Abstract

A new efficient technique that models the behavior of pulsed optical beams in homogenous medium, metallic and dielectric waveguides, is introduced and verified using both linear nondispersive and dispersive examples that have analytical predictions. Excellent accuracy results have been observed. The method is called time-domain beam-propagation method (TD-BPM) because it is similar to the classical continuous-wave BPM with additional time dependence. The explicit finite difference and the Du Fort-Frankel approaches were used to discretize the TD-BPM equation. Comparisons between these techniques are also given with the application of the perfectly matched layers as spatial boundary conditions to the Du Fort-Frankel. Then the TD-BPM was successfully applied to model a two-dimensional dielectric Y-junction. It is concluded that the new technique is more efficient than the traditional finite-difference TD method, especially in modeling large optical devices.

© 2001 IEEE

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  31. R. W. Ziolkowski and J. B. Judkins, "Propagation characteristics of ultrawide-bandwidth pulsed gaussian beams", J. Opt. Soc. Amer. A, vol. 9, no. 11, pp. 2021-2030, Nov. 1992.
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Appl. Opt.

J. Lightwave Technol.

S. Chu and K. Chaudhuri, "A finite-difference time-domain method for the design and analysis of guided-wave optical structures", J. Lightwave Technol., vol. 7, pp. 2033-2038, 1989.

Other

W. P. Haung, S. Chu, A. Goss and K. Chaudhuri, "A scalar finite-difference time-domain approach to guided-wave optics", IEEE Photon. Technol. Lett., vol. 3, pp. 524-526, 1991.

H. A. Jamid and S. J. Al-Bader, "Finite-difference time-domain approach to nonlinear guided waves", Electron. Lett., vol. 29, pp. 83-84, 1993.

R. Y. Chan and J. M. Liu, "Time-domain wave propagation in optical structure", IEEE Photon. Technol. Lett., vol. 6, pp. 1001 -1003, Aug. 1994.

P. Liu, Q. Zhao and F. Choa, "Slow-wave finite-difference beam propagation method", IEEE Photon. Technol. Lett., vol. 7, pp. 890 -892, Aug. 1995.

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, Mar. 1997.

J. Zhenle, F. Junmei and F. Enxin, "An explicit and stable time-domain method for simulation wave propagation in optical structures", Micr. Opt. Technol. Lett., vol. 14, no. 4, pp. 249-252, March 1997.

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, Oct. 1997 .

L. Gomelsky and J. M. Liu, "Extension of beam propagation method to time dependent optical waveforms", IEEE Photon. Technol. Lett., vol. 6, pp. 546-548, Apr. 1994.

K. S. Yee, "Numerical solution of initial boundary problems involving Maxwell's equations in isotropic media", IEEE Trans. Antennas Propagat., vol. AP-14, pp. 302-307, 1966.

R. W. Ziolkowski and J. B. Judkins, "Full-wave vector Maxwell equation modeling of the self-focusing of ultrashort optical pulses in a nonlinear Kerr medium exhibiting a finite response time", J. Opt. Soc. Amer. B, vol. 10, no. 2, pp. 186-198, Feb. 1993.

R. W. Ziolkowski, "The incorporation of microscopic material models into the FDTD approach for ultrafast optical pulse simulations", IEEE Trans. Antennas Propagat., vol. 45, pp. 375-391, Mar. 1997 .

R. M. Joseph and A. Taflove, "FDTD Maxwell's equations models for nonlinear electrodynamics and optics", IEEE Trans. Antennas Propagat., vol. 45, pp. 364-374, Mar. 1997.

A. Taflove, "Review of the formulation and application of the finite-difference time-domain method for numerical modeling of electromagnetic wave infractions with arbitrary structures", Wave Motion, vol. 10, pp. 547-582, 1988.

D. Yevick, "A guide to electric field propagation techniques for guided-wave optics", Opt. Quantum Electron., vol. 26, pp. 185-197, 1994.

H. J. W. M. Hoekstra, "On beam propagation methods for modeling in integrated optics", Opt. Quantum Electron., vol. 29, pp. 157-171, 1997.

Y. Chung and N. Dagli, "Explicit finite difference beam propagation method: Application to semiconductor rib waveguide Y -junction analysis", Electron. Lett., vol. 26, pp. 711-713, 1990.

Y. Chung and N. Dagli, "Analysis of Z -invariant and Z -variant semiconductor rib waveguides by explicit finite difference beam propagation method with nonuniform mesh configuration", IEEE J. Quantum Electron., vol. 27, pp. 2296-2305, 1991.

H. M. Masoudi and J. M. Arnold, "Parallel beam propagation methods", IEEE Photon. Technol. Lett., vol. 6, pp. 848 -850, 1994.

H. M. Masoudi and J. M. Arnold, "Parallel three-dimensional finite-difference beam propagation methods", Int. J. Numer. Mod., vol. 8, pp. 95-107, 1995.

H. M. Masoudi and J. M. Arnold, "Parallel beam propagation method for the analysis of second harmonic generation", IEEE Photon. Technol. Lett., vol. 7, pp. 400-402, Apr. 1995.

H. M. Masoudi, H. M. and J. M. Arnold, "Modeling second-order nonlinear effects in optical waveguides using a parallel-processing beam propagation method", IEEE J. Quantum Electron., vol. 31, pp. 2107 -2113, Dec. 1995.

H. M. Masoudi, "Parallel numerical methods for analyzing optical devices with the BPM", Ph.D. dissertation, Faculty of Engineering,Univ. of Glasgow, 1995.

H. M. Masoudi, M. A. AlSunaidi and J. M. Arnold, "Time-domain finite-difference beam propagation method", IEEE Photon. Technol. Lett., vol. 11, pp. 1274-1276, Oct. 1999.

E. C. Du Fort and S. P. Frankel, "Stability conditions in the numerical treatment of parabolic differential equations", M.T.A.C., vol. 7, pp. 135-153, 1953.

F. Xiang and G. L. Yip, "An explicit and stable finite-difference 2-D vector beam propagation method", IEEE Photon. Technol. Lett., vol. 6, pp. 1248-1250, 1994.

H. M. Masoudi and J. M. Arnold, "Spurious modes in the Du Fort-Frankel finite-difference beam propagation method", IEEE Photon. Technol. Lett., vol. 9, pp. 1382-1384, Oct. 1997.

C. M. Rappaport, "Perfectly matched absorbing boundary conditions based on anisotropic mapping of space", IEEE Microwave Guided Wave Lett., vol. 5, pp. 90-92, Mar. 1995.

W. P. Huang, C. L. Xu, W. Lui and K. Yokoyama, "The perfectly matched layer (PML) boundary condition for the beam propagation method", IEEE Photon. Technol. Lett., vol. 8, pp. 649-651, May 1996.

R. W. Ziolkowski and J. B. Judkins, "Propagation characteristics of ultrawide-bandwidth pulsed gaussian beams", J. Opt. Soc. Amer. A, vol. 9, no. 11, pp. 2021-2030, Nov. 1992.

S. Ramo, J. Whinnery and T. V. Duzer, Fields and Waves in Communication Electronics, New York: Wiley, 1984.

D. L. Lee, Electromagnetic Principles of Integrated Optics, New York: Wiley, 1986.

K. L. Shalager, J. G. Maloney, S. L. Ray and A. F. Peterson, "Relative accuracy of several finite-difference time-domain methods in two and three dimensions", IEEE Trans. Antennas Propagat., vol. 41, pp. 1732-1737, Dec. 1993.

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