Eigenpolarization

Eigenpolarization refers to a special state of polarization of light that, when it propagates through a birefringent medium, retains its polarization state. This is analogous to eigenvectors in linear algebra, which maintain their direction when a linear transformation is applied. In optics, a birefringent medium has different refractive indices for different polarization states. This means that light with different polarizations will travel at different speeds, causing a change in the overall polarization state over distance.

However, for specific initial polarization states, known as eigenpolarizations, the light will emerge from the medium with the same polarization state it had upon entering. These eigenpolarizations are determined by the properties of the birefringent material, specifically its birefringence and orientation. In a simple anisotropic medium, there are typically two orthogonal eigenpolarizations. These are often linear polarizations aligned with the principal axes of the material's refractive index ellipsoid.

When light is launched into a birefringent medium with an eigenpolarization, its polarization state remains constant as it propagates. If the incident light is not an eigenpolarization, it can be decomposed into a superposition of the two eigenpolarizations. Each component will propagate with a different speed, leading to a change in the overall polarization state, often resulting in elliptical polarization. The concept of eigenpolarization is crucial in understanding phenomena like polarization rotation in optical fibers and the behavior of light in anisotropic optical components.