Propagation of an extraordinary beam through a plane-parallel crystal plate

Abstract

Extraordinary light beam propagation through a plane-parallel crystal plate is determined by its specific properties. It has already been demonstrated that when the extraordinary beam is propagated through the plane-parallel plate, its refraction angle is not equal to the angle of radiation incidence on the output side. However, the angle at which the extraordinary beam leaves the plate is equal to the angle of radiation incidence on the plate irrespective of the optical crystal position [1]. In [2] it has been established that when one beam is incident on the plate, four rather than two beams leave the plate, including two ordinary and two extraordinary beams, in the direction of beams reflected from the output side. Moreover, two beams are displaced at a significant distance relative to the plane of incidence. Below we discuss some special features of oblique beam propagation through a plane-parallel crystal plate (Fig. 1). Point 1 here designates the point the beams enter the plate. Incident beams 4 and the normal to the plate lie in the plane of incidence which passes through points 1 and 2. The ordinary beam o leaves the plate at point 2. In this case, the plane of beam incidence and the exit plane coincide for the ordinary beam o. Let us rotate the crystal plate about the axis coinciding with the normal to the plate through an angle ρ (ρ here is the angle between the plane of incidence and the plane of the optical axis). In this case: 1) if the angle ρ = 0°, the exit plane of the extraordinary beam е coincides with the plane of incidence (Fig. 1а); 2) if ρ ≠ 0, the exit plane of the extraordinary beam е is displaced at a distance S = h·tanγ·sinρ (Fig. 1b and c), where γ is the drift angle of the extraordinary beam and ρ is the angle of plate rotation about the normal to the plate. When the crystal plate is rotated about the normal to the input side, motionless point 2 corresponding to the ordinary beam o is seen in the screen, whereas point 3 corresponding to the extraordinary beam е moves along a circle. Plate rotation through 90° also causes point 3 to rotate through an angle of 90°. We note once again the special features of propagation of beams through the plane-parallel plate for the oblique beam incidence. For this case, it is typical that the exit angles for ordinary (o) and extraordinary (е) beams leaving the plate are equal to the angle of beam incidence on the plate α and are independent of the arrangement of the optical crystal axis [1]. At the exit from the plate, the ordinary (o) and extraordinary (е) beams lie in parallel planes and are parallel to one another, but leave the output crystal surface at different points. The exit plane of the extraordinary beam е is displaced relative to the plane of beam incidence at the distance S = f(ρ).