x / y ¯ ] y ¯ γ ¯ [ ( ε z y / a ) g x ] y ¯ γ ¯ ε y z a g x y ¯ + ( γ ¯ 2 ε z z a + 1 ) g x = 0 ,
E x ( y ¯ , z ¯ ) = e x ( y ¯ , z ¯ ) exp ( γ ¯ z ¯ ) ,
G y ( y ¯ , z ¯ ) = g x ( y ¯ , z ¯ ) exp ( γ ¯ z ¯ ) ,
a = ε z z ε y y ε y z ε z y ,
b = ε z z ε y x ε y z ε z x ,
c = ε y y ε z x ε z y ε y x ,
b = ε x y ε z z ε x z ε z y ,
c = ε x z ε y y ε x y ε y z .
2 γ ¯ [ M ( 1 ) ] d { e x } d z ¯ + [ M ( b / a ) ] d { g x } d z ¯ = [ K ( 1 ) ] { e x } + [ M ( γ ¯ 2 + ε x x ε x y b a ε x z c a ) ] { e x } + [ Q ( c a ) ] T { g x } + γ ¯ [ M ( b a ) ] { g x } ,
[ M ( b / a ) ] d { e x } d z ¯ + 2 γ ¯ [ M ( ε z z / a ) ] d { g x } d z ¯ + [ Q ( ε z y / a ) ] d { g x } d z ¯ [ Q ( ε y z / a ) ] T d { g x } d z ¯ = [ Q ( c a ) ] { e x } γ ¯ [ M ( b a ) ] { e x } [ K ( ε y y a ) ] { g x } + γ ¯ [ Q ( ε z y a ) ] { g x } γ ¯ [ Q ( ε y z a ) ] T { g x } + [ M ( γ ¯ 2 ε z z a + 1 ) ] { g x } ,
[ K ( q ) ] = e [ K ( q ) ] e = e e q e ( d { N } / d y ¯ ) ( d { N } T / d y ¯ ) d y ¯ ,
[ M ( q ) ] = e [ M ( q ) ] e = e e q e { N } { N } T d y ¯ ,
[ Q ( q ) ] = e [ Q ( q ) ] e = e e q e ( d { N } / d y ¯ ) { N } T d y ¯ .
[ C ] d { υ } / d z ¯ = [ F ] { υ } ,
[ C ] = [ [ C e e ] [ C e g ] [ C g e ] [ C g g ] ] ,
[ F ] = [ [ F e e ] [ F e g ] [ F g e ] [ F g g ] ] ,
{ υ } = [ { e x } { g x } ] ,
[ C e e ] = 2 γ ¯ [ M ( 1 ) ] ,
[ C e g ] = [ M ( b / a ) ] ,
[ C g e ] = [ M ( b / a ) ] ,
[ C g g ] = 2 γ ¯ [ M ( ε z z / a ) ] + [ Q ( ε z y / a ) ] [ Q ( ε y z / a ) ] T ,
[ F e e ] = [ K ( 1 ) ] + [ M ( γ ¯ 2 + ε x x ε x y b / a ε x z c / a ) ] ,
[ F e g ] = [ Q ( c / a ) ] T + γ ¯ [ M ( b / a ) ] ,
[ F g e ] = [ Q ( c / a ) ] γ ¯ [ M ( b / a ) ] ,
[ F g g ] = [ K ( ε y y / a ) ] + γ ¯ [ Q ( ε z y / a ) ] γ ¯ [ Q ( ε y z / a ) ] T + [ M ( γ ¯ 2 ε z z / a + 1 ) ] .
[ C ] ( { υ } i + 1 { υ } i ) / Δ z ¯ = [ F ] ( θ { υ } i + 1 + ( 1 θ ) { υ } i ) for i = 0 , 1 , 2 , ,
[ L ( θ ) ] { υ } i + 1 = [ L ( θ 1 ) ] { υ } i ,
[ L ( θ ) ] = [ C ] θ Δ z ¯ [ F ] .
