High-Order Split-Step Schemes for Time-Dependent Coupled-Wave Equations

A high-order split-step algorithm is developed and presented to solve the time-dependent coupled-wave equations for traveling-wave optical fields in a variety of grating-based optical devices such as the distributed feedback and distributed Bragg reflector lasers. Based on the Suzuki's fractal decomposition approach, Lie–Trotter–Suzuki product formula is used to construct the higher order solution that converges faster than the conventional split-step method. The accuracy and efficiency of the new scheme are assessed by way of examples and shown to be superior to those of the conventional method.