An Effective $z$-Stretching Adaptive Finite Difference Method for Paraxial Light Beam Propagation Simulations

Abstract

A new $z$-stretching finite difference method is established for simulating the paraxial light beam propagation through a lens in a cylindrically symmetric domain. By introducing proper domain transformations, we solve corresponding difference approximations on a uniform grid in the computational space for great efficiency. A specialized matrix analysis method is constructed to study the numerical stability. Interesting computational results are presented.