Abstract

A theoretical and numerical investigation is presented of the behavior of magneto-optic TE–TM vector spatial solitons in the neighborhood of a waveguide discontinuity. A comprehensive perturbation theory is developed that leads to a global wave equation and a Lagrangian analysis of some of the soliton dynamics. The mathematics is supported by numerical simulations, and nonreciprocity, introduced by the magneto-optical influence, is clearly demonstrated. It is concluded that magneto-optic waveguides have great potential for use in nonlinear optics and in the anticipated improved chip technology.

© 2002 Optical Society of America

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References

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  1. Y. Svirko, N. Zheludev, and M. Osipov, “Bilayered chiral structures,” Appl. Phys. Lett. 78, 498–500 (2001).
    [CrossRef]
  2. F. Jonsson and C. Flytzanis, “Polarization state controlled multistability of a nonlinear magneto-optic cavity,” Phys. Rev. Lett. 82, 1426–1429 (1999).
    [CrossRef]
  3. N. Bahlmann, M. Lohmeyer, O. Zhuromskyy, H. Dötsch, and P. Hertel, “Nonreciprocal coupled waveguides for integrated optical isolators and circulators for TM modes,” Opt. Commun. 161, 330–337 (1999).
    [CrossRef]
  4. A. K. Zvezdin and V. A. Kotov, Modern Magneto-optics and Modern Magneto-optic Materials (Institute of Physics Publishing, Bristol, UK, 1997).
  5. V. I. Karpman, “Envelope solitons in gyrotropic media,” Phys. Rev. Lett. 74, 2455–2458 (1995).
    [CrossRef] [PubMed]
  6. F. Jonsson and C. Flytzanis, “Optical parametric generation phase-matching in magneto-optic media,” Opt. Lett. 24, 1514–1516 (1999).
    [CrossRef]
  7. A. D. Boardman and M. Xie, “Spatial solitons in discontinuous magneto-optic waveguides,” J. Opt. B 3, S244–S250 (2001).
    [CrossRef]
  8. A. D. Boardman and K. Xie, “Vector spatial solitons influenced by magneto-optic effects in cascadable nonlinear media,” Phys. Rev. E 55, 1–11 (1997).
    [CrossRef]
  9. A. D. Boardman and K. Xie, “Magnetic control of optical spatial solitons,” Phys. Rev. Lett. 75, 4591–4594 (1995).
    [CrossRef] [PubMed]
  10. A. D. Boardman, K. Xie, and M. Xie, “Applied magnetooptic soliton dynamics: TM and TE-TM-driven dynamics,” Acta Polon. 99, 7–16 (2001).
  11. J. M. Hammer, J. H. Abeles, and D. J. Channin, “Polycrystalline–metal–ferromagnetic optical waveguide isolator (POWI) for monolithic-integration with diode-laser devices,” IEEE Photon. Technol. Lett. 9, 631–633 (1997).
    [CrossRef]
  12. T. Mizumoto, H. Chihara, N. Tokui, and Y. Naito, “Verification of waveguide-type of optical circulator operation,” Electron. Lett. 26, 199–200 (1990).
    [CrossRef]
  13. O. Zhuromskyy, M. Lohmeyer, N. Bahlmann, H. Dötsch, P. Hertel, and A. F. Popkov, “Analysis of polarization independent Mach–Zehnder-type integrated optical isolator,” J. Lightwave Technol. 17, 1200–1205 (1999).
    [CrossRef]
  14. W. Zaets and K. Ando, “Optical waveguide isolator based on nonreciprical loss/gain of amplifier covered by ferromagnetic layer,” IEEE Photon. Technol. Lett. 11, 1012–1014 (1999).
    [CrossRef]
  15. W. Zaets and K. Ando, “Magnetically programmable bistable laser diode with ferromagnetic layer,” IEEE Photon. Technol. Lett. 13, 185–187 (2001).
    [CrossRef]
  16. H. Dötsch, P. Hertel, B. Lührmann, S. Sure, H. P. Winkler, and M. Ye, “Application of magnetic garnet films in integrated optics,” IEEE Trans. Magn. 28, 2979–2984 (1992).
    [CrossRef]
  17. E. Hecht and A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1974).
  18. J. Petykiewicz, Wave Optics (Kluwer Academic, Dordrecht, The Netherlands, 1992).
  19. S. Sugano and N. Kojima, eds., Magneto-Optics (Springer-Verlag, Berlin, 2000).
  20. T. Shintaku and T. Uno, “Optical waveguide isolator based upon non-reciprocal radiation,” J. Appl. Phys. 75, 8155–8159 (1994).
    [CrossRef]
  21. J. A. Mizumoto and Y. Naito, “Nonreciprocal propagation characteristics of YIG thin film,” IEEE Trans. Microwave Theory Tech. 30, 922–925 (1982).
    [CrossRef]
  22. W. Hübner, “Magneto-optics goes nonlinear,” Phys. World (October 1995), pp. 21–22.
  23. R. J. Hicken and J. Wu, “Observation of ferromagnetic resonances in the time domain,” J. Appl. Phys. 85, 4580–4582 (1999).
    [CrossRef]
  24. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995).
  25. W. A. Schroeder, D. S. McCallum, D. R. Harken, M. D. Dvorak, D. R. Anderson, and A. L. Smirl, “Intrinsic and induced anisotropy of nonlinear absorption and refraction in zinc blende semiconductors,” J. Opt. Soc. Am. B 12, 401–414 (1995).
    [CrossRef]

2001 (4)

Y. Svirko, N. Zheludev, and M. Osipov, “Bilayered chiral structures,” Appl. Phys. Lett. 78, 498–500 (2001).
[CrossRef]

A. D. Boardman and M. Xie, “Spatial solitons in discontinuous magneto-optic waveguides,” J. Opt. B 3, S244–S250 (2001).
[CrossRef]

A. D. Boardman, K. Xie, and M. Xie, “Applied magnetooptic soliton dynamics: TM and TE-TM-driven dynamics,” Acta Polon. 99, 7–16 (2001).

W. Zaets and K. Ando, “Magnetically programmable bistable laser diode with ferromagnetic layer,” IEEE Photon. Technol. Lett. 13, 185–187 (2001).
[CrossRef]

1999 (6)

O. Zhuromskyy, M. Lohmeyer, N. Bahlmann, H. Dötsch, P. Hertel, and A. F. Popkov, “Analysis of polarization independent Mach–Zehnder-type integrated optical isolator,” J. Lightwave Technol. 17, 1200–1205 (1999).
[CrossRef]

W. Zaets and K. Ando, “Optical waveguide isolator based on nonreciprical loss/gain of amplifier covered by ferromagnetic layer,” IEEE Photon. Technol. Lett. 11, 1012–1014 (1999).
[CrossRef]

R. J. Hicken and J. Wu, “Observation of ferromagnetic resonances in the time domain,” J. Appl. Phys. 85, 4580–4582 (1999).
[CrossRef]

F. Jonsson and C. Flytzanis, “Polarization state controlled multistability of a nonlinear magneto-optic cavity,” Phys. Rev. Lett. 82, 1426–1429 (1999).
[CrossRef]

N. Bahlmann, M. Lohmeyer, O. Zhuromskyy, H. Dötsch, and P. Hertel, “Nonreciprocal coupled waveguides for integrated optical isolators and circulators for TM modes,” Opt. Commun. 161, 330–337 (1999).
[CrossRef]

F. Jonsson and C. Flytzanis, “Optical parametric generation phase-matching in magneto-optic media,” Opt. Lett. 24, 1514–1516 (1999).
[CrossRef]

1997 (2)

J. M. Hammer, J. H. Abeles, and D. J. Channin, “Polycrystalline–metal–ferromagnetic optical waveguide isolator (POWI) for monolithic-integration with diode-laser devices,” IEEE Photon. Technol. Lett. 9, 631–633 (1997).
[CrossRef]

A. D. Boardman and K. Xie, “Vector spatial solitons influenced by magneto-optic effects in cascadable nonlinear media,” Phys. Rev. E 55, 1–11 (1997).
[CrossRef]

1995 (3)

A. D. Boardman and K. Xie, “Magnetic control of optical spatial solitons,” Phys. Rev. Lett. 75, 4591–4594 (1995).
[CrossRef] [PubMed]

V. I. Karpman, “Envelope solitons in gyrotropic media,” Phys. Rev. Lett. 74, 2455–2458 (1995).
[CrossRef] [PubMed]

W. A. Schroeder, D. S. McCallum, D. R. Harken, M. D. Dvorak, D. R. Anderson, and A. L. Smirl, “Intrinsic and induced anisotropy of nonlinear absorption and refraction in zinc blende semiconductors,” J. Opt. Soc. Am. B 12, 401–414 (1995).
[CrossRef]

