Abstract

The theoretical approach recently proposed for investigating cross-phase modulation phenomena in weakly guiding waveguides with an arbitrary cross section is revisited. The unidirectional propagation equation is reformulated so that it becomes possible to precisely investigate the evolution of the polarization state in both weakly and strongly guiding devices. For [100]-oriented AlGaAs asymmetric waveguides, it is seen that interaction between the linear and nonlinear birefringences depends on the relative position of the slow axis of the device with respect to the 45° polarization-maintaining axis in the bulk medium. The design of an AlGaAs active polarization converter with a length of 3 cm and an effective area of 6 μm2 and that enables a quasi-total TE–TM conversion when using a peak power of 63 W is proposed.

© 1998 Optical Society of America

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References

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  1. M. Fontaine, “Theoretical approach to investigating cross-phase modulation phenomena in waveguides with an arbitrary cross section,” J. Opt. Soc. Am. B 14, 1444–1452 (1997).
    [CrossRef]
  2. V. P. Tzolov and M. Fontaine, “A passive polarization converter free of longitudinally-periodic structure,” Opt. Commun. 127, 7–13 (1996).
    [CrossRef]
  3. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, New York, 1983).
  4. A. W. Snyder and X.-H. Zheng, “Optical fibers of arbitrary cross sections,” J. Opt. Soc. Am. A 3, 600–609 (1986).
    [CrossRef]
  5. G. I. Stegeman, A. Villeneuve, J. Kang, J. S. Aitchison, C. N. Ironside, K. Al-Hemyari, C. C. Yang, C.-H. Lin, H.-H. Lin, G. T. Kennedy, R. S. Grant, and W. Sibbett, “AlGaAs below half bandgap: the silicon of nonlinear optical materials,” Int. J. Nonlinear Opt. Phys. 3, 347–371 (1994).
    [CrossRef]
  6. D. C. Hutchings, “Nonlinear-optical activity owing to anisotropy of ultrafast nonlinear refraction in cubic materials,” Opt. Lett. 20, 1607–1609 (1995).
    [CrossRef] [PubMed]
  7. D. C. Hutchings, J. S. Aitchison, B. S. Wherrett, G. T. Kennedy, and W. Sibbett, “Polarization dependence of ultrafast nonlinear refraction in an AlGaAs waveguide at the half-band gap,” Opt. Lett. 20, 991–993 (1995).
    [CrossRef] [PubMed]
  8. D. C. Hutchings and B. S. Wherrett, “Theory of the anisotropy of ultrafast nonlinear refraction in zinc-blende semiconductors,” Phys. Rev. B 52, 8150–8159 (1995).
    [CrossRef]
  9. V. P. Tzolov, M. Fontaine, N. Godbout, and S. Lacroix, “Nonlinear self-phase modulation effects: a vectorial first-order perturbation approach,” Opt. Lett. 20, 456–458 (1995).
    [CrossRef] [PubMed]
  10. A. Villeneuve, J. S. Aitchison, B. Vögele, R. Tapella, J. U. Kang, C. Trevino, and G. I. Stegeman, “Waveguide design for minimum nonlinear area and switching energy in AlGaAs at half the bandgap,” Electron. Lett. 31, 549–551 (1995).
    [CrossRef]
  11. V. P. Tzolov and M. Fontaine, “Theoretical analysis of birefringence and form-induced polarization mode dispersion in birefringent optical fibers: a full-vectorial approach,” J. Appl. Phys. 77, 1–6 (1995).
    [CrossRef]
  12. V. P. Tzolov and M. Fontaine, “Nonlinear modal parameters of optical fibers: A full-vectorial approach,” J. Opt. Soc. Am. B 12, 1933–1941 (1995).
    [CrossRef]
  13. M. Fontaine, B. Wu, V. P. Tzolov, W. J. Bock, and W. Urbanczyk, “Theoretical and experimental analysis of thermal stress effects on modal polarization properties of highly birefringent optical fibers,” J. Lightwave Technol. 14, 585–591 (1996).
    [CrossRef]
  14. V. P. Tzolov, M. Fontaine, G. Sewell, and A. Dela⁁ge, “Full vectorial simulation for characterizing loss or gain in optical devices with an accurate and automated finite-element method,” Appl. Opt. 36, 622–628 (1997).
    [CrossRef] [PubMed]
  15. In Ref. 1 the symbol φ used in Section 3 and Table 1 refers to the orientation of the optical axis, making an angle less than 45° with the x⁁ axis. In Table 1 the angle the optical axis x⁁0 makes with x⁁, noted |φ| and equal to 39.7°, is then the angle |η| defined in this paper.
  16. J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The nonlinear optical properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. 33, 341–348 (1997).
    [CrossRef]
  17. A. W. Snyder, D. J. Mitchell, and Y. S. Kivshar, “Unification of linear and nonlinear wave optics,” Mod. Phys. Lett. B 9, 1479–1506 (1995).
    [CrossRef]

