tailieunhanh - General solutions of the theme “Light propagation in optical uniaxial crystals”

In this article, we introduce a new approach to receive general solutions which describe all of the properties of the light propagating across optical uniaxial crystals. In our approach we do not use the conception of refractive index ellipsoid as being done in references. The solutions are given in analytical expressions so we can handly calculate or writing a small program to compute these expressions. | TAÏP CHÍ PHAÙT TRIEÅN KH&CN, TAÄP 20, SOÁ T3–2017 General solutions of the theme “Light propagation in optical uniaxial crystals” Truong Quang Nghia Nguyen Tu Ngoc Huong University of Science, Vietnam National University-Ho Chi Minh City (Received on Deceember 13th 2016, accepted on July 26th 2017) ABSTRACT In this article, we introduce a new approach to receive general solutions which describe all of the properties of the light propagating across optical uniaxial crystals. In our approach we do not use the conception of refractive index ellipsoid as being done in references. The solutions are given in analytical expressions so we can handly calculate or writing a small program to compute these expressions. Keywords: extra-ordinary ray, light polarization, light velocity, Maxwell’s equations, optical uniaxial crystals, ordinary ray, refractive index, tensor INTRODUCTION The problem of lights propagation in optical uniaxial crystals, . crystals of trigonal, tetragonal and hexagonal systems, was solved by the application of Maxwell’s equations. Solving the Maxwell’s equations for a plane wave light propagating in transparent non-magnetic crystals, one can derive two refractive indices of the two propagating modes of light [2, 3]: no ,2e 1 11 22 2 11 2 22 4 122 (1) expression (1), the light direction is taken in parallel to axis OX3 of an arbitrary coordinate axes OX i (i = 1, 2, 3). Unfortunately, in the reality it is difficult to use the general expression (1) to receive two refractive indices, because in references the components of tensor [ ij ] are often given in crystal coordinate axes OX i* (i = 1, 2, 3) where the number of independent components of this tensor is minimum, . 11* and * (for optical uniaxial crystals). 33 In (1), ij (i, j = 1, 2) are the components of the dielectric impermeability tensor of crystal. In X *3 m O X*2 X*1 Fig 1. The crystal coordinate axes OX i* (i = 1, 2, 3) and the light