Coordinate method of the analysis of parametres of electromagnetic waves in crystals

The basic difference of the crystal medium from isotropic medium consists in the phenomenon of double refraction. It means that, in the given direction in crystal, if it not an optical axis, two waves with various phase velocities and directions of polarization are propagation. Planes of polarization of these two waves, if to define them, as arrangement planes in them of vectors of electric displacement , are perpendicular. Attempts of the decision of problems by definition independent polarization, and also the phase velocities, connected with them (or refraction indexes, as that is equivalent) were undertaken by many authors, generally they were carried out using аn ellipsoid of Frenelja or ellipsoid of indexes. However, the mathematical transformations of the equations, used in this case, are difficult enough.

In this report other method - a method of transformation of coordinates, allowing quickly enough to calculate phase velocities and angle, defining a polarization of electromagnetic waves, , at their distribution in oneaxial and biaxial crystal, in any given direction, is offered. In the case of oneaxial crystal similar formulas already have been received earlier, that improved legitimacy of the offered method. The main purpose of the report was obtaining the relation, determinant parametres of electromagnetic waves in biaxial crystal. For example by means of the received formulas the parametres of electromagnetic waves in biaxial crystal of the antimony sulphur iodide are calculated. On the basis of this calculation dependences of refraction indexes for both waves and angle, defining a direction of the vector of electric displacement for one of waves, from a direction of wave propagation are presented graphically.