1994 (1)

T. Shintaku and T. Uno, “Optical waveguide isolator based upon non-reciprocal radiation,” J. Appl. Phys. 75, 8155–8159 (1994).
[CrossRef]

1992 (1)

H. Dötsch, P. Hertel, B. Lührmann, S. Sure, H. P. Winkler, and M. Ye, “Application of magnetic garnet films in integrated optics,” IEEE Trans. Magn. 28, 2979–2984 (1992).
[CrossRef]

1990 (1)

T. Mizumoto, H. Chihara, N. Tokui, and Y. Naito, “Verification of waveguide-type of optical circulator operation,” Electron. Lett. 26, 199–200 (1990).
[CrossRef]

1982 (1)

J. A. Mizumoto and Y. Naito, “Nonreciprocal propagation characteristics of YIG thin film,” IEEE Trans. Microwave Theory Tech. 30, 922–925 (1982).
[CrossRef]

Abeles, J. H.

J. M. Hammer, J. H. Abeles, and D. J. Channin, “Polycrystalline–metal–ferromagnetic optical waveguide isolator (POWI) for monolithic-integration with diode-laser devices,” IEEE Photon. Technol. Lett. 9, 631–633 (1997).
[CrossRef]

Anderson, D. R.

Ando, K.

W. Zaets and K. Ando, “Magnetically programmable bistable laser diode with ferromagnetic layer,” IEEE Photon. Technol. Lett. 13, 185–187 (2001).
[CrossRef]

W. Zaets and K. Ando, “Optical waveguide isolator based on nonreciprical loss/gain of amplifier covered by ferromagnetic layer,” IEEE Photon. Technol. Lett. 11, 1012–1014 (1999).
[CrossRef]

Bahlmann, N.

O. Zhuromskyy, M. Lohmeyer, N. Bahlmann, H. Dötsch, P. Hertel, and A. F. Popkov, “Analysis of polarization independent Mach–Zehnder-type integrated optical isolator,” J. Lightwave Technol. 17, 1200–1205 (1999).
[CrossRef]

N. Bahlmann, M. Lohmeyer, O. Zhuromskyy, H. Dötsch, and P. Hertel, “Nonreciprocal coupled waveguides for integrated optical isolators and circulators for TM modes,” Opt. Commun. 161, 330–337 (1999).
[CrossRef]

Boardman, A. D.

A. D. Boardman and M. Xie, “Spatial solitons in discontinuous magneto-optic waveguides,” J. Opt. B 3, S244–S250 (2001).
[CrossRef]

A. D. Boardman, K. Xie, and M. Xie, “Applied magnetooptic soliton dynamics: TM and TE-TM-driven dynamics,” Acta Polon. 99, 7–16 (2001).

A. D. Boardman and K. Xie, “Vector spatial solitons influenced by magneto-optic effects in cascadable nonlinear media,” Phys. Rev. E 55, 1–11 (1997).
[CrossRef]

A. D. Boardman and K. Xie, “Magnetic control of optical spatial solitons,” Phys. Rev. Lett. 75, 4591–4594 (1995).
[CrossRef] [PubMed]

Channin, D. J.

J. M. Hammer, J. H. Abeles, and D. J. Channin, “Polycrystalline–metal–ferromagnetic optical waveguide isolator (POWI) for monolithic-integration with diode-laser devices,” IEEE Photon. Technol. Lett. 9, 631–633 (1997).
[CrossRef]

Chihara, H.

T. Mizumoto, H. Chihara, N. Tokui, and Y. Naito, “Verification of waveguide-type of optical circulator operation,” Electron. Lett. 26, 199–200 (1990).
[CrossRef]

Dötsch, H.

O. Zhuromskyy, M. Lohmeyer, N. Bahlmann, H. Dötsch, P. Hertel, and A. F. Popkov, “Analysis of polarization independent Mach–Zehnder-type integrated optical isolator,” J. Lightwave Technol. 17, 1200–1205 (1999).
[CrossRef]

N. Bahlmann, M. Lohmeyer, O. Zhuromskyy, H. Dötsch, and P. Hertel, “Nonreciprocal coupled waveguides for integrated optical isolators and circulators for TM modes,” Opt. Commun. 161, 330–337 (1999).
[CrossRef]

H. Dötsch, P. Hertel, B. Lührmann, S. Sure, H. P. Winkler, and M. Ye, “Application of magnetic garnet films in integrated optics,” IEEE Trans. Magn. 28, 2979–2984 (1992).
[CrossRef]

Dvorak, M. D.

