Publication Date

Spring 5-12-2020


The propagation of lasers through different media is a broad topic of study and falls under the larger topic of wave propagation. The focus of this thesis is the development and analysis of a numerical computational model of laser beam propagation through a turbulent atmosphere over a long distance. When a beam propagates through a turbulent atmosphere over a distance exceeding several kilometers it is a strong fluctuation propagation. There exist fewer robust methods to demonstrate how strong fluctuations affect the beam. Beam propagation can be described by the Linear Schr\"{o}dinger Equation (LSE). The fluctuations in the refractive index are mainly caused by random density fluctuations in the atmosphere and this random turbulence is described using statistical methods. In this report a numerical solution of the LSE is solved using a split-step method, and the refractive index fluctuations are accounted for by a method of random phase screens. This solution was then implemented as a computational model. The analysis of the model consists of a convergence study in the resolution of the transverse propagation screens, as well as verification of expected theoretical behaviors, including the expected spectral density of the noise screens and initial Gaussian beam form. As a result, the simulations revealed the giant fluctuations of laser intensity during propagation.

Degree Name


Level of Degree


Department Name

Mathematics & Statistics

First Committee Member (Chair)

Alexander Korotkevich

Second Committee Member

Pavel Lushnikov

Third Committee Member

Stephen Lau




laser, wave propagation, turbulent atmosphere, modeling

Document Type