Lecture

Index ellipsoid: wave equation and dispersion relation

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Description

This lecture covers the derivation of the wave equation in a dielectric medium, considering isotropic and linear properties. It also explores the dispersion relation and the concept of the index ellipsoid, showing how the refractive index depends on the frequency. The continuity equation for energy conservation in the presence of a charge is discussed, along with the power received by the charge. The lecture delves into the complex index of refraction, the damped harmonic oscillator model, and the quantum formalism for computing susceptibility. It concludes with the symmetry of the dielectric tensor and the optical properties of anisotropic materials.

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Related concepts (32)

Refractive index

In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or refracted, when entering a material. This is described by Snell's law of refraction, n1 sin θ1 = n2 sin θ2, where θ1 and θ2 are the angle of incidence and angle of refraction, respectively, of a ray crossing the interface between two media with refractive indices n1 and n2.

Index ellipsoid

In crystal optics, the index ellipsoid (also known as the optical indicatrix or sometimes as the dielectric ellipsoid) is a geometric construction which concisely represents the refractive indices and associated polarizations of light, as functions of the orientation of the wavefront, in a doubly-refractive crystal (provided that the crystal does not exhibit optical rotation).

Birefringence

Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent (or birefractive). The birefringence is often quantified as the maximum difference between refractive indices exhibited by the material. Crystals with non-cubic crystal structures are often birefringent, as are plastics under mechanical stress.

Symmetry

Symmetry () in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is invariant under some transformations, such as translation, reflection, rotation, or scaling. Although these two meanings of the word can sometimes be told apart, they are intricately related, and hence are discussed together in this article.

Anisotropy

Anisotropy (ˌaenaɪˈsɒtrəpi,_ˌænɪ-) is the structural property of non-uniformity in different directions, as opposed to isotropy. An anisotropic object or pattern has properties that differ according to direction of measurement. For example many materials exhibit very different properties when measured along different axes: physical or mechanical properties (absorbance, refractive index, conductivity, tensile strength, etc.). An example of anisotropy is light coming through a polarizer.

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