College of Arts & Sciences

Spencer Schade College of Engineering Architectural Engineering

Faculty Mentor: Dr. Ron Perline

Mathematics

Simulation of Thing Film Optics

We study a set of differential equations which model highly reflecting light rays in thin films of heterogeneous thickness. The solutions depend strongly on the shape of the film. In general, the equations cannot be solved exactly so we compute the solutions numerically.

For particularly simple film configurations (a ``flattened sphere”) the solutions can be computed explicitly, using elliptic functions and elliptic integrals, which are generalizations of trigonometric functions. Using properties of these special functions, we can explicitly calculate the periodic solutions (closed path) for this particular configuration.