Higher-order wide-angle split-step spectral method for non-paraxial beam propagation

We develop a higher-order method for non-paraxial beam propagation based on the wide-angle split-step spectral (WASSS) method previously reported [Clark and Thomas, Opt. Quantum. Electron., 41, 849 (2010)]. The higher-order WASSS (HOWASSS) method approximates the Helmholtz equation by keeping terms up to third-order in the propagation step size, in the Magnus expansion. A symmetric exponential operator splitting technique is used to simplify the resulting exponential operators. The HOWASSS method is applied to the problem of waveguide propagation, where an analytical solution is known, to demonstrate the performance and accuracy of the method. The performance enhancement gained by implementing the HOWASSS method on a graphics processing unit (GPU) is demonstrated. When highly accurate results are required the HOWASSS method is shown to be substantially faster than the WASSS method.