Accurate and efficient leap-frog beam propagation method for modeling micro and nanophotonic structures

In this paper, a novel and efficient approach for solving the beam propagation method (BPM) governing equation is proposed. The approach is based on the reformulation of the beam propagation equation to solve real system matrices only at each propagation step. The reformulated equation utilizes a leap-frog (LF) technique to couple the real and imaginary components of the field in an iterative scheme. The method yields higher processing speed by at least 30% more than that of the conventional BPM method. To validate the proposed LF-BPM method, different photonic systems, including directional couplers and multimode interferometers, are simulated. Results have been experimentally verified by comparing them with results measured for fabricated micro-photonic structures. A stability analysis was performed to study the effect of the design parameters on the performance of the proposed scheme. The proposed LF-BPM approach is considered a promising technique for efficient modeling of optical structures.