1997 (3)

1996 (2)

M. Fontaine, B. Wu, V. P. Tzolov, W. J. Bock, and W. Urbanczyk, “Theoretical and experimental analysis of thermal stress effects on modal polarization properties of highly birefringent optical fibers,” J. Lightwave Technol. 14, 585–591 (1996).
[CrossRef]

V. P. Tzolov and M. Fontaine, “A passive polarization converter free of longitudinally-periodic structure,” Opt. Commun. 127, 7–13 (1996).
[CrossRef]

1995 (8)

D. C. Hutchings and B. S. Wherrett, “Theory of the anisotropy of ultrafast nonlinear refraction in zinc-blende semiconductors,” Phys. Rev. B 52, 8150–8159 (1995).
[CrossRef]

A. Villeneuve, J. S. Aitchison, B. Vögele, R. Tapella, J. U. Kang, C. Trevino, and G. I. Stegeman, “Waveguide design for minimum nonlinear area and switching energy in AlGaAs at half the bandgap,” Electron. Lett. 31, 549–551 (1995).
[CrossRef]

V. P. Tzolov and M. Fontaine, “Theoretical analysis of birefringence and form-induced polarization mode dispersion in birefringent optical fibers: a full-vectorial approach,” J. Appl. Phys. 77, 1–6 (1995).
[CrossRef]

V. P. Tzolov and M. Fontaine, “Nonlinear modal parameters of optical fibers: A full-vectorial approach,” J. Opt. Soc. Am. B 12, 1933–1941 (1995).
[CrossRef]

V. P. Tzolov, M. Fontaine, N. Godbout, and S. Lacroix, “Nonlinear self-phase modulation effects: a vectorial first-order perturbation approach,” Opt. Lett. 20, 456–458 (1995).
[CrossRef] [PubMed]

D. C. Hutchings, J. S. Aitchison, B. S. Wherrett, G. T. Kennedy, and W. Sibbett, “Polarization dependence of ultrafast nonlinear refraction in an AlGaAs waveguide at the half-band gap,” Opt. Lett. 20, 991–993 (1995).
[CrossRef] [PubMed]

D. C. Hutchings, “Nonlinear-optical activity owing to anisotropy of ultrafast nonlinear refraction in cubic materials,” Opt. Lett. 20, 1607–1609 (1995).
[CrossRef] [PubMed]

A. W. Snyder, D. J. Mitchell, and Y. S. Kivshar, “Unification of linear and nonlinear wave optics,” Mod. Phys. Lett. B 9, 1479–1506 (1995).
[CrossRef]

1994 (1)

G. I. Stegeman, A. Villeneuve, J. Kang, J. S. Aitchison, C. N. Ironside, K. Al-Hemyari, C. C. Yang, C.-H. Lin, H.-H. Lin, G. T. Kennedy, R. S. Grant, and W. Sibbett, “AlGaAs below half bandgap: the silicon of nonlinear optical materials,” Int. J. Nonlinear Opt. Phys. 3, 347–371 (1994).
[CrossRef]

1986 (1)

Aitchison, J. S.

