Abstract

Nonlinear optical channel waveguides are modeled. It is demonstrated that a saturable nonlinear permittivity model is essential mathematically when strong nonlinear effects are simulated, so that the nonlinear wave equation possesses realistic solutions. Several precautionary factors in the numerical simulation of self-focusing behavior are addressed. For example, care must be exercised when the threshold power is calculated for some nonlinear structure exhibiting an abrupt all-optical switching phenomenon.

© 1993 Optical Society of America

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  1. C. T. Seaton, Xu Mai, G. I. Stegeman, and H. G. Winful, “Nonlinear guided wave applications,” Opt. Eng. 24, 593–599 (1985).
  2. G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, “Third order nonlinear integrated optics,” J. Lightwave Technol. 6, 953–970 (1988).
    [Crossref]
  3. G. I. Stegeman and R. H. Stolen, “Waveguides and fibers for nonlinear optics,” J. Opt. Soc. Am. B 6, 652–662 (1989).
    [Crossref]
  4. X. H. Wang, “Finite element methods for nonlinear optical waveguides,” Ph.D. dissertation (Monash University, Clayton, Victoria, Australia, 1992).
  5. K. Hayata and M. Koshiba, “Full vectorial analysis of nonlinear-optical waveguides,” J. Opt. Soc. Am. B 5, 2494–2501 (1988).
    [Crossref]
  6. X. H. Wang, L. N. Binh, and G. K. Cambrell, “Vectorial finite-element methods for nonlinear optical waveguides,” in Proceedings of the 13th Australian Conference on Optical Fibre Technology (Institution of Radio and Electronics Engineers, Sydney, Australia, 1988), pp. 129–132.
  7. X. H. Wang, G. K. Cambrell, and L. N. Binh, “Scalar and vector formulations of nonlinear optical waveguides: a comparison,” in Proceedings of the IREECON International 1989 (Institution of Radio and Electronics Engineers, Sydney, Australia, 1989), pp. 551–554.
  8. N. N. Akhmediev, R. F. Nabiev, and Yu. M. Popov, “Three-dimensional modes of a symmetric nonlinear plane waveguide,” Opt. Commun. 69, 247–252 (1989).
    [Crossref]
  9. R. D. Ettinger, F. A. Fernandez, B. M. A. Rahman, and J. B. Davies, “Vector finite element solution of saturable nonlinear strip-loaded optical waveguides,” IEEE Photon. Technol. Lett. 3, 147–149 (1991).
    [Crossref]
  10. N. N. Akhmediev, R. F. Nabiev, and Yu. M. Popov, “Stripe nonlinear surface waves,” Solid State Commun. 66, 981–985 (1988).
    [Crossref]
  11. N. N. Akhmediev, R. F. Naviev, and Yu. M. Popov, “Stripe nonlinear waves in a symmetrical planar structure,” Opt. Commun. 72, 190–194 (1989).
    [Crossref]
  12. A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A 35, 1159–1164 (1987).
    [Crossref] [PubMed]
  13. B. M. A. Rahman and J. B. Davies, “Penalty function improvement of waveguide solution by finite elements,” IEEE Trans. Microwave Theory Tech. MTT-32, 922–928 (1984).
    [Crossref]
  14. X. H. Wang, G. K. Cambrell, and L. N. Binh, “A package for nonlinear optical waveguides based on E-vector finite elements,” in Advances in Electrical Engineering Software, P. P. Silvester, ed. (Computational Mechanics Publications, Boston, Mass., 1990), pp. 151–162.
  15. All the powers in the power-dispersion relations in Ref. 5 should be scaled down by a factor of 2 [K. Hayata, Department of Electrical Engineering, Hokkaido University, Sapporo, Hokkaido 060, Japan (personal communication)]. The corrected values are used here to facilitate the comparison.
  16. L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Oxford, 1984).
  17. U. Langbein, F. Lederer, T. Peschel, and H.-E. Ponath, “Nonlinear guided waves in saturable nonlinear media,” Opt. Lett. 10, 571–573 (1985).
    [Crossref] [PubMed]
  18. G. I. Stegeman, E. M. Wright, C. T. Seaton, J. V. Moloney, T. P. Shen, A. A. Maradudin, and R. F. Wallis, “Nonlinear slab-guided waves in non-Kerr-like media,” IEEE J. Quantum Electron. QE-22, 977–983 (1986).
    [Crossref]
  19. S. J. Al–Bader and H. A. Jamid, “Nonlinear waves in saturable self-focusing thin films bounded by linear media,” IEEE J. Quantum Electron. 24, 2052–2058 (1988).
    [Crossref]
  20. R. Cuykendall and K. H. Strobl, “Effects of soft saturation on nonlinear interface switching,” Phys. Rev. A 41, 352–358 (1990).
    [Crossref] [PubMed]
  21. X. H. Wang, L. N. Binh, and G. K. Cambrell, “Numerical analysis of a nonlinear optical channel waveguide,” in Proceedings of the 14th Australian Conference on Optical Fibre Technology (Institution of Radio and Electronics Engineers, Sydney, Australia, 1989), p. 225–228.
  22. S. J. Al–Bader and H. A. Jamid, “Guided waves in nonlinear saturable self-focusing thin films,” IEEE J. Quantum Electron. QE-23, 1947–1955 (1987).
    [Crossref]
  23. W. C. Banyai, N. Finlayson, C. T. Seaton, G. I. Stegeman, M. O’Neill, T. G. Cullen, and C. N. Ironside, “Saturation of the nonlinear refractive-index change in a semiconductor-doped glass channel waveguide,” Appl. Phys. Lett. 54, 481–483 (1989).
    [Crossref]
  24. S. Y. Auyang and P. A. Wolff, “Free-carrier-induced third-order optical nonlinearities in semiconductors,” J. Opt. Soc. Am. B 6, 595–605 (1989).
    [Crossref]
  25. J. L. Coutaz and M. Kull, “Saturation of the nonlinear index of refraction in semiconductor-doped glass,” J. Opt. Soc. Am. B 8, 95–98 (1991).
    [Crossref]
  26. X. H. Wang and G. K. Cambrell, “All-optical switching and bistability phenomena in nonlinear optical waveguides: Part I Power dispersion relations,” in Proceedings of the 16th Australian Conference on Optical Fibre Technology (Institution of Radio and Electronics Engineers, Sydney, Australia, 1991), pp. 314–317.
  27. X. H. Wang and G. K. Cambrell, “Full vectorial simulation of bistability phenomena in nonlinear optical channel waveguides,” J. Opt. Soc. Am. B 10, 1090–1095 (1993).
    [Crossref]

