2000 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

IEEE Journal of Lightwave Technology
Volume 18 Number 3, March 2000

Table of Contents for this issue

Complete paper in PDF format

Efficient Time-Domain Finite-Difference Beam Propagation Methods for the Analysis of Slab and Circularly Symmetric Waveguides

Jun Shibayama, Member, OSA Tomokazu Takahashi, Junji Yamauchi, Member, IEEE and Hisamatsu Nakano Fellow, IEEE

Page 437.

Abstract:

The generalized Douglas scheme is applied to the time-domain finite-difference beam propagation methods (TD-BPM's) in rectangular and cylindrical coordinates. High accuracy and efficiency are demonstrated through the analysis of optical pulse propagation in slab and circularly symmetric waveguides. As an example of a reflection problem, the TD-BPM in cylindrical coordinates is applied to the analysis of a fiber Bragg grating with a sinusoidal index change. Effectiveness of the present scheme is discussed in comparison with the conventional TD-BPM and the finite-difference time-domain method.

References

  1. W. P. Huang, C. L. Xu and J. Chrostowski, "A time-domain propagating scheme for simulation of dynamics of optical guided-wave devices", IEEE Photon. Technol. Lett., vol. 5, pp.  1071-1073, 1993.
  2. M. Scalora and M. E. Crenshaw, "A beam propagation method that handles reflections", Opt. Commun., vol. 108, pp.  191 -196, 1994.
  3. R. Y. Chan and J. M. Liu, "Time-domain wave propagation in optical structures", IEEE Photon. Technol. Lett., vol. 6, pp.  1001 -1003, 1994.
  4. P. L. Liu, Q. Zhao and F. S. Choa, "Slow-wave finite-difference beam propagation method", IEEE Photon. Technol. Lett., vol. 7, pp.  890 -892, 1995.
  5. Y. Yuan, R. Jambunathan, J. Singh and P. Bhattacharya, "Finite-difference time-domain analysis and experimental examination of the performance of a coupled-cavity MQW laser/active waveguide at 1.54 µm", IEEE J. Quantum Electron., vol. 33, pp.  408-415, 1997.
  6. G. H. Jin, J. Harari, J. P. Vilcot and D. Decoster, "An improved time-domain beam propagation method for integrated optics components", IEEE Photon. Technol. Lett., vol. 9, pp.  348-350, 1997.
  7. F. Ma, "Slowly varying envelope simulation of optical waves in time domain with transparent and absorbing boundary conditions", J. Lightwave Technol., vol. 15, pp.  1974-1985, 1997.
  8. J. Shibayama, J. Yamauchi and H. Nakano, "Formulation of a time-domain finite-difference beam propagation method based on the generalized Douglas scheme", IEICE Trans. C-1, vol. 81, pp.  38-39, 1998.
  9. M. Hikari, M. Koshiba and Y. Tsuji, "A time domain beam propagation method based on a finite element scheme", IEICE Trans. C-1, vol. 81, pp.  667-673, 1998.
  10. J. Yamauchi, J. Shibayama and H. Nakano, "Application of the generalized Douglas scheme to optical waveguide analysis", Opt. Quantum Electron., vol. 31, pp.  675-687, 1999.
  11. J. Shibayama, T. Takahashi, J. Yamauchi and H. Nakano, "Extended time-domain finite-difference beam propagation methods", Integrated Photonics Research, RTuI2, Santa Barbara, 1999.
  12. J. Yamauchi, J. Shibayama, O. Saito, O. Uchiyama and H. Nakano, "Improved finite-difference beam-propagation method based on the generalized Douglas scheme and its application to semivectorial analysis", J. Lightwave Technol., vol. 14, pp.  2401-2406, 1996.
  13. J. Shibayama, K. Matsubara, M. Sekiguchi, J. Yamauchi and H. Nakano, "Efficient nonuniform schemes for paraxial and wide-angle finite-difference beam propagation methods", J. Lightwave Technol., vol. 17, pp.  677-683, 1999.
  14. J. Yamauchi, M. Nibe and H. Nakano, "Scalar FD-TD method for circularly symmetric waveguides", Opt. Quantum Electron., vol. 29, pp.  451-460, 1997.