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The nonlinear optical properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. 33, 341–348 (1997).
[CrossRef]

A. Villeneuve, J. S. Aitchison, B. Vögele, R. Tapella, J. U. Kang, C. Trevino, and G. I. Stegeman, “Waveguide design for minimum nonlinear area and switching energy in AlGaAs at half the bandgap,” Electron. Lett. 31, 549–551 (1995).
[CrossRef]

D. C. Hutchings, J. S. Aitchison, B. S. Wherrett, G. T. Kennedy, and W. Sibbett, “Polarization dependence of ultrafast nonlinear refraction in an AlGaAs waveguide at the half-band gap,” Opt. Lett. 20, 991–993 (1995).
[CrossRef] [PubMed]

G. I. Stegeman, A. Villeneuve, J. Kang, J. S. Aitchison, C. N. Ironside, K. Al-Hemyari, C. C. Yang, C.-H. Lin, H.-H. Lin, G. T. Kennedy, R. S. Grant, and W. Sibbett, “AlGaAs below half bandgap: the silicon of nonlinear optical materials,” Int. J. Nonlinear Opt. Phys. 3, 347–371 (1994).
[CrossRef]

Al-Hemyari, K.

G. I. Stegeman, A. Villeneuve, J. Kang, J. S. Aitchison, C. N. Ironside, K. Al-Hemyari, C. C. Yang, C.-H. Lin, H.-H. Lin, G. T. Kennedy, R. S. Grant, and W. Sibbett, “AlGaAs below half bandgap: the silicon of nonlinear optical materials,” Int. J. Nonlinear Opt. Phys. 3, 347–371 (1994).
[CrossRef]

Bock, W. J.

M. Fontaine, B. Wu, V. P. Tzolov, W. J. Bock, and W. Urbanczyk, “Theoretical and experimental analysis of thermal stress effects on modal polarization properties of highly birefringent optical fibers,” J. Lightwave Technol. 14, 585–591 (1996).
[CrossRef]

Dela?ge, A.

Fontaine, M.

V. P. Tzolov, M. Fontaine, G. Sewell, and A. Dela⁁ge, “Full vectorial simulation for characterizing loss or gain in optical devices with an accurate and automated finite-element method,” Appl. Opt. 36, 622–628 (1997).
[CrossRef] [PubMed]

M. Fontaine, “Theoretical approach to investigating cross-phase modulation phenomena in waveguides with an arbitrary cross section,” J. Opt. Soc. Am. B 14, 1444–1452 (1997).
[CrossRef]

M. Fontaine, B. Wu, V. P. Tzolov, W. J. Bock, and W. Urbanczyk, “Theoretical and experimental analysis of thermal stress effects on modal polarization properties of highly birefringent optical fibers,” J. Lightwave Technol. 14, 585–591 (1996).
[CrossRef]

V. P. Tzolov and M. Fontaine, “A passive polarization converter free of longitudinally-periodic structure,” Opt. Commun. 127, 7–13 (1996).
[CrossRef]

V. P. Tzolov, M. Fontaine, N. Godbout, and S. Lacroix, “Nonlinear self-phase modulation effects: a vectorial first-order perturbation approach,” Opt. Lett. 20, 456–458 (1995).
[CrossRef] [PubMed]

V. P. Tzolov and M. Fontaine, “Nonlinear modal parameters of optical fibers: A full-vectorial approach,” J. Opt. Soc. Am. B 12, 1933–1941 (1995).
[CrossRef]

V. P. Tzolov and M. Fontaine, “Theoretical analysis of birefringence and form-induced polarization mode dispersion in birefringent optical fibers: a full-vectorial approach,” J. Appl. Phys. 77, 1–6 (1995).
[CrossRef]

Godbout, N.

Grant, R. S.

G. I. Stegeman, A. Villeneuve, J. Kang, J. S. Aitchison, C. N. Ironside, K. Al-Hemyari, C. C. Yang, C.-H. Lin, H.-H. Lin, G. T. Kennedy, R. S. Grant, and W. Sibbett, “AlGaAs below half bandgap: the silicon of nonlinear optical materials,” Int. J. Nonlinear Opt. Phys. 3, 347–371 (1994).
[CrossRef]

Hutchings, D. C.

