Modeling of Pulse Propagation in Layered Structures With Resonant Nonlinearities Using a Generalized Time-Domain Transfer Matrix Method

We introduce a generalized time-domain transfer- matrix (TDTM) method, the only method to our knowledge that is capable of modeling high-index-contrast layered structures with dispersion and slow resonant nonlinearities. In this method transfer matrix is implemented in the time domain, either by switching between time and frequency domains using Fourier transform and its inverse operation, or by replacing the frequency variable (ω) with its temporal operator (-i (d/dt)). This approach allows us to implement the transfer matrix method (which can easily incorporate dispersion, is analytical in nature, and requires less computation time) in the time domain, where we can incorporate nonlinearity of various kinds, instantaneous (such as Kerr nonlinearity), or slow resonant nonlinearity (such as carrier-induced nonlinearity). This generalized TDTM method is capable of incorporate non-analytical forms of dispersion and of nonlinearity, making it a versatile tool for modeling optical devices where dispersion and nonlinearities are obtained phenomenologically. We also provide a few numerical examples to compare our method with the standard finite-difference time- domain (FDTD) method, as well as to examine the range of validity of our method. For pico-second and longer pulses, our results agree with the FDTD simulation results to within 1% and the computation time of our method is more than 100 fold reduced compared to that of FDTD for the longest pulse we used.