refraktivitetstensor

The refraktivitetstensor, also known as the susceptibility tensor or dielectric susceptibility tensor, is a mathematical object that describes the linear response of a material to an applied electric field. In many materials, particularly anisotropic ones, the electric polarization induced within the material is not directly proportional to the applied electric field in terms of direction. The refraktivitetstensor quantifies this directional relationship.

When an electric field E is applied to a material, it induces an electric polarization P. In general, P is not parallel to E. The relationship between P and E can be expressed using the refraktivitetstensor, often denoted by the Greek letter chi ($\chi$), as $P = \epsilon_0 \chi E$, where $\epsilon_0$ is the permittivity of free space. The tensor $\chi$ is a second-rank tensor, meaning it has nine components in three-dimensional space. These components relate the components of the electric field to the components of the induced polarization. For example, $P_i = \epsilon_0 \sum_j \chi_{ij} E_j$, where i and j represent the spatial directions (x, y, or z).

The components of the refraktivitetstensor depend on the material's properties and the frequency of the applied electric field. In isotropic materials, the polarization is always parallel to the electric field, and the refraktivitetstensor is a scalar multiple of the identity tensor, simplifying the relationship to $P = \epsilon_0 \chi E$ where $\chi$ is a scalar. For anisotropic materials, such as crystals, the tensor form is necessary to accurately describe the optical and electrical behavior, influencing phenomena like birefringence and piezoelectricity. The refraktivitetstensor is closely related to the permittivity tensor, which describes the dielectric properties of the material.