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The nonlinear optical properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. 33, 341–348 (1997).
[CrossRef]

D. C. Hutchings and B. S. Wherrett, “Theory of the anisotropy of ultrafast nonlinear refraction in zinc-blende semiconductors,” Phys. Rev. B 52, 8150–8159 (1995).
[CrossRef]

D. C. Hutchings, J. S. Aitchison, B. S. Wherrett, G. T. Kennedy, and W. Sibbett, “Polarization dependence of ultrafast nonlinear refraction in an AlGaAs waveguide at the half-band gap,” Opt. Lett. 20, 991–993 (1995).
[CrossRef] [PubMed]

D. C. Hutchings, “Nonlinear-optical activity owing to anisotropy of ultrafast nonlinear refraction in cubic materials,” Opt. Lett. 20, 1607–1609 (1995).
[CrossRef] [PubMed]

Ironside, C. N.

G. I. Stegeman, A. Villeneuve, J. Kang, J. S. Aitchison, C. N. Ironside, K. Al-Hemyari, C. C. Yang, C.-H. Lin, H.-H. Lin, G. T. Kennedy, R. S. Grant, and W. Sibbett, “AlGaAs below half bandgap: the silicon of nonlinear optical materials,” Int. J. Nonlinear Opt. Phys. 3, 347–371 (1994).
[CrossRef]

Kang, J.

G. I. Stegeman, A. Villeneuve, J. Kang, J. S. Aitchison, C. N. Ironside, K. Al-Hemyari, C. C. Yang, C.-H. Lin, H.-H. Lin, G. T. Kennedy, R. S. Grant, and W. Sibbett, “AlGaAs below half bandgap: the silicon of nonlinear optical materials,” Int. J. Nonlinear Opt. Phys. 3, 347–371 (1994).
[CrossRef]

Kang, J. U.

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The nonlinear optical properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. 33, 341–348 (1997).
[CrossRef]

A. Villeneuve, J. S. Aitchison, B. Vögele, R. Tapella, J. U. Kang, C. Trevino, and G. I. Stegeman, “Waveguide design for minimum nonlinear area and switching energy in AlGaAs at half the bandgap,” Electron. Lett. 31, 549–551 (1995).
[CrossRef]

Kennedy, G. T.

D. C. Hutchings, J. S. Aitchison, B. S. Wherrett, G. T. Kennedy, and W. Sibbett, “Polarization dependence of ultrafast nonlinear refraction in an AlGaAs waveguide at the half-band gap,” Opt. Lett. 20, 991–993 (1995).
[CrossRef] [PubMed]

G. I. Stegeman, A. Villeneuve, J. Kang, J. S. Aitchison, C. N. Ironside, K. Al-Hemyari, C. C. Yang, C.-H. Lin, H.-H. Lin, G. T. Kennedy, R. S. Grant, and W. Sibbett, “AlGaAs below half bandgap: the silicon of nonlinear optical materials,” Int. J. Nonlinear Opt. Phys. 3, 347–371 (1994).
[CrossRef]

Kivshar, Y. S.

A. W. Snyder, D. J. Mitchell, and Y. S. Kivshar, “Unification of linear and nonlinear wave optics,” Mod. Phys. Lett. B 9, 1479–1506 (1995).
[CrossRef]

Lacroix, S.

Lin, C.-H.

G. I. Stegeman, A. Villeneuve, J. Kang, J. S. Aitchison, C. N. Ironside, K. Al-Hemyari, C. C. Yang, C.-H. Lin, H.-H. Lin, G. T. Kennedy, R. S. Grant, and W. Sibbett, “AlGaAs below half bandgap: the silicon of nonlinear optical materials,” Int. J. Nonlinear Opt. Phys. 3, 347–371 (1994).
[CrossRef]

Lin, H.-H.

