Crystal Optical Research

The study of the propagation of light, and associated phenomena, in crystalline solids. For a simple cubic crystal the atomicarrangement is such that in each direction through the crystal the crystal presents the same optical appearance. The atomsin anisotropic crystals are closer together in some planes through the material than in others. In anisotropic crystals theoptical characteristics are different in different directions. In classical physics the progress of an electromagnetic wavethrough a material involves the periodic displacement of electrons. In anisotropic substances the forces resisting thesedisplacements depend on the displacement direction. Thus the velocity of a light wave is different in different directions andfor different states of polarization. The absorption of the wave may also be different in different directions. See Dichroism, Trichroism

In an isotropic medium the light from a point source spreads out in a spherical shell. The light from a point source embeddedin an anisotropic crystal spreads out in two wave surfaces, one of which travels at a faster rate than the other. Thepolarization of the light varies from point to point over each wave surface, and in any particular direction from the source thepolarization of the two surfaces is opposite. The characteristics of these surfaces can be determined experimentally bymaking measurements on a given crystal.

In the most general case of a transparent anisotropic medium, the dielectric constant is different along each of threeorthogonal axes. This means that when the light vector is oriented along each direction, the velocity of light is different. Onemethod for calculating the behavior of a transparent anisotropic material is through the use of the index ellipsoid, also calledthe reciprocal ellipsoid, optical indicatrix, or ellipsoid of wave normals. This is the surface obtained by plotting the value ofthe refractive index in each principal direction for a linearly polarized light vector lying in that direction (see illustration). Thedifferent indices of refraction, or wave velocities associated with a given propagation direction, are then given by sectionsthrough the origin of the coordinates in which the index ellipsoid is drawn. These sections are ellipses, and the major andminor axes of the ellipse represent the fast and slow axes for light proceeding along the normal to the plane of the ellipse.The length of the axes represents the refractive indices for the fast and slow wave, respectively. The most asymmetric typeof ellipsoid has three unequal axes. It is a general rule in crystallography that no property of a crystal will have lesssymmetry than the class in which the crystal belongs.

Optics,Wafers and Crystals

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