Abstract

A novel solution method based on the semivectorial spectral collocation method with domain decomposition is proposed to calculate the modal characteristics of rib waveguides. We formulate the scheme in terms of the transverse magnetic components mmb Hx and mmb Hy. The optical field expanded by a suitable set of orthogonal basis functions and the refractive index profile are all represented on a grid of discrete points in each subdomain. In addition, the a priori determination of the scaling factor of Laguerre-Gauss (LG) functions is introduced by means of the effective index method. The subdomains are then patched by imposing the continuities of longitudinal electric component mmbEz and magnetic component mmbHz at all internal dielectric interfaces. Because of the zero divergence constraint of magnetic field vector explicitly included, the occurrence of spurious modes is prevented. The present method is tested for various rib waveguide structures with lossless or lossy materials. Even with a coarse mesh, our results are still found to be in good agreement with those produced by other various full-vectorial methods, but without complexity of the latter approaches.

© 2005 IEEE

PDF Article

References

  • View by:
  • |

  1. K. S. Chiang, "Review of numerical and approximate methods for the modal analysis of general optical dielectric waveguides", Opt. Quantum Electron., vol. 26, no. 6, pp. 113-134, Jun. 1994.
  2. S. Banerjee and A. Sharma, "Propagation characteristics of optical waveguiding structure by direct solution of the Helmholtz equation for total fields", J. Opt. Soc. Amer. A, vol. 6, no. 12, pp. 1884-1894, Dec. 1989.
  3. A. Sharma and S. Banerjee, "Method for propagation of total fields or beams through optical waveguides", Opt. Lett., vol. 14, no. 1, pp. 96-98, Jan. 1989.
  4. F. Causa and J. Sarma, "A versatile method for analyzing paraxial optical propagation in dielectric structures", J. Lightw. Technol., vol. 18, no. 10, pp. 1445-1452, Oct. 2000.
  5. Q. H. Liu, C. Cheng and H. Z. Massoud, "The spectral grid method: A novel fast Schrdinger-equation solver for semiconductor nanodevice simulation", IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., vol. 23, pp. 1200-1208, Aug. 2004.
  6. J. P. Meunier, T. Pigeon and J. N. Massot, "A numerical technique for the determination of propagation characteristics of inhomogeneous planar optical waveguides", Opt. Quantum Electron., vol. 15, no. 1, pp. 77-85, Jan. 1983.
  7. C. H. Henry and B. H. Verbeek, "Solution of the scalar wave equation for arbitrarily shaped dielectric waveguides by two-dimensional Fourier analysis", J. Lightw. Technol., vol. 7, no. 2, pp. 308-313, Feb. 1989.
  8. A. Weisshaar, J. Li, R. L. Gallawa and I. C. Goyal, "Vector and quasi-vector solutions for optical waveguide modes using efficient Galerkin's method with Hermite-Gauss basis functions", J. Lightw. Technol., vol. 13, no. 8, pp. 1795-1800, Aug. 1995.
  9. C. C. Huang, C. C. Huang and J. Y. Yang, "An efficient method for computing optical waveguides with discontinuous refractive index profiles using spectral collocation method with domain decomposition", J. Lightw. Technol., vol. 21, no. 10, pp. 2284-2296, Oct. 2003.
  10. J. P. Boyd, "Chebyshev and Fourier spectral methods," in Lecture Notes in Engineering, 2nd ed. New York: Dover, 2000.
  11. C. Canuto, M. Y. Hussaini, A. Quarteroni and T. A. Zang, "Spectral methods in fluid dynamics," in Springer Series in Computational Physics, New York: Springer Verlag, 1988.
  12. T. Tang, "The Hermite spectral method for Gauss-type functions", SIAM J. Sci. Comput., vol. 14, no. 3, pp. 594-605, May 1993.
  13. T. Tamir, Guided-Wave Optoelectronics, New York: Springer-Verlag, 1988.
  14. N. Ramanujam, L. Li, J. J. Burke and M. A. Gribbons, "Determination of the truncation order and numerical window for modeling general dielectric waveguides by the Fourier method", J. Lightw. Technol., vol. 14, no. 3, pp. 500-508, Mar. 1996.
  15. S. Selleri and J. Petracek, "Modal analysis of rib waveguide through finite element and mode matching methods", Opt. Quantum Electron., vol. 33, no. 4-5, pp. 373-386, Apr. 2001.
  16. M. S. Stern, "Semivectorial polarized H field solutions for dielectric waveguides with arbitrary index profiles", Proc. Inst. Elect. Eng. J., vol. 135, no. 5, pp. 333-338, Oct. 1988.
  17. 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.
  18. C. J. Smartt, T. M. Benson, G. M. Berry, S. V. Burke, P. C. Kendall and P. N. Robson, "Exact polarized rib waveguide analysis", Electron. Lett., vol. 30, no. 14, pp. 1127-1128, Jul. 1994.
  19. P. L. Liu and B. J. Li, "Semivectorial polarized H field solutions for dielectric waveguides with arbitrary index profiles", IEEE J. Quantum Electron., vol. 28, no. 4, pp. 778-782, Apr. 1992.
  20. C. Vasallo, "Improvement of finite difference methods for step-index optical waveguides", Proc. Inst. Elect. Eng. J., vol. 139, no. 2, pp. 137-142, Apr. 1992.
  21. P. Lusse, K. Ramm and H. G. Unger, "Comparison of a vectorial and new semivectorial finite-difference approach for optical waveguides", Opt. Quantum Electron., vol. 29, no. 2, pp. 115-120, Jan. 1997.
  22. K. Ramm, P. Lusse and H. G. Unger, "Multigrid eigenvalue solver for mode calculation of planar optical waveguides", IEEE Photon. Technol. Lett., vol. 9, no. 7, pp. 967-969, Jul. 1997.
  23. D. U. Li and H. C. Chang, "An efficient full-vectorial finite-element modal analysis of dielectric waveguides incorporating inhomogeneous elements across dielectric discontinuities", IEEE J. Quantum Electron., vol. 36, no. 11, pp. 1251-1261, Nov. 2000.
  24. T. Rozzi, G. Cerri, M. N. Husain and L. Zappelli, "Variational analysis of the dielectric rib waveguide using the concept of"transition function"and including edge singularities", IEEE Trans. Microw. Theory Tech., vol. 39, pp. 247-257, Feb. 1991.

Other (24)

K. S. Chiang, "Review of numerical and approximate methods for the modal analysis of general optical dielectric waveguides", Opt. Quantum Electron., vol. 26, no. 6, pp. 113-134, Jun. 1994.

S. Banerjee and A. Sharma, "Propagation characteristics of optical waveguiding structure by direct solution of the Helmholtz equation for total fields", J. Opt. Soc. Amer. A, vol. 6, no. 12, pp. 1884-1894, Dec. 1989.

A. Sharma and S. Banerjee, "Method for propagation of total fields or beams through optical waveguides", Opt. Lett., vol. 14, no. 1, pp. 96-98, Jan. 1989.

F. Causa and J. Sarma, "A versatile method for analyzing paraxial optical propagation in dielectric structures", J. Lightw. Technol., vol. 18, no. 10, pp. 1445-1452, Oct. 2000.

Q. H. Liu, C. Cheng and H. Z. Massoud, "The spectral grid method: A novel fast Schrdinger-equation solver for semiconductor nanodevice simulation", IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., vol. 23, pp. 1200-1208, Aug. 2004.

J. P. Meunier, T. Pigeon and J. N. Massot, "A numerical technique for the determination of propagation characteristics of inhomogeneous planar optical waveguides", Opt. Quantum Electron., vol. 15, no. 1, pp. 77-85, Jan. 1983.