G. I. Stegeman, A. Villeneuve, J. Kang, J. S. Aitchison, C. N. Ironside, K. Al-Hemyari, C. C. Yang, C.-H. Lin, H.-H. Lin, G. T. Kennedy, R. S. Grant, and W. Sibbett, “AlGaAs below half bandgap: the silicon of nonlinear optical materials,” Int. J. Nonlinear Opt. Phys. 3, 347–371 (1994).
[CrossRef]

Mitchell, D. J.

A. W. Snyder, D. J. Mitchell, and Y. S. Kivshar, “Unification of linear and nonlinear wave optics,” Mod. Phys. Lett. B 9, 1479–1506 (1995).
[CrossRef]

Sewell, G.

Sibbett, W.

D. C. Hutchings, J. S. Aitchison, B. S. Wherrett, G. T. Kennedy, and W. Sibbett, “Polarization dependence of ultrafast nonlinear refraction in an AlGaAs waveguide at the half-band gap,” Opt. Lett. 20, 991–993 (1995).
[CrossRef] [PubMed]

G. I. Stegeman, A. Villeneuve, J. Kang, J. S. Aitchison, C. N. Ironside, K. Al-Hemyari, C. C. Yang, C.-H. Lin, H.-H. Lin, G. T. Kennedy, R. S. Grant, and W. Sibbett, “AlGaAs below half bandgap: the silicon of nonlinear optical materials,” Int. J. Nonlinear Opt. Phys. 3, 347–371 (1994).
[CrossRef]

Snyder, A. W.

A. W. Snyder, D. J. Mitchell, and Y. S. Kivshar, “Unification of linear and nonlinear wave optics,” Mod. Phys. Lett. B 9, 1479–1506 (1995).
[CrossRef]

A. W. Snyder and X.-H. Zheng, “Optical fibers of arbitrary cross sections,” J. Opt. Soc. Am. A 3, 600–609 (1986).
[CrossRef]

Stegeman, G. I.

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The nonlinear optical properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. 33, 341–348 (1997).
[CrossRef]

A. Villeneuve, J. S. Aitchison, B. Vögele, R. Tapella, J. U. Kang, C. Trevino, and G. I. Stegeman, “Waveguide design for minimum nonlinear area and switching energy in AlGaAs at half the bandgap,” Electron. Lett. 31, 549–551 (1995).
[CrossRef]

G. I. Stegeman, A. Villeneuve, J. Kang, J. S. Aitchison, C. N. Ironside, K. Al-Hemyari, C. C. Yang, C.-H. Lin, H.-H. Lin, G. T. Kennedy, R. S. Grant, and W. Sibbett, “AlGaAs below half bandgap: the silicon of nonlinear optical materials,” Int. J. Nonlinear Opt. Phys. 3, 347–371 (1994).
[CrossRef]

Tapella, R.

A. Villeneuve, J. S. Aitchison, B. Vögele, R. Tapella, J. U. Kang, C. Trevino, and G. I. Stegeman, “Waveguide design for minimum nonlinear area and switching energy in AlGaAs at half the bandgap,” Electron. Lett. 31, 549–551 (1995).
[CrossRef]

Trevino, C.

A. Villeneuve, J. S. Aitchison, B. Vögele, R. Tapella, J. U. Kang, C. Trevino, and G. I. Stegeman, “Waveguide design for minimum nonlinear area and switching energy in AlGaAs at half the bandgap,” Electron. Lett. 31, 549–551 (1995).
[CrossRef]

Tzolov, V. P.

V. P. Tzolov, M. Fontaine, G. Sewell, and A. Dela⁁ge, “Full vectorial simulation for characterizing loss or gain in optical devices with an accurate and automated finite-element method,” Appl. Opt. 36, 622–628 (1997).
[CrossRef] [PubMed]

V. P. Tzolov and M. Fontaine, “A passive polarization converter free of longitudinally-periodic structure,” Opt. Commun. 127, 7–13 (1996).
[CrossRef]

M. Fontaine, B. Wu, V. P. Tzolov, W. J. Bock, and W. Urbanczyk, “Theoretical and experimental analysis of thermal stress effects on modal polarization properties of highly birefringent optical fibers,” J. Lightwave Technol. 14, 585–591 (1996).
[CrossRef]

V. P. Tzolov, M. Fontaine, N. Godbout, and S. Lacroix, “Nonlinear self-phase modulation effects: a vectorial first-order perturbation approach,” Opt. Lett. 20, 456–458 (1995).
[CrossRef] [PubMed]

V. P. Tzolov and M. Fontaine, “Nonlinear modal parameters of optical fibers: A full-vectorial approach,” J. Opt. Soc. Am. B 12, 1933–1941 (1995).
[CrossRef]

V. P. Tzolov and M. Fontaine, “Theoretical analysis of birefringence and form-induced polarization mode dispersion in birefringent optical fibers: a full-vectorial approach,” J. Appl. Phys. 77, 1–6 (1995).
[CrossRef]

Urbanczyk, W.

M. Fontaine, B. Wu, V. P. Tzolov, W. J. Bock, and W. Urbanczyk, “Theoretical and experimental analysis of thermal stress effects on modal polarization properties of highly birefringent optical fibers,” J. Lightwave Technol. 14, 585–591 (1996).
[CrossRef]

Villeneuve, A.

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The nonlinear optical properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. 33, 341–348 (1997).
[CrossRef]

A. Villeneuve, J. S. Aitchison, B. Vögele, R. Tapella, J. U. Kang, C. Trevino, and G. I. Stegeman, “Waveguide design for minimum nonlinear area and switching energy in AlGaAs at half the bandgap,” Electron. Lett. 31, 549–551 (1995).
[CrossRef]

G. I. Stegeman, A. Villeneuve, J. Kang, J. S. Aitchison, C. N. Ironside, K. Al-Hemyari, C. C. Yang, C.-H. Lin, H.-H. Lin, G. T. Kennedy, R. S. Grant, and W. Sibbett, “AlGaAs below half bandgap: the silicon of nonlinear optical materials,” Int. J. Nonlinear Opt. Phys. 3, 347–371 (1994).
[CrossRef]

Vögele, B.

A. Villeneuve, J. S. Aitchison, B. Vögele, R. Tapella, J. U. Kang, C. Trevino, and G. I. Stegeman, “Waveguide design for minimum nonlinear area and switching energy in AlGaAs at half the bandgap,” Electron. Lett. 31, 549–551 (1995).
[CrossRef]

Wherrett, B. S.

Wu, B.

M. Fontaine, B. Wu, V. P. Tzolov, W. J. Bock, and W. Urbanczyk, “Theoretical and experimental analysis of thermal stress effects on modal polarization properties of highly birefringent optical fibers,” J. Lightwave Technol. 14, 585–591 (1996).
[CrossRef]

Yang, C. C.

G. I. Stegeman, A. Villeneuve, J. Kang, J. S. Aitchison, C. N. Ironside, K. Al-Hemyari, C. C. Yang, C.-H. Lin, H.-H. Lin, G. T. Kennedy, R. S. Grant, and W. Sibbett, “AlGaAs below half bandgap: the silicon of nonlinear optical materials,” Int. J. Nonlinear Opt. Phys. 3, 347–371 (1994).
[CrossRef]

Zheng, X.-H.

Appl. Opt. (1)

Electron. Lett. (1)

A. Villeneuve, J. S. Aitchison, B. Vögele, R. Tapella, J. U. Kang, C. Trevino, and G. I. Stegeman, “Waveguide design for minimum nonlinear area and switching energy in AlGaAs at half the bandgap,” Electron. Lett. 31, 549–551 (1995).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The nonlinear optical properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. 33, 341–348 (1997).
[CrossRef]

Int. J. Nonlinear Opt. Phys. (1)

G. I. Stegeman, A. Villeneuve, J. Kang, J. S. Aitchison, C. N. Ironside, K. Al-Hemyari, C. C. Yang, C.-H. Lin, H.-H. Lin, G. T. Kennedy, R. S. Grant, and W. Sibbett, “AlGaAs below half bandgap: the silicon of nonlinear optical materials,” Int. J. Nonlinear Opt. Phys. 3, 347–371 (1994).
[CrossRef]