Flytzanis, C.

F. Jonsson and C. Flytzanis, “Polarization state controlled multistability of a nonlinear magneto-optic cavity,” Phys. Rev. Lett. 82, 1426–1429 (1999).
[CrossRef]

F. Jonsson and C. Flytzanis, “Optical parametric generation phase-matching in magneto-optic media,” Opt. Lett. 24, 1514–1516 (1999).
[CrossRef]

Hammer, J. M.

J. M. Hammer, J. H. Abeles, and D. J. Channin, “Polycrystalline–metal–ferromagnetic optical waveguide isolator (POWI) for monolithic-integration with diode-laser devices,” IEEE Photon. Technol. Lett. 9, 631–633 (1997).
[CrossRef]

Harken, D. R.

Hertel, P.

O. Zhuromskyy, M. Lohmeyer, N. Bahlmann, H. Dötsch, P. Hertel, and A. F. Popkov, “Analysis of polarization independent Mach–Zehnder-type integrated optical isolator,” J. Lightwave Technol. 17, 1200–1205 (1999).
[CrossRef]

N. Bahlmann, M. Lohmeyer, O. Zhuromskyy, H. Dötsch, and P. Hertel, “Nonreciprocal coupled waveguides for integrated optical isolators and circulators for TM modes,” Opt. Commun. 161, 330–337 (1999).
[CrossRef]

H. Dötsch, P. Hertel, B. Lührmann, S. Sure, H. P. Winkler, and M. Ye, “Application of magnetic garnet films in integrated optics,” IEEE Trans. Magn. 28, 2979–2984 (1992).
[CrossRef]

Hicken, R. J.

R. J. Hicken and J. Wu, “Observation of ferromagnetic resonances in the time domain,” J. Appl. Phys. 85, 4580–4582 (1999).
[CrossRef]

Hübner, W.

W. Hübner, “Magneto-optics goes nonlinear,” Phys. World (October 1995), pp. 21–22.

Jonsson, F.

F. Jonsson and C. Flytzanis, “Polarization state controlled multistability of a nonlinear magneto-optic cavity,” Phys. Rev. Lett. 82, 1426–1429 (1999).
[CrossRef]

F. Jonsson and C. Flytzanis, “Optical parametric generation phase-matching in magneto-optic media,” Opt. Lett. 24, 1514–1516 (1999).
[CrossRef]

Karpman, V. I.

V. I. Karpman, “Envelope solitons in gyrotropic media,” Phys. Rev. Lett. 74, 2455–2458 (1995).
[CrossRef] [PubMed]

Lohmeyer, M.

N. Bahlmann, M. Lohmeyer, O. Zhuromskyy, H. Dötsch, and P. Hertel, “Nonreciprocal coupled waveguides for integrated optical isolators and circulators for TM modes,” Opt. Commun. 161, 330–337 (1999).
[CrossRef]

O. Zhuromskyy, M. Lohmeyer, N. Bahlmann, H. Dötsch, P. Hertel, and A. F. Popkov, “Analysis of polarization independent Mach–Zehnder-type integrated optical isolator,” J. Lightwave Technol. 17, 1200–1205 (1999).
[CrossRef]

Lührmann, B.

H. Dötsch, P. Hertel, B. Lührmann, S. Sure, H. P. Winkler, and M. Ye, “Application of magnetic garnet films in integrated optics,” IEEE Trans. Magn. 28, 2979–2984 (1992).
[CrossRef]

McCallum, D. S.

Mizumoto, J. A.

J. A. Mizumoto and Y. Naito, “Nonreciprocal propagation characteristics of YIG thin film,” IEEE Trans. Microwave Theory Tech. 30, 922–925 (1982).
[CrossRef]

Mizumoto, T.

T. Mizumoto, H. Chihara, N. Tokui, and Y. Naito, “Verification of waveguide-type of optical circulator operation,” Electron. Lett. 26, 199–200 (1990).
[CrossRef]

Naito, Y.

