Time-domain beam propagation method and its application to photonic crystal circuits

A time-domain beam propagation method (BPM) based on the finite-element scheme is described for the analysis of reflections of both transverse electric and transverse magnetic polarized pulses in waveguiding structures containing arbitrarily shaped discontinuities. In order to avoid nonphysical reflections from the computational window edges, the perfectly matched layer boundary condition is introduced. The present algorithm using the Pade approximation is, to our knowledge, the first time-domain beam propagation method which can treat wide-band optical pulses. After validating this method for an optical grating with modulated refractive indexes, various photonic crystal circuit components are simulated.