Manifestation of optical activity at oblique incidence of light in crystals of classes $$\overline 4 $$
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ICAL PROPERTIES OF CRYSTALS
Manifestation of Optical Activity at Oblique Incidence of Light in Crystals of Classes 42m and 4 T. G. Golovina*, A. F. Konstantinova, and K. K. Konstantinov Shubnikov Institute of Crystallography, Federal Scientific Research Centre “Crystallography and Photonics,” Russian Academy of Sciences, Moscow, 119333 Russia *e-mail: [email protected] Received December 14, 2016
Abstract—The polarization azimuths and ellipticities of the reflected and transmitted light have been calculated as functions of the angle of incidence for transparent crystals of classes 4 2m and 4 . Analytical expressions for these parameters are obtained. It is shown that in the general case the polarization azimuths and ellipticities for a plate cut parallel to the optical axis differ for positive and negative angles of incidence of light. DOI: 10.1134/S1063774517030087
POLARIZATION OF REFLECTED LIGHT IN 4 2m AND 4 CRYSTALS
INTRODUCTION Although the optical activity in uniaxial crystals has been well studied, there are still some open questions. Investigations have generally been performed at normal incidence of light onto a crystal. The influence of the optical activity at oblique incidence of light has been considered much more rarely. This is especially holds true for crystals of classes 4 2m and 4 , in which the optical activity manifests itself in a peculiar way [1]: the rotation of the plane of polarization in the direction of the optical axis is absent. The optical activity in these classes was found for the first time for AgGaS2 (class 4 2m) and CdGa2S4 (class 4 ) crystals, which have an isotropic point [2, 3]. In this case, the refractive indices of the ordinary and extraordinary waves coincide at a certain wavelength, and one can observe rotation of the plane of polarization in the directions different from the optical axis. A new method for determining the components of the gyration tensor was later proposed, which can be applied for crystals without an isotropic point [4, 5]. Manifestation of the optical activity in crystals of classes 4 2m and 4 under at incidence of light was theoretically described in detail in [6–8]. Polarization of transmitted light at oblique incidence for 4 2m crystals was considered in [9]; however, no analytical expressions were given therein. In this paper, we report the results of a more thorough investigation of polarizations of the reflected and transmitted light for such crystals at oblique incidence of light.
Gyration Tensor in 4 2m and 4 Crystals For crystals of classes 4 2m and 4 , the gyration tensor has the form [1]
⎛ α11 α12 0 ⎞ (1) α = ⎜ α12 −α11 0 ⎟ . ⎜⎜ ⎟⎟ 0 0⎠ ⎝ 0 For class 4 2m, we have α12 = 0 if the X and Y coordinate axes are directed along the second-order symmetry axes oriented parallel to the [100] and [010] crystallographic directions. If X and Y are chosen as perpendiculars to the symmetry planes, we obtain α11 = 0 and α12 ≠ 0. The symmetry elements for this crystal and cut of the gyration surface by a plane oriented perpendicular to the 4 axis are show
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