T. Mizumoto, H. Chihara, N. Tokui, and Y. Naito, “Verification of waveguide-type of optical circulator operation,” Electron. Lett. 26, 199–200 (1990).
[CrossRef]

J. A. Mizumoto and Y. Naito, “Nonreciprocal propagation characteristics of YIG thin film,” IEEE Trans. Microwave Theory Tech. 30, 922–925 (1982).
[CrossRef]

Osipov, M.

Y. Svirko, N. Zheludev, and M. Osipov, “Bilayered chiral structures,” Appl. Phys. Lett. 78, 498–500 (2001).
[CrossRef]

Popkov, A. F.

Schroeder, W. A.

Shintaku, T.

T. Shintaku and T. Uno, “Optical waveguide isolator based upon non-reciprocal radiation,” J. Appl. Phys. 75, 8155–8159 (1994).
[CrossRef]

Smirl, A. L.

Sure, S.

H. Dötsch, P. Hertel, B. Lührmann, S. Sure, H. P. Winkler, and M. Ye, “Application of magnetic garnet films in integrated optics,” IEEE Trans. Magn. 28, 2979–2984 (1992).
[CrossRef]

Svirko, Y.

Y. Svirko, N. Zheludev, and M. Osipov, “Bilayered chiral structures,” Appl. Phys. Lett. 78, 498–500 (2001).
[CrossRef]

Tokui, N.

T. Mizumoto, H. Chihara, N. Tokui, and Y. Naito, “Verification of waveguide-type of optical circulator operation,” Electron. Lett. 26, 199–200 (1990).
[CrossRef]

Uno, T.

T. Shintaku and T. Uno, “Optical waveguide isolator based upon non-reciprocal radiation,” J. Appl. Phys. 75, 8155–8159 (1994).
[CrossRef]

Winkler, H. P.

H. Dötsch, P. Hertel, B. Lührmann, S. Sure, H. P. Winkler, and M. Ye, “Application of magnetic garnet films in integrated optics,” IEEE Trans. Magn. 28, 2979–2984 (1992).
[CrossRef]

Wu, J.

R. J. Hicken and J. Wu, “Observation of ferromagnetic resonances in the time domain,” J. Appl. Phys. 85, 4580–4582 (1999).
[CrossRef]

Xie, K.

A. D. Boardman, K. Xie, and M. Xie, “Applied magnetooptic soliton dynamics: TM and TE-TM-driven dynamics,” Acta Polon. 99, 7–16 (2001).

A. D. Boardman and K. Xie, “Vector spatial solitons influenced by magneto-optic effects in cascadable nonlinear media,” Phys. Rev. E 55, 1–11 (1997).
[CrossRef]

A. D. Boardman and K. Xie, “Magnetic control of optical spatial solitons,” Phys. Rev. Lett. 75, 4591–4594 (1995).
[CrossRef] [PubMed]

Xie, M.

A. D. Boardman and M. Xie, “Spatial solitons in discontinuous magneto-optic waveguides,” J. Opt. B 3, S244–S250 (2001).
[CrossRef]

A. D. Boardman, K. Xie, and M. Xie, “Applied magnetooptic soliton dynamics: TM and TE-TM-driven dynamics,” Acta Polon. 99, 7–16 (2001).

Ye, M.

H. Dötsch, P. Hertel, B. Lührmann, S. Sure, H. P. Winkler, and M. Ye, “Application of magnetic garnet films in integrated optics,” IEEE Trans. Magn. 28, 2979–2984 (1992).
[CrossRef]

Zaets, W.

W. Zaets and K. Ando, “Magnetically programmable bistable laser diode with ferromagnetic layer,” IEEE Photon. Technol. Lett. 13, 185–187 (2001).
[CrossRef]

W. Zaets and K. Ando, “Optical waveguide isolator based on nonreciprical loss/gain of amplifier covered by ferromagnetic layer,” IEEE Photon. Technol. Lett. 11, 1012–1014 (1999).
[CrossRef]

Zheludev, N.

Y. Svirko, N. Zheludev, and M. Osipov, “Bilayered chiral structures,” Appl. Phys. Lett. 78, 498–500 (2001).
[CrossRef]

Zhuromskyy, O.

