Abstract

A wave equation-based semivectorial compact 2-D finite-difference time-domain (2-D-FDTD) method is developed and validated for optical waveguide modal analysis. This approach is a combination of the Maxwell's equation-based compact 2-D-FDTD and the wave equation-based semivectorial FDTD methods. Perfectly matched layer (PML) absorbing boundary condition (ABC) is also extended to this approach. Excellent accuracy is achieved for the entire spectrum even in the region near the cutoff. Through extensive study on the excitation conditions,it indicates that this method, when used as an explicit optical mode solver, is extremely robust.

© 2004 IEEE

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  1. M. S. Stern, "Semivectorial polarized finite difference method for optical waveguides with arbitrary index profiles", in IEE Proc. J., vol. 135, 1988, pp. 56-63.
  2. B. M. A. Rahman, F. A. Fernandez and J. B. Davies, "Review of finite element methods for microwave and optical waveguides", Proc. IEEE, vol. 79, pp. 1442-1448, 1991.
  3. P. C. Kendall, P. W. A. Mcllroy and M. S. Stern, "Spectral index method for rib waveguide analysis", Electron. Lett., vol. 25, pp. 107-108, 1989.
  4. X. Zhang, J. Fang, K. K. Mei and Y. Liu, "Calculations of dispersive characteristics of microstrips by the time-domain finite difference method", IEEE Trans. Microwave Theory Tech., vol. 36, pp. 263-267, Feb. 1988 .
  5. S. Xiao, R. Vahldieck and H. Jin, "Full-wave analysis of guided wave structures using a novel 2-D FDTD", IEEE Microwave Guided Wave Lett., vol. 2, pp. 165-167, 1992.
  6. A. Asi and L. Shafai, "Dispersion analysis of anisotropic inhomogeneous waveguides using compact 2D-FDTD", Electron. Lett., vol. 28, pp. 1451-1452, 1992.
  7. S. Xiao and R. Vahldieck, "An efficient 2-D FDTD algorithm using real variables", IEEE Microwave Guided Wave Lett., vol. 3, pp. 127-129, May 1993.
  8. A. C. Cangellaris, "Numerical stability and numerical dispersion of a compact 2-D/FDTD method used for the dispersion analysis of waveguides", IEEE Microwave Guided Wave Lett., vol. 3, pp. 3-5, 1993.
  9. M. Okoniewski, "Vector wave equation 2-D-FDTD method for guided wave problems", IEEE Microwave Guided Wave Lett., vol. 3, no. 9, pp. 307-309, Sept. 1993.
  10. A. P. Zhao, J. Juntunen and A. V. Raisanen, "Relationship between the compact complex and real variable 2-D FDTD methods in arbitrary dielectric waveguides", in IEEE Microwave Theory Tech.-S Dig., TU1D-6, 1997, pp. 83-87.
  11. A. P. Zhao, J. Juntunen and A. V. Raisanen, "Analysis of hybrid modes in channel multilayer optical waveguides with the compact 2-D FDTD method", Microwave Opt. Technol. Lett., vol. 15, no. 6, pp. 398-403, 1997.
  12. F. Zepparelli, et al. "Rigorous analysis of 3D optical and optoelectronic devices by the compact-2D-FDTD method", Opt. Quantum Electron., vol. 31, pp. 827-841, 1999.
  13. W. P. Huang, S. T. Chu and S. K. Chaudhuri, "A semivectorial finite-difference time-domain method", IEEE Photon. Technol. Lett., vol. 3, pp. 803 -805, 1991.
  14. G. Mur, "Absorbing boundary conditions for the finite difference approximation of the time-domain electromagnetic-field equations", IEEE Trans. Electromagn. Compat., vol. EMC-23, pp. 377-382, 1981.
  15. J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves", J. Comput. Phys., vol. 114, pp. 185-200, 1981.
  16. W. C. Chew and W. H. Weedon, "A 3-D perfectly matched medium from modified Maxwell's equation with stretched coordinates", Micowave Opt. Technol. Lett., vol. 7, pp. 599-604, Sept. 1994.
  17. D. Zhou, W.-P. Huang, C.-L. Xu, D. G. Fang and B. Chen, "The perfectly matched layer boundary condition for scalar finite-difference time domain method", IEEE Photon. Technol. Lett., pp. 454-456, May 2001.
  18. J. E. Goell, "A circular-hamonic computer analysis of rectangular dielectric waveguides", Bell Syst. Tech. J., vol. 48, pp. 2133-2160, 1969.
  19. D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. New York: Academic, 1991.
  20. V. Jandhyala, E. Michielssen and R. Mittra, "FDTD signal extrapolation using the forward-backward autoregressive (AR) model", IEEE Microwave Guided Wave Lett., vol. 4, pp. 163-165, 1994.
  21. Y. Chen, M.-S. Tong and R. Mittra, "Efficient and accurate finite-difference time-domain analysis of resonant structures using the Blackman-Harris window function", Microwave Opt. Technol. Lett., vol. 15, no. 6, pp. 389-392, 1997.
  22. M.-S. Tong and Y. Chen, "Analysis of propagation characteristics and field images for printed transmission lines on anisotropic substrates using a 2-D FDTD method", IEEE Trans. Microwave Theory Tech., vol. 46, pp. 1507-1510, Oct. 1998.

Other (22)

M. S. Stern, "Semivectorial polarized finite difference method for optical waveguides with arbitrary index profiles", in IEE Proc. J., vol. 135, 1988, pp. 56-63.

B. M. A. Rahman, F. A. Fernandez and J. B. Davies, "Review of finite element methods for microwave and optical waveguides", Proc. IEEE, vol. 79, pp. 1442-1448, 1991.

P. C. Kendall, P. W. A. Mcllroy and M. S. Stern, "Spectral index method for rib waveguide analysis", Electron. Lett., vol. 25, pp. 107-108, 1989.

X. Zhang, J. Fang, K. K. Mei and Y. Liu, "Calculations of dispersive characteristics of microstrips by the time-domain finite difference method", IEEE Trans. Microwave Theory Tech., vol. 36, pp. 263-267, Feb. 1988 .

S. Xiao, R. Vahldieck and H. Jin, "Full-wave analysis of guided wave structures using a novel 2-D FDTD", IEEE Microwave Guided Wave Lett., vol. 2, pp. 165-167, 1992.

A. Asi and L. Shafai, "Dispersion analysis of anisotropic inhomogeneous waveguides using compact 2D-FDTD", Electron. Lett., vol. 28, pp. 1451-1452, 1992.

S. Xiao and R. Vahldieck, "An efficient 2-D FDTD algorithm using real variables", IEEE Microwave Guided Wave Lett., vol. 3, pp. 127-129, May 1993.

A. C. Cangellaris, "Numerical stability and numerical dispersion of a compact 2-D/FDTD method used for the dispersion analysis of waveguides", IEEE Microwave Guided Wave Lett., vol. 3, pp. 3-5, 1993.

M. Okoniewski, "Vector wave equation 2-D-FDTD method for guided wave problems", IEEE Microwave Guided Wave Lett., vol. 3, no. 9, pp. 307-309, Sept. 1993.

A. P. Zhao, J. Juntunen and A. V. Raisanen, "Relationship between the compact complex and real variable 2-D FDTD methods in arbitrary dielectric waveguides", in IEEE Microwave Theory Tech.-S Dig., TU1D-6, 1997, pp. 83-87.

A. P. Zhao, J. Juntunen and A. V. Raisanen, "Analysis of hybrid modes in channel multilayer optical waveguides with the compact 2-D FDTD method", Microwave Opt. Technol. Lett., vol. 15, no. 6, pp. 398-403, 1997.

F. Zepparelli, et al. "Rigorous analysis of 3D optical and optoelectronic devices by the compact-2D-FDTD method", Opt. Quantum Electron., vol. 31, pp. 827-841, 1999.

W. P. Huang, S. T. Chu and S. K. Chaudhuri, "A semivectorial finite-difference time-domain method", IEEE Photon. Technol. Lett., vol. 3, pp. 803 -805, 1991.

G. Mur, "Absorbing boundary conditions for the finite difference approximation of the time-domain electromagnetic-field equations", IEEE Trans. Electromagn. Compat., vol. EMC-23, pp. 377-382, 1981.

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves", J. Comput. Phys., vol. 114, pp. 185-200, 1981.

W. C. Chew and W. H. Weedon, "A 3-D perfectly matched medium from modified Maxwell's equation with stretched coordinates", Micowave Opt. Technol. Lett., vol. 7, pp. 599-604, Sept. 1994.

D. Zhou, W.-P. Huang, C.-L. Xu, D. G. Fang and B. Chen, "The perfectly matched layer boundary condition for scalar finite-difference time domain method", IEEE Photon. Technol. Lett., pp. 454-456, May 2001.

J. E. Goell, "A circular-hamonic computer analysis of rectangular dielectric waveguides", Bell Syst. Tech. J., vol. 48, pp. 2133-2160, 1969.

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. New York: Academic, 1991.

V. Jandhyala, E. Michielssen and R. Mittra, "FDTD signal extrapolation using the forward-backward autoregressive (AR) model", IEEE Microwave Guided Wave Lett., vol. 4, pp. 163-165, 1994.

Y. Chen, M.-S. Tong and R. Mittra, "Efficient and accurate finite-difference time-domain analysis of resonant structures using the Blackman-Harris window function", Microwave Opt. Technol. Lett., vol. 15, no. 6, pp. 389-392, 1997.

M.-S. Tong and Y. Chen, "Analysis of propagation characteristics and field images for printed transmission lines on anisotropic substrates using a 2-D FDTD method", IEEE Trans. Microwave Theory Tech., vol. 46, pp. 1507-1510, Oct. 1998.

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