Time Domain FD-BPM for Calculating Pulse Propagation Properties of MMI Device with Photonic Crystal Structure

A time domain beam propagation method (TD-BPM) based on the finite-difference alternating direction implicit method is described for the numerical analysis of reflections in multimode interference circuits with photonic crystal structures. It is shown that TD-BPM using the Pade (1, 1) approximation is less sensitive to the choice of spatial step and allows a larger time step size to be used compared to the FD-TD method. Furthermore, the validity and accuracy of the TD-BPM based on the ADI method will be discussed through numerical examples in MMI circuits with photonic crystal structures.