1993 (1)

1991 (2)

R. D. Ettinger, F. A. Fernandez, B. M. A. Rahman, and J. B. Davies, “Vector finite element solution of saturable nonlinear strip-loaded optical waveguides,” IEEE Photon. Technol. Lett. 3, 147–149 (1991).
[Crossref]

J. L. Coutaz and M. Kull, “Saturation of the nonlinear index of refraction in semiconductor-doped glass,” J. Opt. Soc. Am. B 8, 95–98 (1991).
[Crossref]

1990 (1)

R. Cuykendall and K. H. Strobl, “Effects of soft saturation on nonlinear interface switching,” Phys. Rev. A 41, 352–358 (1990).
[Crossref] [PubMed]

1989 (5)

W. C. Banyai, N. Finlayson, C. T. Seaton, G. I. Stegeman, M. O’Neill, T. G. Cullen, and C. N. Ironside, “Saturation of the nonlinear refractive-index change in a semiconductor-doped glass channel waveguide,” Appl. Phys. Lett. 54, 481–483 (1989).
[Crossref]

N. N. Akhmediev, R. F. Nabiev, and Yu. M. Popov, “Three-dimensional modes of a symmetric nonlinear plane waveguide,” Opt. Commun. 69, 247–252 (1989).
[Crossref]

S. Y. Auyang and P. A. Wolff, “Free-carrier-induced third-order optical nonlinearities in semiconductors,” J. Opt. Soc. Am. B 6, 595–605 (1989).
[Crossref]

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

N. N. Akhmediev, R. F. Naviev, and Yu. M. Popov, “Stripe nonlinear waves in a symmetrical planar structure,” Opt. Commun. 72, 190–194 (1989).
[Crossref]

1988 (4)

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

K. Hayata and M. Koshiba, “Full vectorial analysis of nonlinear-optical waveguides,” J. Opt. Soc. Am. B 5, 2494–2501 (1988).
[Crossref]

N. N. Akhmediev, R. F. Nabiev, and Yu. M. Popov, “Stripe nonlinear surface waves,” Solid State Commun. 66, 981–985 (1988).
[Crossref]

S. J. Al–Bader and H. A. Jamid, “Nonlinear waves in saturable self-focusing thin films bounded by linear media,” IEEE J. Quantum Electron. 24, 2052–2058 (1988).
[Crossref]

