Albion College

Mathematics and Computer Science

Mathematics and Computer Science

COLLOQUIUM

Laser Propagation through the Atmosphere

Sophia Potoczak Bragdon '12

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.