FDTD basic references
[1] Yee, K. S., “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Transactions on Antennas and Propagation, 302-307, (1966).
[2] Chu, S. T., Chaudhuri, S.K., “A finite-difference time-domain method for the design and analysis of guided-wave optical structures,” Journal of Lightwave Technology, 2033-2038, (1989).
[3] Taflove, A., Hagness, S., “Computational Electrodynamics: The Finite-Difference Time-Domain Method,” Second edition, Artech House, Boston, (2000).
Material models
[1] Ziolkowski, R. W., “Incorporation of microscopic material models into FDTD approach for ultrafast optical propagation,” IEEE Transactions on Antennas and Propagation, 375-391, (1997).
[2] Liang, T., Ziolkowski, R. W., “Dispersion effects on grating-assisted output couplers under ultrafast pulse excitations”, Microwave and Opt. Tech. Lett., 17, 17-23, (1998).
Anisotropic Perfectly Matched Layer (Anisotropic PML) boundary conditions
[1] Bérenger, J. P., “A perfectly matched layer for the absorption of electromagnetic waves,” Journal of Computational Physics, 114, 185-200, (1994).
[2] Gedney, S. D., “An anisotropic perfectly matched layer absorbing media for the truncation of FDTD lattices,” IEEE Transactions on Antennas and Propagation, 1630-1639, (1996).
[3] Taflove, A., “Advances in Computational Electrodynamics—The Finite-Difference Time-Domain Method”, Artech House, Boston, Ch. 5, (1998).
Nonlinearity
[1] Ziolkowski, Richard W., Judkins, Justin B., “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. Am. B, 2, 186-198 (1993).
[2] Ziolkowski, Richard W., Judkins, Justin B., “Nonlinear finite-difference time-domain modeling of linear and nonlinear corrugated waveguides”, J. Opt. Soc. Am. B, 9, 1565-1575, (1994).
[3] Ziolkowski, Richard W., Judkins, Justin B., “Applications of the nonlinear fainted difference time-domain(NL-FDTD) method to pulse propagation in nonlinear media: self-focusing and linear-nonlinear interfaces”, Radio Science, 901-911, (1993).
[4] Ziolkowski, Richard W., “The incorporation of microscopic material models into the FDTD approach for ultrafast optical pulse simulations”, IEEE Trans. On Antenna and Propagation, 3, 375-391, (1997).
[5] Joseph, Rose M., Taflove, Allen, “FDTD Maxwell’s equations models for nonlinear
electrodynamics and optic”, IEEE Trans. On Antenna and Propagation, 3, 364-374, 1997).
[6] Goorjian, Peter M., Taflove, Allen, Joseph, Rose M., “Computational modeling of Femtosecond optical soliton from Maxwell’s equation”, IEEE Journal of Quantum electronics, 10, 2416-2422, (1992).
[7] Joseph, Rose M., Taflove, Allen, ” Spatial soliton deflection mechanism indicated by FD-TD Maxwell’s equations modeling”, IEEE Photonics Technology Letters, 10, 1251-1254, (1994).