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

A time-domain beam propagation method (BPM) based on the finite-element sch eme is described for the analysis of reflections of both transverse electri c and transverse magnetic polarized pulses in waveguiding structures contai ning arbitrarily shaped discontinuities. In order to avoid nonphysical refl ections from the computational window edges, the perfectly matched layer bo undary condition is introduced. The present algorithm using the Pade approx imation 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 refrative indexes, various photonic crys tal circuit components are simulated.