refraktivitetstensorn

Refraktivitetstensorn, also known as the refractive index tensor, is a mathematical object used in electromagnetism and optics to describe the optical properties of anisotropic materials. Unlike isotropic materials where the refractive index is a single scalar value, anisotropic materials have optical properties that vary with direction. The refraktivitetstensor captures this directional dependence.

In a vacuum, the refractive index is one, and light propagates at the speed of light, c. In a material, the refractive index, n, is the ratio of the speed of light in a vacuum to the speed of light in the material. For anisotropic media, the speed of light depends on its polarization and direction of propagation. The refraktivitetstensor, often denoted by $\mathbf{n}$, relates the electric displacement field $\mathbf{D}$ to the electric field $\mathbf{E}$ through the equation $\mathbf{D} = \epsilon_0 \mathbf{n} \mathbf{E}$, where $\epsilon_0$ is the permittivity of free space. In this context, the refractive index is related to the square root of the relative permittivity tensor.

The components of the refraktivitetstensor are typically represented in a diagonal matrix form when aligned with the principal optical axes of the material. In this principal axis system, the tensor has three principal refractive indices, $n_1$, $n_2$, and $n_3$, corresponding to the refractive indices for light polarized along these axes. Light entering an anisotropic material can split into two distinct polarized rays, known as the ordinary ray and the extraordinary ray, with different refractive indices. The refraktivitetstensor provides a comprehensive description of how light interacts with such materials, enabling predictions of phenomena like birefringence and optical activity.