Novel generalized finite-difference beam propagation method

An efficient finite-difference beam propagation method is developed for integrated optic devices. It is based on a numerically efficient and strictly unitary rational approximation of the Helmholtz propagation operator, and is evaluated recursively without matrix inversions. This method satisfies energy conservation in lossless waveguides, is unconditionally stable, and an optimum propagation step can be assessed analytically. Photonic devices with step-index distributions, small layer thicknesses, and arbitrarily large index differences can be simulated. The accuracy and applicability of this new technique is demonstrated for several 2D and 3D examples. Furthermore, the algorithm can easily be implemented even for 3D problems.>