An effective z-stretching method for paraxial light beam propagation simulations

A z-stretching finite difference method is developed for simulating the paraxial light beam propagation through a lens in a cylindrically symmetric domain. By introducing a domain transformation in the z-direction, we solve the corresponding complex difference equations containing an interface singularity over a computational space for great simplicity and efficiency. A specially designed matrix analysis is constructed to the study the numerical stability. Computational experiments are carried out for demonstrating our results.