We develop a general procedure that allows the determination of the spectral transmittance and reflectance at normal incidence for arbitrary one-dimensional continuous materials as well as the analysis of the time-domain propagation of pulses through them. This procedure consists of a generalization of Fresnel equations, and it is supported by an iterative algorithm also developed here: the polynomial fixed-point algorithm (PFPA). We apply these theoretical results to some concrete examples, such as determining the transmittance and reflectance for an absorptionless photonic crystal, an optical rugate filter, and a photonic crystal with periodic absorption. We also analyze the time-domain propagation of ultrashort Gaussian pulses through different structures.
© 2007 Optical Society of America
Original Manuscript: September 22, 2006
Manuscript Accepted: January 21, 2007
Published: May 17, 2007
M. Perez-Molina and Luis Carretero-Lopez, "Polynomial fixed-point algorithm applied to the electromagnetic analysis of one-dimensional continuous structures," J. Opt. Soc. Am. B 24, 1354-1364 (2007)