1987 (2)

S. J. Al–Bader and H. A. Jamid, “Guided waves in nonlinear saturable self-focusing thin films,” IEEE J. Quantum Electron. QE-23, 1947–1955 (1987).
[Crossref]

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A 35, 1159–1164 (1987).
[Crossref] [PubMed]

1986 (1)

G. I. Stegeman, E. M. Wright, C. T. Seaton, J. V. Moloney, T. P. Shen, A. A. Maradudin, and R. F. Wallis, “Nonlinear slab-guided waves in non-Kerr-like media,” IEEE J. Quantum Electron. QE-22, 977–983 (1986).
[Crossref]

1985 (2)

C. T. Seaton, Xu Mai, G. I. Stegeman, and H. G. Winful, “Nonlinear guided wave applications,” Opt. Eng. 24, 593–599 (1985).

U. Langbein, F. Lederer, T. Peschel, and H.-E. Ponath, “Nonlinear guided waves in saturable nonlinear media,” Opt. Lett. 10, 571–573 (1985).
[Crossref] [PubMed]

1984 (1)

B. M. A. Rahman and J. B. Davies, “Penalty function improvement of waveguide solution by finite elements,” IEEE Trans. Microwave Theory Tech. MTT-32, 922–928 (1984).
[Crossref]

Akhmediev, N. N.

N. N. Akhmediev, R. F. Nabiev, and Yu. M. Popov, “Three-dimensional modes of a symmetric nonlinear plane waveguide,” Opt. Commun. 69, 247–252 (1989).
[Crossref]

N. N. Akhmediev, R. F. Naviev, and Yu. M. Popov, “Stripe nonlinear waves in a symmetrical planar structure,” Opt. Commun. 72, 190–194 (1989).
[Crossref]

N. N. Akhmediev, R. F. Nabiev, and Yu. M. Popov, “Stripe nonlinear surface waves,” Solid State Commun. 66, 981–985 (1988).
[Crossref]

Al–Bader, S. J.

S. J. Al–Bader and H. A. Jamid, “Nonlinear waves in saturable self-focusing thin films bounded by linear media,” IEEE J. Quantum Electron. 24, 2052–2058 (1988).
[Crossref]

S. J. Al–Bader and H. A. Jamid, “Guided waves in nonlinear saturable self-focusing thin films,” IEEE J. Quantum Electron. QE-23, 1947–1955 (1987).
[Crossref]

Auyang, S. Y.

Banyai, W. C.

W. C. Banyai, N. Finlayson, C. T. Seaton, G. I. Stegeman, M. O’Neill, T. G. Cullen, and C. N. Ironside, “Saturation of the nonlinear refractive-index change in a semiconductor-doped glass channel waveguide,” Appl. Phys. Lett. 54, 481–483 (1989).
[Crossref]

Binh, L. N.

X. H. Wang, L. N. Binh, and G. K. Cambrell, “Numerical analysis of a nonlinear optical channel waveguide,” in Proceedings of the 14th Australian Conference on Optical Fibre Technology (Institution of Radio and Electronics Engineers, Sydney, Australia, 1989), p. 225–228.

X. H. Wang, G. K. Cambrell, and L. N. Binh, “A package for nonlinear optical waveguides based on E-vector finite elements,” in Advances in Electrical Engineering Software, P. P. Silvester, ed. (Computational Mechanics Publications, Boston, Mass., 1990), pp. 151–162.

X. H. Wang, G. K. Cambrell, and L. N. Binh, “Scalar and vector formulations of nonlinear optical waveguides: a comparison,” in Proceedings of the IREECON International 1989 (Institution of Radio and Electronics Engineers, Sydney, Australia, 1989), pp. 551–554.

X. H. Wang, L. N. Binh, and G. K. Cambrell, “Vectorial finite-element methods for nonlinear optical waveguides,” in Proceedings of the 13th Australian Conference on Optical Fibre Technology (Institution of Radio and Electronics Engineers, Sydney, Australia, 1988), pp. 129–132.

Boardman, A. D.

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A 35, 1159–1164 (1987).
[Crossref] [PubMed]

Cambrell, G. K.