N. Bahlmann, M. Lohmeyer, O. Zhuromskyy, H. Dötsch, and P. Hertel, “Nonreciprocal coupled waveguides for integrated optical isolators and circulators for TM modes,” Opt. Commun. 161, 330–337 (1999).
[CrossRef]

O. Zhuromskyy, M. Lohmeyer, N. Bahlmann, H. Dötsch, P. Hertel, and A. F. Popkov, “Analysis of polarization independent Mach–Zehnder-type integrated optical isolator,” J. Lightwave Technol. 17, 1200–1205 (1999).
[CrossRef]

Acta Polon. (1)

A. D. Boardman, K. Xie, and M. Xie, “Applied magnetooptic soliton dynamics: TM and TE-TM-driven dynamics,” Acta Polon. 99, 7–16 (2001).

Appl. Phys. Lett. (1)

Y. Svirko, N. Zheludev, and M. Osipov, “Bilayered chiral structures,” Appl. Phys. Lett. 78, 498–500 (2001).
[CrossRef]

Electron. Lett. (1)

T. Mizumoto, H. Chihara, N. Tokui, and Y. Naito, “Verification of waveguide-type of optical circulator operation,” Electron. Lett. 26, 199–200 (1990).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

J. M. Hammer, J. H. Abeles, and D. J. Channin, “Polycrystalline–metal–ferromagnetic optical waveguide isolator (POWI) for monolithic-integration with diode-laser devices,” IEEE Photon. Technol. Lett. 9, 631–633 (1997).
[CrossRef]

W. Zaets and K. Ando, “Optical waveguide isolator based on nonreciprical loss/gain of amplifier covered by ferromagnetic layer,” IEEE Photon. Technol. Lett. 11, 1012–1014 (1999).
[CrossRef]

W. Zaets and K. Ando, “Magnetically programmable bistable laser diode with ferromagnetic layer,” IEEE Photon. Technol. Lett. 13, 185–187 (2001).
[CrossRef]

IEEE Trans. Magn. (1)

H. Dötsch, P. Hertel, B. Lührmann, S. Sure, H. P. Winkler, and M. Ye, “Application of magnetic garnet films in integrated optics,” IEEE Trans. Magn. 28, 2979–2984 (1992).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

J. A. Mizumoto and Y. Naito, “Nonreciprocal propagation characteristics of YIG thin film,” IEEE Trans. Microwave Theory Tech. 30, 922–925 (1982).
[CrossRef]

J. Appl. Phys. (2)

R. J. Hicken and J. Wu, “Observation of ferromagnetic resonances in the time domain,” J. Appl. Phys. 85, 4580–4582 (1999).
[CrossRef]

T. Shintaku and T. Uno, “Optical waveguide isolator based upon non-reciprocal radiation,” J. Appl. Phys. 75, 8155–8159 (1994).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. B (1)

A. D. Boardman and M. Xie, “Spatial solitons in discontinuous magneto-optic waveguides,” J. Opt. B 3, S244–S250 (2001).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

N. Bahlmann, M. Lohmeyer, O. Zhuromskyy, H. Dötsch, and P. Hertel, “Nonreciprocal coupled waveguides for integrated optical isolators and circulators for TM modes,” Opt. Commun. 161, 330–337 (1999).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. E (1)

A. D. Boardman and K. Xie, “Vector spatial solitons influenced by magneto-optic effects in cascadable nonlinear media,” Phys. Rev. E 55, 1–11 (1997).
[CrossRef]

Phys. Rev. Lett. (3)

A. D. Boardman and K. Xie, “Magnetic control of optical spatial solitons,” Phys. Rev. Lett. 75, 4591–4594 (1995).
[CrossRef] [PubMed]

V. I. Karpman, “Envelope solitons in gyrotropic media,” Phys. Rev. Lett. 74, 2455–2458 (1995).
[CrossRef] [PubMed]

F. Jonsson and C. Flytzanis, “Polarization state controlled multistability of a nonlinear magneto-optic cavity,” Phys. Rev. Lett. 82, 1426–1429 (1999).
[CrossRef]

Phys. World (1)

W. Hübner, “Magneto-optics goes nonlinear,” Phys. World (October 1995), pp. 21–22.

Other (5)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995).

A. K. Zvezdin and V. A. Kotov, Modern Magneto-optics and Modern Magneto-optic Materials (Institute of Physics Publishing, Bristol, UK, 1997).

E. Hecht and A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1974).

J. Petykiewicz, Wave Optics (Kluwer Academic, Dordrecht, The Netherlands, 1992).

S. Sugano and N. Kojima, eds., Magneto-Optics (Springer-Verlag, Berlin, 2000).

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Figures (7)

Fig. 1
Fig. 1

Discontinuous waveguide structure: MO, magneto-optic material; NON-MO, nonmagnetic material.