J. Appl. Phys. (1)

V. P. Tzolov and M. Fontaine, “Theoretical analysis of birefringence and form-induced polarization mode dispersion in birefringent optical fibers: a full-vectorial approach,” J. Appl. Phys. 77, 1–6 (1995).
[CrossRef]

J. Lightwave Technol. (1)

M. Fontaine, B. Wu, V. P. Tzolov, W. J. Bock, and W. Urbanczyk, “Theoretical and experimental analysis of thermal stress effects on modal polarization properties of highly birefringent optical fibers,” J. Lightwave Technol. 14, 585–591 (1996).
[CrossRef]

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

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

Mod. Phys. Lett. B (1)

A. W. Snyder, D. J. Mitchell, and Y. S. Kivshar, “Unification of linear and nonlinear wave optics,” Mod. Phys. Lett. B 9, 1479–1506 (1995).
[CrossRef]

Opt. Commun. (1)

V. P. Tzolov and M. Fontaine, “A passive polarization converter free of longitudinally-periodic structure,” Opt. Commun. 127, 7–13 (1996).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. B (1)

D. C. Hutchings and B. S. Wherrett, “Theory of the anisotropy of ultrafast nonlinear refraction in zinc-blende semiconductors,” Phys. Rev. B 52, 8150–8159 (1995).
[CrossRef]

Other (2)

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, New York, 1983).

In Ref. 1 the symbol φ used in Section 3 and Table 1 refers to the orientation of the optical axis, making an angle less than 45° with the x⁁ axis. In Table 1 the angle the optical axis x⁁0 makes with x⁁, noted |φ| and equal to 39.7°, is then the angle |η| defined in this paper.

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Figures (3)

Fig. 1
Fig. 1

Cross section of a right-asymmetric angle-facet rib waveguide. The geometrical parameters are d1=1.8 μm, d2=1.6 μm, and s=0.2 μm. The refractive indices are n1=3.342591 (Al0.18Ga0.82As), n2=3.322381 (Al0.22Ga0.78As), and n3=1.0 (air). The facet angle α=45°, and the rib width w=4.0 μm.

Fig. 2
Fig. 2

Power distribution along the xˆ and yˆ axes as a function of the propagation distance with a linearly x-polarized input, assuming a linear regime of propagation. The solid curve is the power along xˆ computed with the VC approach, the dotted curve is the power along yˆ computed with the VC approach, the dashed curve is the power along xˆ computed with the 3D-BPM, and the dashed-dotted curve is the power along yˆ computed with the 3D-BPM.

Fig. 3
Fig. 3

Power distribution along the xˆ-axis, 1/[1+|u(z)|2], as a function of the propagation distance with a linearly x-polarized input for (a) the device described in Ref. 1 and (b) the device described in this paper. The solid curve is for Pin/2=0 W, and the dashed curve is for Pin/2=125 W.

Equations (62)

