Additional beams in optically uniaxial crystals

Abstract

Reasons for occurrence of additional beams are established for rays reflected from a tilted prism face and transmitted through the interface between two crystal media.In anisotropic media, an arbitrarily polarized light wave is split into two linearly polarized waves. When passing through the interface between two crystal media or reflecting from this interface, each linearly polarized light wave is split into two linearly polarized waves. In the second medium, four light waves are formed [1][2][3].A reason for occurrence of additional waves in the second anisotropic medium is noncoincidence of planes of the main crystal cross sections for incident rays and rays transmitted into the second medium [1,2]. However, in [4-6] cases were described in which the planes of the main cross section seemed to be coinciding for the incident, transmitted, and reflected beams; nevertheless, four beams passed into the second medium or were reflected from the interface. Attention is drawn to the fact that in all cases examined in [4][5][6], beams in one anisotropic medium were propagated at small angles to the optical axis, and in another medium, they were propagated in the vicinity of the normal to it (Fig. 1).Four beams also arise when the ray is reflected from faces of a prism, for example, of the Fresnel rhombic prism (Figs. 1c and 2а) [7,8]. In all cases (Figs. 1 and 2), the plane of the main crystal cross section lies in the figure plane. It would seem that if the ordinary (extraordinary) beam arose in medium 1, it would remain ordinary (extraordinary) in medium 2 or 3 because the planes of the main crystal cross sections for the incident, transmitted, and reflected rays coincide.The present work considers the given anomalies and explains reasons of their occurrence. Experimental investigations demonstrated that generally, four rays each pair of which is polarized in mutually perpendicular directions leave polarization devices like bifocal lenses, Senarmont prisms, and Fresnel rhombs. In a particular case, for a certain position of the prism, only two rays leave it.Results of observations of four split rays leaving the Fresnel rhombic prism fabricated from the lithium niobate crystal (Fig. 2) are presented below. The sizes of the input prism slit were 18 × 5 mm. The prism faces were tilted at an angle of 45° to the optical crystal axis. A ray of unpolarized radiation of a helium-neon laser was incident on input face 1 and then propagated as ordinary and extraordinary rays. These rays were incident at angles α on lateral face 2 from which two rays polarized in mutually orthogonal directions were reflected at angles α o and α е .The rays reflected from face 2 propagated in the vicinity of the optical crystal axis and were incident on opposite lateral face 4. Angles of ray incidence on face 4 were equal to α o and α е , respectively. Because n е < n о (the uniaxial negative crystal), α е < α o in accordance with the reflection law.We note that rays reflected from face 2 are considered ordinary and extraordinary only when they p...