Light propagates at different speeds in different materials. This gives rise to well-known phenomena such as refraction (bending of light), and interface reflection (the reason you can see your own reflection in a clear pool of water). Using the wave theory of light, these phenomena can be expressed in succint mathematical formulas known as Snell's Law (of refraction) and Fresnel's law (of interface reflection).

Birefringent materials are materials in which the speed of light is different in different directions. For such materials, the laws of refraction and interface reflection cannot be succintly expressed. Furthermore, birefringent materials exhibit certain phenomena which are qualitatively unique. The most well known among these is beam splitting - the quality of forming two images of one object.

In this project, we created new methods of computing the light propagation through birefringent media. Even though light propagation through birefringent media follows a linear model, the modes that will be excited due to a particular excitation are not obvious to calculate. The calculation of these modes requires solution of a non-linear eigen-like equation. We formulated this equation and created a novel solution method which could be termed a non-linear Rayleigh quotient method.

The resulting simulations can be used to find birefringence parameters (refractive index tensor) of physical samples, and also to understand and design behavior of birefringent objects such as single- and multi-layer birefringent films.

## Expertise

This project showcases the following expertise of Noumenon Multiphysics: