Abstract

A new three-dimensional (3-D) full-vectorial finite-difference (FD)-based beam-propagation method (BPM) is introduced for the analysis of magnetooptic and nonlinear materials. The refractive-index growth in the nonlinear material is allowed to saturate at high optical power densities (cubic-quintic media). The new formalism is capable of handling any combination of linear, nonlinear, and magnetooptic media, and combines, for the first time, the alternating-direction implicit technique (to improve computational performance) with the leapfrog longitudinal scheme (to simplify the solution of the coupled equations for transverse field components). The result is a numerical method that is both computationally efficient and numerically robust. The proposed BPM formalism is applied to investigate a (nonreciprocal) magnetooptic rib waveguide, as well as the new striking phenomena of light condensates propagation in cubic-quintic (saturable) media, the dynamics of which resemble those of liquid droplets.

© 2005 IEEE

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  1. T. Ando, T. Murata, H. Nakayama, J. Yamauchi and H. Nakano, "Analysis and measurement of polarization conversion in a periodically loaded dielectric waveguide", IEEE Photon. Technol. Lett., vol. 14, no. 9, pp. 1288-1290, Sep. 2002.
  2. S. S. A. Obayya, N. Somasiri, B. M. A. Rahman and K. T. V. Grattan, "Full vectorial finite element modeling of novel polarization rotators", Opt. Quantum Electron., vol. 35, no. 4, pp. 297-312, Mar.-Apr. 2003.
  3. N. Somasiri and B. M. A. Rahman, "Polarization crosstalk in high index contrast planar silica waveguides with slanted sidewalls", J. Lightw. Technol., vol. 21, no. 1, pp. 54-60, Jan. 2003.
  4. B. M. A. Rahman, N. Somasiri and M. Windmann, "Polarization crosstalk in high index contrast planar silica waveguides", IEEE Photon. Technol. Lett., vol. 14, no. 8, pp. 1109-1111, Aug. 2002.
  5. D. Li, H. VanBrug and H. J. Frankena, "Application of a fully vectorial beam propagation method", Opt. Quantum Electron., vol. 29, no. 2, pp. 313-322, Feb. 1997.
  6. L. D. S. Alcantara, F. L. Teixeira, A. C. César and B.-H. V. Borges, "An improved wide-angle FD-BPM for nonlinear and nonreciprocal waveguides", IEEE Trans. Magn., vol. 39, no. 3, pp. 1223-1226, May 2003.
  7. C. L. Xu, W. Huang, J. Chrostowski and S. Chaudhuri, "A full vectorial beam-propagation method for anisotropic waveguides", J. Lightw. Technol., vol. 12, no. 11, pp. 1926-1931, Nov. 1994.
  8. S. Selleri, L. Vincetti and M. Zoboli, "Full-vector finite-element beam propagation method for anisotropic optical device analysis", IEEE J. Quantum Electron., vol. 36, no. 12, pp. 1392-1401, Dec. 2000.
  9. S. S. A. Obayya, B. M. A. Rahman and H. A. El-Mikati, "Full-vectorial finite-element beam propagation method for nonlinear directional coupler devices", IEEE J. Quantum Electron., vol. 36, no. 5, pp. 556-562, May 2000.
  10. T. Fujisawa and M. Koshiba, "Full-vector finite-element beam propagation method for three-dimensional nonlinear optical waveguides", J. Lightw. Technol., vol. 20, no. 10, pp. 1876-1884, Oct. 2002.
  11. T. Fujisawa and M. Koshiba, "Full-vector finite-element beam propagation method for three-dimensional nonlinear optical waveguides", Electron. Commun. Jpn., Part 2 Electron., vol. 86, no. 2, pp. 19-27, 2003.
  12. H. Michinel, J. Campo-Táboas, R. García-Fernández, J. R. Salgueiro and M. L. Quiroga-Teixeiro, "Liquid light condensates", Phys. Rev. E, vol. 65, no. 6, p. 6604, 2002.
  13. J. Yamauchi, G. Takahashi and H. Nakano, "Full vectorial beam-propagation method based on the McKee-Mitchell scheme with improved finite-difference formulas", J. Lightw. Technol., vol. 16, no. 12, pp. 2458-2464, Dec. 1998.
  14. G. Hadley, "Transparent boundary condition for beam propagation", Opt. Lett., vol. 16, no. 9, pp. 624-626, May 1991.
  15. S. Selleri, L. Vincetti and M. Zoboli, "Full-vector finite-element beam propagation method for anisotropic optical device analysis", IEEE J. Quantum Electron., vol. 36, no. 12, pp. 1392-1401, Dec. 2000.
  16. R. Wolfe, R. Lieberman, V. Fratello, R. Scotti and N. Kopylov, "Etch-tuned ridged waveguide magneto-optic isolator", Appl. Phys. Lett., vol. 56, no. 5, pp. 426-428, Jan. 1990.
  17. W. Królikowskiy, C. Denzz, A. Stepkenz, M. Saffmanx and B. Luther-Daviesy, "Interaction of spatial photorefractive solitons", Quantum Semiclassical Opt., vol. 10, no. 6, pp. 823-837, 1998.
  18. S. K. Johansen, O. Bang and M. P. Sørensen, "Escape angles in bulk \chi(2) soliton interactions", Phys. Rev. E, vol. 65, no. 2, pp. 1-4, 2002.
  19. B. Tan and J. P. Boyd, "Coupled-mode envelope solitary waves in a pair of cubic Schrödinger equations with cross modulation: Analytical solution and collisions with application to Rossby waves", Chaos, Solitons Fractals, vol. 11, no. 7, pp. 1113-1129, Jun. 2000.
  20. W. C. K. Mak, B. A. Malomed and P. L. Chu, "Formation of a standing-light pulse through collision of gap solitons", Phys. Rev., E Stat. Nonlinear Soft Matter Phys., vol. 68, no. 2, pp. 1-9, Aug. 22, 2003.
  21. A. W. Snyder and A. P. Sheppard, "Collisions, steering and guidance with spatial solitons", Opt. Lett., vol. 18, no. 7, pp. 482-484, Apr. 1, 1993.
  22. R. Mcleod, K. Wagner and S. Blair, "(3 + 1)-dimensional optical soliton dragging logic", Phys. Rev. A, vol. 52, no. 4, pp. 3254-3283, Oct. 1995.

Other (22)

T. Ando, T. Murata, H. Nakayama, J. Yamauchi and H. Nakano, "Analysis and measurement of polarization conversion in a periodically loaded dielectric waveguide", IEEE Photon. Technol. Lett., vol. 14, no. 9, pp. 1288-1290, Sep. 2002.

S. S. A. Obayya, N. Somasiri, B. M. A. Rahman and K. T. V. Grattan, "Full vectorial finite element modeling of novel polarization rotators", Opt. Quantum Electron., vol. 35, no. 4, pp. 297-312, Mar.-Apr. 2003.

N. Somasiri and B. M. A. Rahman, "Polarization crosstalk in high index contrast planar silica waveguides with slanted sidewalls", J. Lightw. Technol., vol. 21, no. 1, pp. 54-60, Jan. 2003.

B. M. A. Rahman, N. Somasiri and M. Windmann, "Polarization crosstalk in high index contrast planar silica waveguides", IEEE Photon. Technol. Lett., vol. 14, no. 8, pp. 1109-1111, Aug. 2002.

D. Li, H. VanBrug and H. J. Frankena, "Application of a fully vectorial beam propagation method", Opt. Quantum Electron., vol. 29, no. 2, pp. 313-322, Feb. 1997.

L. D. S. Alcantara, F. L. Teixeira, A. C. César and B.-H. V. Borges, "An improved wide-angle FD-BPM for nonlinear and nonreciprocal waveguides", IEEE Trans. Magn., vol. 39, no. 3, pp. 1223-1226, May 2003.

