Albion College
Mathematics and Computer Science
Laser Propagation through the Atmosphere
Sophia Potoczak Bragdon '12


Colorado State University

This talk focuses on modeling the propagation of laser light through the atmosphere using a new approximation procedure called the variational scaling law. Beginning with the modeling assumptions, I will introduce the paraxial Helmholtz equation which is a stochastic partial differential equation commonly used to model the propagation of a laser beam and discuss why approximation methods, like scaling laws, are useful in the application of laser weapons. The variational scaling law is then derived using a variational formulation of the paraxial Helmholtz equation paired with a Gaussian ansatz that depends on particular laser beam parameters. The variational scaling law is a system of stochastic ODEs that describes the evolution of the Gaussian beam parameters in the direction of propagation. Finally, I will conclude with numerical results that indicate the variational scaling law provides, at least, an order-one approximation to the solution of the paraxial Helmholtz equation in the presence of atmospheric turbulence. This work originated from my internship with the Air Force Research Lab through their summer scholar program and this is a program that is open to both undergraduate and graduate-level science students.
7:00 PM
All are welcome!
Palenske 227
March 11, 2021