Total internal reflection in anisotropic crystals
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ICAL PROPERTIES OF CRYSTALS
Total Internal Reflection in Anisotropic Crystals A. F. Konstantinovaa, K. K. Konstantinovb, E. A. Evdishchenkoa, K. B. Imangazievac, and B. V. Nabatova, d a
Shubnikov Institute of Crystallography, Russian Academy of Sciences, Leninskiœ pr. 59, Moscow, 119333 Russia e-mail: [email protected] b OOO YuFK Servis, Moscow, Russia c Issyk–Kul State University, ul. Pervogo Maya 32, Karakol, 720044 Kyrgyzstan d Institute of Organic Chemistry, Russian Academy of Sciences, Moscow, Russia Received January 14, 2008
Abstract—Examples of total internal reflection manifestation have been considered on the basis of a solution to boundary problems of crystal optics using the Berreman matrix method and applying the Mathematica-5 system. It is shown how optical activity manifests itself in the total internal reflection and how this effect can be used to monitor the quality and homogeneity of film coatings. PACS numbers: 61.66.Fn, 78.66.-w DOI: 10.1134/S1063774508050180
INTRODUCTION To date, many problem of crystal optics concerning light propagation in anisotropic media have been solved (for example, in [1–7]). Recently, many methods have been proposed to solve boundary problems of light propagation in anisotropic media. Most of these methods are very complicated and some of the problems cannot be completed because the calculations are very cumbersome. However, various systems of computer mathematics have been developed lately, and new possibilities for solving the boundary problems of crystal optics have appeared. To solve the problem of light reflection from an interface between an external medium and a thin anisotropic film on a substrate while taking into account multiple reflections, we can use the method of 4 × 4 matrices proposed by Berreman [8, 9] to solve problems of propagation of light incident at a certain angle on a layered planar anisotropic media. With the use of this method, such a problem was solved in [10]. In [11, 12], a similar problem was solved using the Mathematica-5 package: programs for calculating the parameters of reflected and transmitted light (in particular, coefficients of reflection and transmission matrices) were developed. Using the developed programs, one can solve various direct problems of crystal optics (problems of light propagation in matter). However, we will dwell on the problem of total internal reflection, because there are no studies of the effects related to total internal reflection from anisotropic films on substrates. The investigations of the total internal reflection from optically active materials have not been investigated.
GENERAL RELATIONS It is known that, when light is incident on a medium, four eigenwaves propagate in it: two waves in the incident wave propagation direction (positive values of the refractive index) and two in the opposite direction (negative values). Their refractive indices are determined from the equation of normals [3]. When light is incident at an angle φi, the solution to the equation of normals is ηj, related to the re
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