Fig. 2
Fig. 2

Variation of ε¯e and ε¯m with film thickness d for d=0.3 µm and of Qyz with d. n1=1, n2=3.32, n3=2.56, nGGG=1.95, Q=4.2×10-3.

Fig. 3
Fig. 3

Variation of U(x1, x2) with x2=x2 cos α and with x1=x1 sin α, where α=λ/4. U(x) is a particular potential energy plot for α=π/4, and x1=x2. v1=1.0, v2=0.0, w11=0.0, w12=0.3, w21=0.0, w22=0.4.

Fig. 4
Fig. 4

Simulations of vector soliton splitting. Top, forward transmission with magnetic field H0 directed along x>0; v1=1.1, v2=0.0, ξ=0.7. Bottom, result of magnetic field reversal: v1=-1.1. Typical values are H0=23.87 Oe, LD=2β2D02(w/c)0.585 mm, β2=2.8862, λ=1.55 µm, and D0=5 µm.

Fig. 5
Fig. 5

Nonreciprocal behavior of a vector soliton sitting in a potential well. v1=±1.0, v2=0.0, w11=0.0, w12=0.3, w21=0.0, w22=0.4, ξ=0.5. Typical values are as in Fig. 4.

Fig. 6
Fig. 6

Dependence of critical angle on vector soliton content, as measured by α. v1=1.0, v2=0.0, w11=0.0, w12=0.1, w21=0.0, w22=0.4. Typical values are as in Fig. 4.

Fig. 7
Fig. 7

Magneto-optic vector soliton trajectories: v1=±1.0, v2=0.0, ξ=0.5. Typical values are as in Fig. 4.

Equations (54)