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

dudz=iu2 Dxy2β˜+(Dxx-Dyy)2β˜ u-Dyx2β˜=i2β˜ Dxy(u+a+)(u+a-).
Ex,y=ψ(x, y)fx,y(z)exp(iβ˜z).
t2ψ(x, y)+[k02ε(x, y)-β˜2]ψ(x, y)=0.
Dp,q=Aψ ψp  ln(ε)q dAAψ2dA,
a+=(Dxx-Dyy)2Dxy+(Dyy-Dxx)2+4DxyDyx2Dxy,
a-=(Dxx-Dyy)2Dxy-(Dyy-Dxx)2+4DxyDyx2Dxy,
|φ| = |tan-1(a+)|,
|η| = |tan-1(a-)|,
u(z)=1-expi 2πL za+-a- expi 2πL z,
2πL=12β˜ |(a+-a-)Dxy|.
|φ| = |tan-1(a+)| =tan-1±Aε(x, y)ey2(x, y)dxdyAε(x, y)ex2(x, y)dxdy,
|η| = |tan-1(a-)| =tan-1Aε(x, y)ex2(x, y)dxdyAε(x, y)ey2(x, y)dxdy.
2ex,yx2+2ex,yy2+(k02ε-β2)ex,y
+x,y ex  ln(ε)x+ey  ln(ε)y=0.
L=2π|β+-β-|,
dudz=i 2πL (u+a+)(u+a-)(a+-a-)=i|(β+-β-)| (u+a+)(u+a-)(a+-a-).
|u(z=L/2)| =2a++a-=-2a±1-(a±)2=-2 tan|φ|(|η|)1-tan2|φ|(|η|)= |tan[-2φ(η)]|.
dudz=0,|u(z=0)| = |(a±)|.
dudz=i|(β+-β-)|u.
dudz-i|(β+-β-)| (u+a+)(u+a-)(a+-a-)
+i2 γPinδ+σ2 1-|u|21+|u|2u
+δ-σ2 u31+|u|2-|u|21+|u|2 1u=0,
γ=2πλ n2L[001] 1Aeff,
dudz-i|(β+-β-)| (u+a+)(u+a-)(a+-a-)
+i2 γPinσ2 |u|21+|u|2u+δ+σ2
×1-|u|21+|u|2u+δ-σ2×u31+|u|2-|u|21+|u|2 1u=0.
2iβ exz=x -exx-ex x [ln(ε)]-ey y [ln(ε)]+y -exy-(k02ε-β2)ex,
2iβ eyz=x -eyx+y -eyy-ex x [ln(ε)]-ey y [ln(ε)]-(k02ε-β2)ey.
Px(z)Aε(x, y)|ex(x, y, z)|2dxdyAε(x, y)|ex(x, y, z=2L)|2dxdy,
Py(z)Aε(x, y)|ey(x, y, z)|2dxdyAε(x, y)|ex(x, y, z=2L)|2dxdy.
θ=tan-1Py(z)Px(z)1/2,
Px(z)= |fx(z)|2=11+|u(z)|2.
Py(z)= |fy(z)|2=|u(z)|21+|u(z)|2.
×E=iω0μ0H,
×H=-iω0(ε0εE+PNL),
(ε0εE+PNL)=0,
H=0,
2Exz2-iω0μ0 Hzy+k02εEx-x Ezz
+ω02μ0PxNL=0,
2Eyz2+iω0μ0 Hzx+k02εEy-y Ezz
+ω02μ0PyNL=0.
AEx 2Eyz2-Ey 2Exz2dA+iω0μ0A(EttHz)dA
+AEy x Ezz-Ex y EzzdA
+ω02μ0A(ExPyNL-EyPxNL)dA=0.
Ex,y=ψ(x, y)fx,y(z)exp(iβ˜z),
t2ψ(x, y)+[k02ε(x, y)-β˜2]ψ(x, y)=0,
iω0μ0A(EttHz)dA
=exp(2iβ˜z)[fx(z)fy(z)(Dxx-Dyy)+fy(z)2Dxy
-fx(z)2Dyx]Aψ2(x, y)dA,
Dp,q=Aψ ψp  ln(ε)q dAAψ2dA.
t(UAt)=U(tAt)+AttU,
iω0μ0A(EttHz)dA
=-AEyx-Exy Exx+EyydA.
AEy x Ezz-Ex y EzzdA
=Ax Ey Ezz-y Ex EzzdA-AEyx-Exy Ezz dA=-+Ey Ezz-+dy--+Ex Ezz-+dx-AEyx-Exy Ezz dA
=-AEyx-Exy Ezz dA.
iω0μ0A(EttHz)dA+AEy x Ezz
-Ex y EzzdA
=-AEyx-Exy Exx+Eyy+EzzdA.
AEyx-Exy Ex  ln(ε)x+Ey  ln(ε)ydA
=exp(2iβ˜z)[fx(z)fy(z)(Dxx-Dyy)+fy(z)2Dxy
-fx(z)2Dyx]Aψ2(x, y)dA

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