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Basic Theoretical Physics: A Concise Overview P20. This concise treatment embraces, in four parts, all the main aspects of theoretical physics (I . Mechanics and Basic Relativity, II. Electrodynamics and Aspects of Optics, III. Non-relativistic Quantum Mechanics, IV. Thermodynamics and Statistical Physics). It summarizes the material that every graduate student, physicist working in industry, or physics teacher should master during his or her degree course. It thus serves both as an excellent revision and preparation tool, and as a convenient reference source, covering the whole of theoretical physics. It may also be successfully employed to deepen its readers’ insight and. | 21.3 Crystal Optics and Birefringence 191 On the one hand the vector E should be perpendicular to the tangential plane of the index ellipsoid viz by the Poinsot construction on the other hand it should belong to the plane defined by D and k. As one can show these two conditions can only be satisfied if the direction of D is a principal direction of the above-mentioned section. This allows only two orthogonal polarization directions of D thus the two corresponding sets of dielectric constants are also fixed. In general they are different from each other and the corresponding phase velocities co yfâD differ as well. In addition in general the ray velocities group velocities are different from the phase velocities see above i.e. two different ray velocities also arise. Usually the incident wave has contributions from both polarizations. As a consequence even if in vacuo the wave has a unique linear polarization direction not parallel to a principal axis of the dielectric tensor in the interior of the crystal generally a superposition of two orthogonal linearly polarized components arises which propagate with different velocities. The phenomenon becomes particularly simple if one is dealing with optically uniaxial systems. In this case the index ellipsoid is an ellipsoid of revolution i.e. with two identical dielectric constants 1 2 and a different value 3. Under these circumstances one of the two above-mentioned polarization directions of the vector D can be stated immediately viz the direction of the plane corresponding to k x e3 . For this polarization one has simultaneously E D i.e. also S k i.e. one is dealing with totally usual relations as in a vacuum the so-called ordinary beam . In contrast for orthogonal polarization the vectors E and D and S and k have different directions so that one speaks of an extraordinary beam. If the phase-propagation vector k is e.g. in the x1 x3 -plane under a general angle then the in-plane polarized wave is ordinary whereas the .