E in = x ˆ E x + exp ( j ϕ ) ( y ˆ E y + z ˆ E z ) ,
e z y ¯ ( e y z ¯ γ ¯ e y ) = g x ,
e x z ¯ γ ¯ e x = g y ,
e x y ¯ = g z ,
g z y ¯ ( g y z ¯ γ ¯ g y ) = ( ε x x e x + ε x y e y + ε x z e z ) ,
g x z ¯ γ ¯ g x = ( ε y x e x + ε y y e y + ε y z e z ) ,
g x y ¯ = ( ε z x e x + ε z y e y + ε z z e z ) ,
g y = e x / z ¯ + γ ¯ e x ,
g z = e x / y ¯ .
e y = ε z z a ( g x z ¯ γ ¯ g x ) ε y z a g x y ¯ b a e x ,
e z = ε z y a ( g x z ¯ γ ¯ g x ) + ε y y a g x y ¯ c a e x ,
[ K ( q ) ] e = L ¯ e 1 [ K 11 K 12 K 13 K 12 K 22 K 23 K 13 K 23 K 33 ] ,
K 11 = ( 37 q 1 / 30 ) ( q 2 / 10 ) + ( 6 q 3 / 5 ) ,
K 12 = ( 7 q 1 / 30 ) + ( 7 q 2 / 30 ) ( 2 q 3 / 15 ) ,
K 13 = ( 22 q 1 / 15 ) ( 2 q 2 / 15 ) ( 16 q 3 / 15 ) ,
K 22 = ( q 1 / 10 ) + ( 37 q 2 / 30 ) + ( 6 q 3 / 5 ) ,
K 23 = ( 2 q 1 / 15 ) ( 22 q 2 / 15 ) ( 16 q 3 / 15 ) ,
K 33 = ( 8 q 1 / 5 ) + ( 8 q 2 / 5 ) + ( 32 q 3 / 15 ) .
[ M ( q ) ] e = L ¯ e [ M 11 M 12 M 13 M 12 M 22 M 23 M 13 M 23 M 33 ] ,
M 11 = ( 13 q 1 / 140 ) ( q 2 / 140 ) + ( q 3 / 21 ) ,
M 12 = ( q 1 / 140 ) ( q 2 / 140 ) ( 2 q 3 / 105 ) ,
M 13 = ( q 1 / 21 ) ( 2 q 2 / 105 ) + ( 4 q 3 / 105 ) ,
M 22 = ( q 1 / 140 ) + ( 13 q 2 / 140 ) + ( q 3 / 21 ) ,
M 23 = ( 2 q 1 / 105 ) + ( q 2 / 21 ) + ( 4 q 3 / 105 ) ,
M 33 = ( 4 q 1 / 105 ) + ( 4 q 2 / 105 ) + ( 16 q 3 / 35 ) ,
[ Q ( q ) ] e = [ Q 11 Q 12 Q 13 Q 21 Q 22 Q 23 Q 31 Q 32 Q 33 ] ,
Q 11 = ( q 1 / 3 ) + ( q 2 / 30 ) ( q 3 / 5 ) ,
Q 12 = ( q 1 / 30 ) + ( q 2 / 15 ) + ( q 3 / 15 ) ,
Q 13 = ( q 1 / 5 ) + ( q 2 / 15 ) ( 8 q 3 / 15 ) ,
Q 21 = ( q 1 / 15 ) ( q 2 / 30 ) ( q 3 / 15 ) ,
Q 22 = ( q 1 / 30 ) + ( q 2 / 3 ) + ( q 3 / 5 ) ,
Q 23 = ( q 1 / 15 ) + ( q 2 / 5 ) + ( 8 q 3 / 15 ) ,
Q 31 = ( 2 q 1 / 5 ) + ( 4 q 3 / 15 ) ,
Q 32 = ( 2 q 2 / 5 ) ( 4 q 3 / 15 ) ,
Q 33 = ( 4 q 1 / 15 ) ( 4 q 2 / 15 ) .

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