X. H. Wang and G. K. Cambrell, “Full vectorial simulation of bistability phenomena in nonlinear optical channel waveguides,” J. Opt. Soc. Am. B 10, 1090–1095 (1993).
[Crossref]

X. H. Wang, L. N. Binh, and G. K. Cambrell, “Vectorial finite-element methods for nonlinear optical waveguides,” in Proceedings of the 13th Australian Conference on Optical Fibre Technology (Institution of Radio and Electronics Engineers, Sydney, Australia, 1988), pp. 129–132.

X. H. Wang, G. K. Cambrell, and L. N. Binh, “Scalar and vector formulations of nonlinear optical waveguides: a comparison,” in Proceedings of the IREECON International 1989 (Institution of Radio and Electronics Engineers, Sydney, Australia, 1989), pp. 551–554.

X. H. Wang, G. K. Cambrell, and L. N. Binh, “A package for nonlinear optical waveguides based on E-vector finite elements,” in Advances in Electrical Engineering Software, P. P. Silvester, ed. (Computational Mechanics Publications, Boston, Mass., 1990), pp. 151–162.

X. H. Wang, L. N. Binh, and G. K. Cambrell, “Numerical analysis of a nonlinear optical channel waveguide,” in Proceedings of the 14th Australian Conference on Optical Fibre Technology (Institution of Radio and Electronics Engineers, Sydney, Australia, 1989), p. 225–228.

X. H. Wang and G. K. Cambrell, “All-optical switching and bistability phenomena in nonlinear optical waveguides: Part I Power dispersion relations,” in Proceedings of the 16th Australian Conference on Optical Fibre Technology (Institution of Radio and Electronics Engineers, Sydney, Australia, 1991), pp. 314–317.

Coutaz, J. L.

Cullen, T. G.

W. C. Banyai, N. Finlayson, C. T. Seaton, G. I. Stegeman, M. O’Neill, T. G. Cullen, and C. N. Ironside, “Saturation of the nonlinear refractive-index change in a semiconductor-doped glass channel waveguide,” Appl. Phys. Lett. 54, 481–483 (1989).
[Crossref]

Cuykendall, R.

R. Cuykendall and K. H. Strobl, “Effects of soft saturation on nonlinear interface switching,” Phys. Rev. A 41, 352–358 (1990).
[Crossref] [PubMed]

Davies, J. B.

R. D. Ettinger, F. A. Fernandez, B. M. A. Rahman, and J. B. Davies, “Vector finite element solution of saturable nonlinear strip-loaded optical waveguides,” IEEE Photon. Technol. Lett. 3, 147–149 (1991).
[Crossref]

B. M. A. Rahman and J. B. Davies, “Penalty function improvement of waveguide solution by finite elements,” IEEE Trans. Microwave Theory Tech. MTT-32, 922–928 (1984).
[Crossref]

Ettinger, R. D.

R. D. Ettinger, F. A. Fernandez, B. M. A. Rahman, and J. B. Davies, “Vector finite element solution of saturable nonlinear strip-loaded optical waveguides,” IEEE Photon. Technol. Lett. 3, 147–149 (1991).
[Crossref]

Fernandez, F. A.

R. D. Ettinger, F. A. Fernandez, B. M. A. Rahman, and J. B. Davies, “Vector finite element solution of saturable nonlinear strip-loaded optical waveguides,” IEEE Photon. Technol. Lett. 3, 147–149 (1991).
[Crossref]

Finlayson, N.

W. C. Banyai, N. Finlayson, C. T. Seaton, G. I. Stegeman, M. O’Neill, T. G. Cullen, and C. N. Ironside, “Saturation of the nonlinear refractive-index change in a semiconductor-doped glass channel waveguide,” Appl. Phys. Lett. 54, 481–483 (1989).
[Crossref]

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

Hayata, K.

K. Hayata and M. Koshiba, “Full vectorial analysis of nonlinear-optical waveguides,” J. Opt. Soc. Am. B 5, 2494–2501 (1988).
[Crossref]

All the powers in the power-dispersion relations in Ref. 5 should be scaled down by a factor of 2 [K. Hayata, Department of Electrical Engineering, Hokkaido University, Sapporo, Hokkaido 060, Japan (personal communication)]. The corrected values are used here to facilitate the comparison.

Ironside, C. N.

W. C. Banyai, N. Finlayson, C. T. Seaton, G. I. Stegeman, M. O’Neill, T. G. Cullen, and C. N. Ironside, “Saturation of the nonlinear refractive-index change in a semiconductor-doped glass channel waveguide,” Appl. Phys. Lett. 54, 481–483 (1989).
[Crossref]

Jamid, H. A.

