An Analytical and Computational Study of the Paraxial Wave Equation with Applications to Laser Beam Propagation
Abstract
In this project, we approximate solutions to the Paraxial Wave Equation by posing an initial boundary value problem (IBVP). The Paraxial Wave Equation is a model of laser beam propagation. A variable refractive index term is introduced within this partial differential equation to account for a nonhomogeneous medium. We apply Spectral methods to approximate the transverse Laplacian operator and an adaptive Runge-Kutta method using MATLABs ordinary differential equation solvers to propagate the beam forward in space. Three Spectral methods are considered: a Fourier Galerkin method, a Fourier collocation method, and a Chebyshev collocation method. These methods are verified in two ways: (1) by comparing the numerical IBVP solution to the exact solution in unbounded space for a Gaussian beam propagating in homogeneous media and (2) by applying the method of manufactured solutions. We apply a Fourier collocation method to model laser beam propagation through a nonhomogeneous medium.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 16, 2022
- Accession Number
- AD1171856
Entities
People
- Kyle G. Jung
Organizations
- United States Naval Academy