C. L. Xu, W. Huang, J. Chrostowski and S. Chaudhuri, "A full vectorial beam-propagation method for anisotropic waveguides", J. Lightw. Technol., vol. 12, no. 11, pp. 1926-1931, Nov. 1994.

S. Selleri, L. Vincetti and M. Zoboli, "Full-vector finite-element beam propagation method for anisotropic optical device analysis", IEEE J. Quantum Electron., vol. 36, no. 12, pp. 1392-1401, Dec. 2000.

S. S. A. Obayya, B. M. A. Rahman and H. A. El-Mikati, "Full-vectorial finite-element beam propagation method for nonlinear directional coupler devices", IEEE J. Quantum Electron., vol. 36, no. 5, pp. 556-562, May 2000.

T. Fujisawa and M. Koshiba, "Full-vector finite-element beam propagation method for three-dimensional nonlinear optical waveguides", J. Lightw. Technol., vol. 20, no. 10, pp. 1876-1884, Oct. 2002.

T. Fujisawa and M. Koshiba, "Full-vector finite-element beam propagation method for three-dimensional nonlinear optical waveguides", Electron. Commun. Jpn., Part 2 Electron., vol. 86, no. 2, pp. 19-27, 2003.

H. Michinel, J. Campo-Táboas, R. García-Fernández, J. R. Salgueiro and M. L. Quiroga-Teixeiro, "Liquid light condensates", Phys. Rev. E, vol. 65, no. 6, p. 6604, 2002.

J. Yamauchi, G. Takahashi and H. Nakano, "Full vectorial beam-propagation method based on the McKee-Mitchell scheme with improved finite-difference formulas", J. Lightw. Technol., vol. 16, no. 12, pp. 2458-2464, Dec. 1998.

G. Hadley, "Transparent boundary condition for beam propagation", Opt. Lett., vol. 16, no. 9, pp. 624-626, May 1991.

S. Selleri, L. Vincetti and M. Zoboli, "Full-vector finite-element beam propagation method for anisotropic optical device analysis", IEEE J. Quantum Electron., vol. 36, no. 12, pp. 1392-1401, Dec. 2000.

R. Wolfe, R. Lieberman, V. Fratello, R. Scotti and N. Kopylov, "Etch-tuned ridged waveguide magneto-optic isolator", Appl. Phys. Lett., vol. 56, no. 5, pp. 426-428, Jan. 1990.

W. Królikowskiy, C. Denzz, A. Stepkenz, M. Saffmanx and B. Luther-Daviesy, "Interaction of spatial photorefractive solitons", Quantum Semiclassical Opt., vol. 10, no. 6, pp. 823-837, 1998.

S. K. Johansen, O. Bang and M. P. Sørensen, "Escape angles in bulk \chi(2) soliton interactions", Phys. Rev. E, vol. 65, no. 2, pp. 1-4, 2002.

B. Tan and J. P. Boyd, "Coupled-mode envelope solitary waves in a pair of cubic Schrödinger equations with cross modulation: Analytical solution and collisions with application to Rossby waves", Chaos, Solitons Fractals, vol. 11, no. 7, pp. 1113-1129, Jun. 2000.

W. C. K. Mak, B. A. Malomed and P. L. Chu, "Formation of a standing-light pulse through collision of gap solitons", Phys. Rev., E Stat. Nonlinear Soft Matter Phys., vol. 68, no. 2, pp. 1-9, Aug. 22, 2003.

A. W. Snyder and A. P. Sheppard, "Collisions, steering and guidance with spatial solitons", Opt. Lett., vol. 18, no. 7, pp. 482-484, Apr. 1, 1993.

R. Mcleod, K. Wagner and S. Blair, "(3 + 1)-dimensional optical soliton dragging logic", Phys. Rev. A, vol. 52, no. 4, pp. 3254-3283, Oct. 1995.

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