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

E1=T1(z)ξxxˆ exp-iωcβ1zexp(iωt),
E2=T2(z)ξyyˆ exp-iωcβ2z+ξzzˆ exp-iωcβ2zexp(iωt),
(·E)-2E=ω2c2εisE+ω2c2 Pm=ω2c2ε·E,
Pm=(ε-εis)E=0iεxyiεxz-iεxy0iεyz-iεxz-iεyz0ExEyEz,
 E1*·(·E)dy=0,
2iωcT1z=iω2c2T2 εxyξyξx*+εxzξzξx*dyβ1|ξx|2dy×exp-iωcγz,
2iωcT1z=iω2c2(ε¯xy+iε¯xz)exp-iωcγzT2,
ε¯xy= εxyξyξx*dyβ1 |ξx|2dy,ε¯xz=- εxz(iξz)ξx*dyβ1 |ξx|2dy,
2iωcT2z=-iω2c2T1(ε¯xy-iε¯xz)×expiωcγz+2ω2c2ε¯yzT2,
ε¯yz=cω εyzξyξyydyβ22 (|ξy|2+|ξz|2)dy.
T1z=0,iT2z=ωcε¯yzT2.
PNLx=¾[2χxxyy(|Ex|2+|Ey|2+|Ez|2)×Ex+χxyyx(Ex2+Ey2+Ez2)Ex*].
(·E)-2E=ω2c2εisE+ω2c2 PNL,
E1*·PNL=Ex*Px,E2*·PNL=Ey*Py+Ez*Pz.
2iωcT1z=ω2c2χ¯eT1|T1|2+ω2c2χ¯cT1|T2|2+ω2c2×χ¯FT22 exp-2iωcγz,
2iωcT2z=ω2c2χ¯mT2|T2|2+ω2c2χ¯cT2|T1|2+ω2c2χ¯FT2*T12 exp2iωcγz,
χ¯m=34 χxxxx[ξy4+ξz4+2(1-δ)ξy2ξz2+2δξy2ξz2]dyβ2 ξx2dyχ¯e,
χ¯cχ¯e1-δ,χ¯Fχ¯eδ,
2icωT1z=c2ω2β12T1x2+χ¯e(|T1|2+|T2|2)T1+χ¯eδT1*T22 exp-2iγωcz-χ¯eδT1|T2|2,
2icωT2z=c2ω2β12T2x2+2ε¯yzT2+χ¯e(|T1|2+|T2|2)T2-χ¯eδT2|T1|2+χ¯eδT1*T12 exp2iωcγz,
x=D0x,z=LDz,
T1=cωD02β1χ¯eψ1,T2=cωD02β1χ¯eψ2,
v=2β1ω2c2D02ε¯yz,γ=2β1ω2c2D02γ.
iψ1z=2ψ1x2+2(|ψ1|2+|ψ2|2)ψ1+2δψ1*ψ22 exp(-2iγz)-2δψ1|ψ2|2,
iψ2z=2ψ2x2+vψ2+2(|ψ1|2+|ψ2|2)ψ2-2δψ2|ψ1|2+2δψ2*ψ1 exp(2iγz),
iψ1z=2ψ1x2+2[|ψ1|2+(1-δ)|ψ2|2]ψ1,
iψ2z=2ψ2x2+2[(1-δ)|ψ1|2+|ψ2|2]2ψ2+vψ2.
εis=n12,y<0,
=n22,0<y<d,
=n33,y>d.
TE:2icωT1z=2(εis-εis)|ξx|2dy2β1 |ξx|2dyT1=2ε¯eT1,
2icωT2z=2(εis-εis)(|ξy|2+|ξz|2)dyβ2 εisβ22|ξy|2+|ξy|2+|ξz|2dy1=2ε¯mT2,
iψ1z=2ψ1x2+w1ψ1+2[|ψ1|2+(1-δ)|ψ2|2]ψ1,
iψ2z=2ψ2x2+(w2+v)ψ2+2[(1-δ)|ψ1|2+|ψ2|2]ψ2,
w1=2β1ω2c2D02ε¯e,w2=2β1ω2c2D02ε¯m.
v=v(x)=v1x<x0v2x>x0,
w1=w1(x)=w11x<x0w12x>x0,
w2=w2(x)=w21x<x0w22x>x0.
ε¯e=dd(nNL2-nm2)|ξx|2dy+d(nGGG2-nm2)|ξx|2dy2β1 -|ξx|2dy.
ε¯m=dd(nNL2-nm2)(|ξy|2+|ξz|2)dy+d(nGGG2-nm2)(|ξy|2+|ξz|2)dyβ2 -εisβ22|ξy|2+|ξy|2+|ξz|2dy.
v1=2β2ω2c2D02in32Qβ1d ξyξzdy-|ξx|2dy=2β2ω2c2D02in32β1Qyz,
L=j=12i2ψj*zψj-ψj*ψjz-ψjx2+|ψj|4+v|ψ2|2+2(1-δ)|ψ1|2|ψ2|2+w1|ψ1|2+w2|ψ2|2,
ψ1=A1 sin α,ψ2=A2 cos α,
Aj=ηj sech[ηj(x-xj)]exp[iξj(x-xj)+iθj],
L=- Ldx.
12dx1dz2+12dx2dz2=U(x1, x2),
U(x1, x2)=-tanhηx0-x1sin α(w11-w12)×sin2 α+(w11+w12)sin2 α+tanh×ηx0-x2cos α(v1-v2+w21-w22)cos2 α+(v1+w21+v2+w22)×cos2 α+16η3x2cos α-x1sin α×sin2 α cos2 α csch22ηx2cos α-x1sin α×coth2ηx2cos α-x1sin α-8η2 sin2 α cos2 α csch×2ηx2cos α-x1sin α+C.
ξ2>43sin2 α cos2 α.
12dxdz2=C1 tanh[η(x0-x)]+C2,
C1=(w11-w12)sin2 α+(v1+w21-v2-w22)cos2 α,
C2=2ξ02+[(w12-w11)sin2 α+(v2+w22-v1-w11)cos2 α]tanh[η(x0-x¯)]=2ξ02-C1 tanh[η(x0-x¯)].
U(x)=-C1 tanh[η(x0-x)].
z=-1η122C1+C2 lnC1+C2+{C1 tanh[η(x0-x)+C2]}1/2C1+C2-{C1 tanh[η(x0-x)+C2]}1/2+122C1-C2×ln{C1 tanh[η(x0-x)+C2]}1/2-C2-C1}{C1 tanh[η(x0-x)+C2]}1/2+C2-C1,
z=-12η1C1-C2 arctan{C1 tanh[η(x0-x)+C2]}1/2C1-C2+12C1+C2×lnC1+C2+{C1 tanh[η(x0-x)+C2]}1/2C1+C2-{C1 tanh[η(x0-x)+C2]}1/2+C.

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