Optic Axes and Elliptic Cone Equation in Coordinate-Invariant Treatment  

作　　者：Alfred Wünsche Alfred Wünsche(Institut für Physik, Humboldt-Universität, Newtonstr, Berlin, Germany)

机构地区：[1]Institut für Physik, Humboldt-Universitä t, Newtonstr, Berlin, Germany

出　　处：《Journal of Modern Physics》2022年第6期1001-1043,共43页现代物理（英文）

摘　　要：We derive for crystal optics in coordinate-invariant way the cone approximation of refraction vectors in the neighborhood of optic axes and determine its invariants and eigenvectors. It proved to describe an elliptic cone. The second invariant of the operator of the wave equation with respect to similarity transformations determines the special cases of degeneration including the optic axes where the polarization of the waves due to self-intersection of the dispersion surface is not uniquely determined. This second invariant is included in all investigations and it is taken into account in the illustrations. It is biquadratic in the refraction vectors and the corresponding forth-order surface in three-dimensional space splits in two separate shells and a non-rational product decomposition describing this is found. We give also a more general classification of all possible solutions of an equation with an arbitrary three-dimensional operator.We derive for crystal optics in coordinate-invariant way the cone approximation of refraction vectors in the neighborhood of optic axes and determine its invariants and eigenvectors. It proved to describe an elliptic cone. The second invariant of the operator of the wave equation with respect to similarity transformations determines the special cases of degeneration including the optic axes where the polarization of the waves due to self-intersection of the dispersion surface is not uniquely determined. This second invariant is included in all investigations and it is taken into account in the illustrations. It is biquadratic in the refraction vectors and the corresponding forth-order surface in three-dimensional space splits in two separate shells and a non-rational product decomposition describing this is found. We give also a more general classification of all possible solutions of an equation with an arbitrary three-dimensional operator.

关 键 词：Permittivity Tensor Principal Permittivities Three-Dimensional Operator of Wave Equation Operator Invariants Refraction Vector Ray Vector Cone Ap-proximation in Neighborhood of Optic Axis Conical Refraction 

分 类 号：O17[理学—数学]