S. J. Al–Bader and H. A. Jamid, “Nonlinear waves in saturable self-focusing thin films bounded by linear media,” IEEE J. Quantum Electron. 24, 2052–2058 (1988).
[Crossref]

S. J. Al–Bader and H. A. Jamid, “Guided waves in nonlinear saturable self-focusing thin films,” IEEE J. Quantum Electron. QE-23, 1947–1955 (1987).
[Crossref]

Koshiba, M.

Kull, M.

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Oxford, 1984).

Langbein, U.

Lederer, F.

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Oxford, 1984).

Mai, Xu

C. T. Seaton, Xu Mai, G. I. Stegeman, and H. G. Winful, “Nonlinear guided wave applications,” Opt. Eng. 24, 593–599 (1985).

Maradudin, A. A.

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A 35, 1159–1164 (1987).
[Crossref] [PubMed]

G. I. Stegeman, E. M. Wright, C. T. Seaton, J. V. Moloney, T. P. Shen, A. A. Maradudin, and R. F. Wallis, “Nonlinear slab-guided waves in non-Kerr-like media,” IEEE J. Quantum Electron. QE-22, 977–983 (1986).
[Crossref]

Moloney, J. V.

G. I. Stegeman, E. M. Wright, C. T. Seaton, J. V. Moloney, T. P. Shen, A. A. Maradudin, and R. F. Wallis, “Nonlinear slab-guided waves in non-Kerr-like media,” IEEE J. Quantum Electron. QE-22, 977–983 (1986).
[Crossref]

Nabiev, R. F.

N. N. Akhmediev, R. F. Nabiev, and Yu. M. Popov, “Three-dimensional modes of a symmetric nonlinear plane waveguide,” Opt. Commun. 69, 247–252 (1989).
[Crossref]

N. N. Akhmediev, R. F. Nabiev, and Yu. M. Popov, “Stripe nonlinear surface waves,” Solid State Commun. 66, 981–985 (1988).
[Crossref]

Naviev, R. F.

N. N. Akhmediev, R. F. Naviev, and Yu. M. Popov, “Stripe nonlinear waves in a symmetrical planar structure,” Opt. Commun. 72, 190–194 (1989).
[Crossref]

O’Neill, M.

W. C. Banyai, N. Finlayson, C. T. Seaton, G. I. Stegeman, M. O’Neill, T. G. Cullen, and C. N. Ironside, “Saturation of the nonlinear refractive-index change in a semiconductor-doped glass channel waveguide,” Appl. Phys. Lett. 54, 481–483 (1989).
[Crossref]

Peschel, T.

Ponath, H.-E.

Popov, Yu. M.

N. N. Akhmediev, R. F. Naviev, and Yu. M. Popov, “Stripe nonlinear waves in a symmetrical planar structure,” Opt. Commun. 72, 190–194 (1989).
[Crossref]

N. N. Akhmediev, R. F. Nabiev, and Yu. M. Popov, “Three-dimensional modes of a symmetric nonlinear plane waveguide,” Opt. Commun. 69, 247–252 (1989).
[Crossref]

N. N. Akhmediev, R. F. Nabiev, and Yu. M. Popov, “Stripe nonlinear surface waves,” Solid State Commun. 66, 981–985 (1988).
[Crossref]

Rahman, B. M. A.

R. D. Ettinger, F. A. Fernandez, B. M. A. Rahman, and J. B. Davies, “Vector finite element solution of saturable nonlinear strip-loaded optical waveguides,” IEEE Photon. Technol. Lett. 3, 147–149 (1991).
[Crossref]

B. M. A. Rahman and J. B. Davies, “Penalty function improvement of waveguide solution by finite elements,” IEEE Trans. Microwave Theory Tech. MTT-32, 922–928 (1984).
[Crossref]

Seaton, C. T.

W. C. Banyai, N. Finlayson, C. T. Seaton, G. I. Stegeman, M. O’Neill, T. G. Cullen, and C. N. Ironside, “Saturation of the nonlinear refractive-index change in a semiconductor-doped glass channel waveguide,” Appl. Phys. Lett. 54, 481–483 (1989).
[Crossref]

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

G. I. Stegeman, E. M. Wright, C. T. Seaton, J. V. Moloney, T. P. Shen, A. A. Maradudin, and R. F. Wallis, “Nonlinear slab-guided waves in non-Kerr-like media,” IEEE J. Quantum Electron. QE-22, 977–983 (1986).
[Crossref]

C. T. Seaton, Xu Mai, G. I. Stegeman, and H. G. Winful, “Nonlinear guided wave applications,” Opt. Eng. 24, 593–599 (1985).