C. H. Henry and B. H. Verbeek, "Solution of the scalar wave equation for arbitrarily shaped dielectric waveguides by two-dimensional Fourier analysis", J. Lightw. Technol., vol. 7, no. 2, pp. 308-313, Feb. 1989.

A. Weisshaar, J. Li, R. L. Gallawa and I. C. Goyal, "Vector and quasi-vector solutions for optical waveguide modes using efficient Galerkin's method with Hermite-Gauss basis functions", J. Lightw. Technol., vol. 13, no. 8, pp. 1795-1800, Aug. 1995.

C. C. Huang, C. C. Huang and J. Y. Yang, "An efficient method for computing optical waveguides with discontinuous refractive index profiles using spectral collocation method with domain decomposition", J. Lightw. Technol., vol. 21, no. 10, pp. 2284-2296, Oct. 2003.

J. P. Boyd, "Chebyshev and Fourier spectral methods," in Lecture Notes in Engineering, 2nd ed. New York: Dover, 2000.

C. Canuto, M. Y. Hussaini, A. Quarteroni and T. A. Zang, "Spectral methods in fluid dynamics," in Springer Series in Computational Physics, New York: Springer Verlag, 1988.

T. Tang, "The Hermite spectral method for Gauss-type functions", SIAM J. Sci. Comput., vol. 14, no. 3, pp. 594-605, May 1993.

T. Tamir, Guided-Wave Optoelectronics, New York: Springer-Verlag, 1988.

N. Ramanujam, L. Li, J. J. Burke and M. A. Gribbons, "Determination of the truncation order and numerical window for modeling general dielectric waveguides by the Fourier method", J. Lightw. Technol., vol. 14, no. 3, pp. 500-508, Mar. 1996.

S. Selleri and J. Petracek, "Modal analysis of rib waveguide through finite element and mode matching methods", Opt. Quantum Electron., vol. 33, no. 4-5, pp. 373-386, Apr. 2001.

M. S. Stern, "Semivectorial polarized H field solutions for dielectric waveguides with arbitrary index profiles", Proc. Inst. Elect. Eng. J., vol. 135, no. 5, pp. 333-338, Oct. 1988.

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.

C. J. Smartt, T. M. Benson, G. M. Berry, S. V. Burke, P. C. Kendall and P. N. Robson, "Exact polarized rib waveguide analysis", Electron. Lett., vol. 30, no. 14, pp. 1127-1128, Jul. 1994.

P. L. Liu and B. J. Li, "Semivectorial polarized H field solutions for dielectric waveguides with arbitrary index profiles", IEEE J. Quantum Electron., vol. 28, no. 4, pp. 778-782, Apr. 1992.

C. Vasallo, "Improvement of finite difference methods for step-index optical waveguides", Proc. Inst. Elect. Eng. J., vol. 139, no. 2, pp. 137-142, Apr. 1992.

P. Lusse, K. Ramm and H. G. Unger, "Comparison of a vectorial and new semivectorial finite-difference approach for optical waveguides", Opt. Quantum Electron., vol. 29, no. 2, pp. 115-120, Jan. 1997.

K. Ramm, P. Lusse and H. G. Unger, "Multigrid eigenvalue solver for mode calculation of planar optical waveguides", IEEE Photon. Technol. Lett., vol. 9, no. 7, pp. 967-969, Jul. 1997.

D. U. Li and H. C. Chang, "An efficient full-vectorial finite-element modal analysis of dielectric waveguides incorporating inhomogeneous elements across dielectric discontinuities", IEEE J. Quantum Electron., vol. 36, no. 11, pp. 1251-1261, Nov. 2000.

T. Rozzi, G. Cerri, M. N. Husain and L. Zappelli, "Variational analysis of the dielectric rib waveguide using the concept of"transition function"and including edge singularities", IEEE Trans. Microw. Theory Tech., vol. 39, pp. 247-257, Feb. 1991.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.