Symmetries of Wave Equations of Statistical Optics

The Lie method is used to derive the symmetry group of various sets of wave equations, and Noether's theorem is applied to find conservation laws of the wave equations. Symmetries and conservation laws of the wave equations of scalar statistical optics and vector statistical optics are studied and compared to the symmetries and conservation laws of the wave equations of deterministic wave optics. Generalizations of the deterministic conservation laws are found and seen to correspond to the usual laws in the deterministic limit. In the scalar statistical optics case, symmetries of two-time and stationary wave equations are compared. The statistically stationary wave equations are shown not to contain inversion symmetries, so the conservation laws differ from the conservation laws of the two-time wave equations. In the vector statistical optics case, continuous Larmor-Rainich-like symmetries are found among the dependent variables. Nongeometrical symmetries of these sets of equations, which are infinitesimal but not continuous, are also studied.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical and Computer Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Mitofsky, Andrea M.

Contributors dc:contributor

• P. Scott Carney

• Engineering, Electronics and Electrical

Language dc:language

eng

Identifier

(MiAaPQ)AAI3337877

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/81101