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

TL;DR

This paper introduces a novel $z$-stretching finite difference method for efficient and stable simulation of paraxial light beam propagation through lenses in cylindrical symmetry, using domain transformations and specialized matrix analysis.

Contribution

The paper presents a new $z$-stretching finite difference approach with stability analysis for simulating light beams, improving computational efficiency and accuracy.

Findings

Efficient simulation of paraxial light beams in cylindrical domains.

Stable numerical method established through matrix analysis.

Computational results demonstrate effectiveness of the approach.

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.