Shen, T. P.

G. I. Stegeman, E. M. Wright, C. T. Seaton, J. V. Moloney, T. P. Shen, A. A. Maradudin, and R. F. Wallis, “Nonlinear slab-guided waves in non-Kerr-like media,” IEEE J. Quantum Electron. QE-22, 977–983 (1986).
[Crossref]

Stegeman, G. I.

W. C. Banyai, N. Finlayson, C. T. Seaton, G. I. Stegeman, M. O’Neill, T. G. Cullen, and C. N. Ironside, “Saturation of the nonlinear refractive-index change in a semiconductor-doped glass channel waveguide,” Appl. Phys. Lett. 54, 481–483 (1989).
[Crossref]

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

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

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A 35, 1159–1164 (1987).
[Crossref] [PubMed]

G. I. Stegeman, E. M. Wright, C. T. Seaton, J. V. Moloney, T. P. Shen, A. A. Maradudin, and R. F. Wallis, “Nonlinear slab-guided waves in non-Kerr-like media,” IEEE J. Quantum Electron. QE-22, 977–983 (1986).
[Crossref]

C. T. Seaton, Xu Mai, G. I. Stegeman, and H. G. Winful, “Nonlinear guided wave applications,” Opt. Eng. 24, 593–599 (1985).

Stolen, R. H.

Strobl, K. H.

R. Cuykendall and K. H. Strobl, “Effects of soft saturation on nonlinear interface switching,” Phys. Rev. A 41, 352–358 (1990).
[Crossref] [PubMed]

Twardowski, T.

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A 35, 1159–1164 (1987).
[Crossref] [PubMed]

Wallis, R. F.

G. I. Stegeman, E. M. Wright, C. T. Seaton, J. V. Moloney, T. P. Shen, A. A. Maradudin, and R. F. Wallis, “Nonlinear slab-guided waves in non-Kerr-like media,” IEEE J. Quantum Electron. QE-22, 977–983 (1986).
[Crossref]

Wang, X. H.

X. H. Wang and G. K. Cambrell, “Full vectorial simulation of bistability phenomena in nonlinear optical channel waveguides,” J. Opt. Soc. Am. B 10, 1090–1095 (1993).
[Crossref]

X. H. Wang and G. K. Cambrell, “All-optical switching and bistability phenomena in nonlinear optical waveguides: Part I Power dispersion relations,” in Proceedings of the 16th Australian Conference on Optical Fibre Technology (Institution of Radio and Electronics Engineers, Sydney, Australia, 1991), pp. 314–317.

X. H. Wang, “Finite element methods for nonlinear optical waveguides,” Ph.D. dissertation (Monash University, Clayton, Victoria, Australia, 1992).

X. H. Wang, L. N. Binh, and G. K. Cambrell, “Numerical analysis of a nonlinear optical channel waveguide,” in Proceedings of the 14th Australian Conference on Optical Fibre Technology (Institution of Radio and Electronics Engineers, Sydney, Australia, 1989), p. 225–228.

X. H. Wang, G. K. Cambrell, and L. N. Binh, “A package for nonlinear optical waveguides based on E-vector finite elements,” in Advances in Electrical Engineering Software, P. P. Silvester, ed. (Computational Mechanics Publications, Boston, Mass., 1990), pp. 151–162.

X. H. Wang, L. N. Binh, and G. K. Cambrell, “Vectorial finite-element methods for nonlinear optical waveguides,” in Proceedings of the 13th Australian Conference on Optical Fibre Technology (Institution of Radio and Electronics Engineers, Sydney, Australia, 1988), pp. 129–132.

X. H. Wang, G. K. Cambrell, and L. N. Binh, “Scalar and vector formulations of nonlinear optical waveguides: a comparison,” in Proceedings of the IREECON International 1989 (Institution of Radio and Electronics Engineers, Sydney, Australia, 1989), pp. 551–554.

Winful, H. G.

C. T. Seaton, Xu Mai, G. I. Stegeman, and H. G. Winful, “Nonlinear guided wave applications,” Opt. Eng. 24, 593–599 (1985).

Wolff, P. A.

Wright, E. M.

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

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A 35, 1159–1164 (1987).
[Crossref] [PubMed]

G. I. Stegeman, E. M. Wright, C. T. Seaton, J. V. Moloney, T. P. Shen, A. A. Maradudin, and R. F. Wallis, “Nonlinear slab-guided waves in non-Kerr-like media,” IEEE J. Quantum Electron. QE-22, 977–983 (1986).
[Crossref]

Zanoni, R.

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

Appl. Phys. Lett. (1)

W. C. Banyai, N. Finlayson, C. T. Seaton, G. I. Stegeman, M. O’Neill, T. G. Cullen, and C. N. Ironside, “Saturation of the nonlinear refractive-index change in a semiconductor-doped glass channel waveguide,” Appl. Phys. Lett. 54, 481–483 (1989).
[Crossref]

IEEE J. Quantum Electron. (3)

S. J. Al–Bader and H. A. Jamid, “Guided waves in nonlinear saturable self-focusing thin films,” IEEE J. Quantum Electron. QE-23, 1947–1955 (1987).
[Crossref]

G. I. Stegeman, E. M. Wright, C. T. Seaton, J. V. Moloney, T. P. Shen, A. A. Maradudin, and R. F. Wallis, “Nonlinear slab-guided waves in non-Kerr-like media,” IEEE J. Quantum Electron. QE-22, 977–983 (1986).
[Crossref]

S. J. Al–Bader and H. A. Jamid, “Nonlinear waves in saturable self-focusing thin films bounded by linear media,” IEEE J. Quantum Electron. 24, 2052–2058 (1988).
[Crossref]

IEEE Photon. Technol. Lett. (1)

R. D. Ettinger, F. A. Fernandez, B. M. A. Rahman, and J. B. Davies, “Vector finite element solution of saturable nonlinear strip-loaded optical waveguides,” IEEE Photon. Technol. Lett. 3, 147–149 (1991).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

B. M. A. Rahman and J. B. Davies, “Penalty function improvement of waveguide solution by finite elements,” IEEE Trans. Microwave Theory Tech. MTT-32, 922–928 (1984).
[Crossref]

J. Lightwave Technol. (1)

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

J. Opt. Soc. Am. B (5)

Opt. Commun. (2)

N. N. Akhmediev, R. F. Naviev, and Yu. M. Popov, “Stripe nonlinear waves in a symmetrical planar structure,” Opt. Commun. 72, 190–194 (1989).
[Crossref]

N. N. Akhmediev, R. F. Nabiev, and Yu. M. Popov, “Three-dimensional modes of a symmetric nonlinear plane waveguide,” Opt. Commun. 69, 247–252 (1989).
[Crossref]

Opt. Eng. (1)

C. T. Seaton, Xu Mai, G. I. Stegeman, and H. G. Winful, “Nonlinear guided wave applications,” Opt. Eng. 24, 593–599 (1985).

Opt. Lett. (1)

Phys. Rev. A (2)

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A 35, 1159–1164 (1987).
[Crossref] [PubMed]

R. Cuykendall and K. H. Strobl, “Effects of soft saturation on nonlinear interface switching,” Phys. Rev. A 41, 352–358 (1990).
[Crossref] [PubMed]

Solid State Commun. (1)

N. N. Akhmediev, R. F. Nabiev, and Yu. M. Popov, “Stripe nonlinear surface waves,” Solid State Commun. 66, 981–985 (1988).
[Crossref]

Other (8)

X. H. Wang, L. N. Binh, and G. K. Cambrell, “Vectorial finite-element methods for nonlinear optical waveguides,” in Proceedings of the 13th Australian Conference on Optical Fibre Technology (Institution of Radio and Electronics Engineers, Sydney, Australia, 1988), pp. 129–132.

X. H. Wang, G. K. Cambrell, and L. N. Binh, “Scalar and vector formulations of nonlinear optical waveguides: a comparison,” in Proceedings of the IREECON International 1989 (Institution of Radio and Electronics Engineers, Sydney, Australia, 1989), pp. 551–554.

X. H. Wang, “Finite element methods for nonlinear optical waveguides,” Ph.D. dissertation (Monash University, Clayton, Victoria, Australia, 1992).

X. H. Wang, L. N. Binh, and G. K. Cambrell, “Numerical analysis of a nonlinear optical channel waveguide,” in Proceedings of the 14th Australian Conference on Optical Fibre Technology (Institution of Radio and Electronics Engineers, Sydney, Australia, 1989), p. 225–228.

X. H. Wang, G. K. Cambrell, and L. N. Binh, “A package for nonlinear optical waveguides based on E-vector finite elements,” in Advances in Electrical Engineering Software, P. P. Silvester, ed. (Computational Mechanics Publications, Boston, Mass., 1990), pp. 151–162.

All the powers in the power-dispersion relations in Ref. 5 should be scaled down by a factor of 2 [K. Hayata, Department of Electrical Engineering, Hokkaido University, Sapporo, Hokkaido 060, Japan (personal communication)]. The corrected values are used here to facilitate the comparison.

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Oxford, 1984).

X. H. Wang and G. K. Cambrell, “All-optical switching and bistability phenomena in nonlinear optical waveguides: Part I Power dispersion relations,” in Proceedings of the 16th Australian Conference on Optical Fibre Technology (Institution of Radio and Electronics Engineers, Sydney, Australia, 1991), pp. 314–317.

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Figures (15)

Fig. 1
Fig. 1

Classical structure of a rectangular channel waveguide with electric wall boundaries.

Fig. 2
Fig. 2

Mesh network of the rectangular channel waveguide structure (116 second-order elements, 265 nodes).

Fig. 3
Fig. 3

Magnetic field distributions of the fundamental mode ( H 11 x or E 11 y) for the rectangular channel waveguide in the linear case.

Fig. 4
Fig. 4

Power dispersion curve of the fundamental nonlinear mode. The effective index is β/k0, and the optical power is in units of microwatts.

Fig. 5
Fig. 5

Magnetic field distributions of the fundamental nonlinear mode at P = 80 μW, with the mesh shown in Fig. 2.

Fig. 6
Fig. 6

Refined mesh network of the rectangular channel waveguide structure (176 second-order elements, 389 nodes).

Fig. 7
Fig. 7

Power-dispersion curve of the fundamental nonlinear mode corresponding to both the original and the refined meshes. The effective index is β/k0, and the optical power is in units of microwatts.

Fig. 8
Fig. 8

Convergence behavior of the effective index during the nonlinear iteration procedure for P = 80 μW, with both the original and the refined meshes.

Fig. 9
Fig. 9

Magnetic field distributions of the fundamental nonlinear mode at P = 80 μW, with the refined mesh after 23 nonlinear iterations.

Fig. 10
Fig. 10

Comparison of the magnetic field magnitude distributions of the fundamental nonlinear mode ||H||2 at P = 80 μW resulting from (a) the original mesh and (b) the refined mesh after 23 nonlinear iterations.

Fig. 11
Fig. 11

Convergence behavior of the effective index with respect to mesh refinement for P = 60 μW.

Fig. 12
Fig. 12

Convergence behavior of the effective index during the nonlinear iteration procedure for P = 80 μW with three different mesh structures, where the three mesh structures of second-order triangular elements are 166 elements with 367 nodes, 216 elements with 475 nodes, and 270 elements with 585 nodes.

Fig. 13
Fig. 13

Power-dispersion curve of the fundamental nonlinear mode corresponding to both the original and the refined meshes for the model with saturation. The optical power is in units of microwatts.

Fig. 14
Fig. 14

Magnetic field distributions of the fundamental nonlinear mode for the saturating model at P = 80 μW, with the original mesh.

Fig. 15
Fig. 15

Magnetic field distributions of the fundamental nonlinear mode for the saturating model at P = 80 μW, with the refined mesh.

Equations (13)

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ˆ r = ˆ r l = ˆ r n .
ˆ r n = [ 1 n 0 0 0 2 n 0 0 0 3 n ] .
i n = a ( | E i | 2 + b j = i ( j i ) 3 | E j | 2 ) , i = 1 , 2 , 3 ,
a = c 0 0 r l n 2 ,
b = { 1 electrostriction and heating 1 3 electronic distortion 1 2 molecular orientation .
× ( ˆ r 1 · × H ) p μ ˆ r · · ( μ ˆ r · H ) = k 0 2 μ ˆ r · H ,
P = Z 0 2 k 0 ( { Ω [ H * × ( ˆ r 1 · × H ) ] · a z d x d y } ) ,
r l = { 1.55 2 core 1.55 2 cladding .
λ i + 1 λ i λ i + 1 1.0 × 10 6 ,
r n = a | E | 2 1 + α a | E | 2
r n = 1 α [ 1 exp ( α a | E | 2 ) ] ,
i n = a f i ( E ) 1 + α a f i ( E ) , i = 1 , 2 , 3
i n = a ( E 2 ) 2 1 + α a ( E 2 ) 2 , i = 1 , 2 , 3 ,

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