V. A. SHAMBUROV

ROTATION OF THE PLANE OF POLARIZATION OF LIGHT BY CRYSTALS UNDER THE ACTION OF AN ELECTRIC FIELD

(Presented by Academician A. V. Shubnikov, 8 VI 1964)

In a plane-parallel \(z\)-cut plate of a tetragonal crystal of symmetry class \(\bar{4}\cdot m\) (of the ADP type), when it is acted upon by an electric field directed along the optical axis \(z\), one can observe the phenomenon of rotation of the plane of polarization of light in directions parallel to the coordinate planes \(xz\) and \(yz\), and making such angles with the optical axis \(z\) of the crystal that the path difference of the rays in the plate is equal to an odd number of half-waves. In practice this phenomenon can be detected by considering the conoscopic pattern (Fig. 1a) formed by such a plate in crossed polarizers (\(P\) and \(A\)), with the axes \(x\) and \(y\) parallel or at an angle of \(45^\circ\) to the directions of vibration in the polarizers. The points of intersection of the circles passing through the middle of the bright rings of the conoscopic pattern and corresponding to directions of light in the plate with path differences of the rays equal to an odd number of half-waves \(\lambda/2\), with mutually perpendicular straight lines passing through the center of the conoscopic pattern and parallel to the axes \(x\) and \(y\), correspond to the indicated directions of the rays in the plate. When the plate is set with the axes \(x\) and \(y\) parallel to the directions of vibration in the crossed polarizers, these points will be dark and will be located on the arms of the cross of the conoscopic pattern (Fig. 1a). In the case of rotation of the plate through an angle of \(45^\circ\), these points, on the contrary, have maximum illumination. Under the action of an increasing electric field, these points in the first case become illuminated (Fig. 1b), while in the second their illumination decreases. With a field of moderate intensity (\(E = 10\) kV/cm), at which the path difference arising along the optical axis \(z\) does not exceed \(0.1\lambda\), by rotating the analyzer through an angle within \(11^\circ20'\) the points illuminated in the first case can practically be extinguished again, while in the second case the reduced illumination of the points can be restored to the initial one, since the ellipticity of the vibrations arising upon rotation of the plane of polarization does not exceed \(0.6\%\) for a plate thickness of 2 mm. At higher voltages, however, the ellipticity will increase rapidly, and by rotating the analyzer it is no longer possible to establish the initial darkness or maximum illumination of these points. Until now no one has paid attention to the change in illumination at the indicated points of the pattern and to the possibility of its considerable, though partial, compensation by rotating the analyzer.

In order to observe the phenomenon discovered by us more distinctly and to make it quite obvious, two \(z\)-cut plates of a KDP crystal, identical in thickness (9 mm), were used; these were cemented in a crossed position, i.e., the \(x\) axis of one plate coincided in direction with the \(y\) axis of the other. When an electric field was applied along the \(z\) axis by means of transparent electrode glasses with conducting films of tin oxide, the birefringence arising along the \(z\) axis in the plates was mutually compensated; therefore the center of the conoscopic pattern (Fig. 2) remained dark in crossed polarizers. The points of intersection of the odd dark rings with straight lines parallel to the axes \(x'\) and \(y'\) (Fig. 2), however, became illuminated to a considerably greater degree under the action of the field and could again be extinguished by rotating the analyzer. The degree of extinction, as in the preceding observation, decreased as the magnitude of the applied field increased, for the same reasons.

Fig. 1. Conoscopic patterns of one \(z\)-cut plate of a KDP crystal between crossed polarizers \((P, A)\). The points of intersection of the dashed circles with the \(x\) and \(y\) axes correspond to directions in the plate along which the phenomenon of rotation of the plane of polarization of light is observed. \(a\)—no field; \(b\)—the field acts along the \(z\) axis.

Fig. 2. Conoscopic pattern of two identical crossed \(z\)-cut plates of a KDP crystal between crossed polarizers \((P, A)\). The points of intersection of the dashed circles with the \(x, y\) and \(x', y'\) axes correspond to directions in the plates along which the phenomenon of rotation of the plane of polarization of light is observed.

In Fig. \(3b, c, d, e, f, g, h, i\) the change in the initial conoscopic pattern (Fig. \(3a\)) is shown as the magnitude of the applied field increases. The angles of rotation of the analyzer are conventionally shown by straight lines inclined to the \(y'\) axis. In Fig. \(3i\) this angle is \(90^\circ\), and a noticeable brightening is seen at the points of intersection of the \(y'\) axis not only with the first, but also with the third and fifth dark rings.

In Fig. \(4b, c, d, e, f, g, h, i\) the corresponding changes in the conoscopic pattern under the action of the field are shown for a pair of plates when their \(x\) and \(y\) axes are parallel to the directions of vibration in the crossed polarizers (Fig. \(4a\)). In this case the phenomenon under consideration is observed especially clearly, and it may be interpreted in the following way. Since the odd dark rings of the conoscopic pattern correspond to those directions for which the path difference of the rays in the pair of cemented plates is equal to the corresponding odd numbers of wavelengths, in each plate the path differences along these directions will be half as large, i.e., equal to odd numbers of half-wavelengths. Under the action of the field along the \(z\) axis, the ellipses of the sections of the optical indicatrices of the plates normal to these directions rotate through equal angles \(\chi\) in magnitude, but in opposite directions. Therefore, the plane of polarization of linearly polarized light, after its passage through one plate, will rotate through twice the angle \(2\chi\) of rotation of the ellipse of this plate in the same direction, and after the light subsequently passes through the second plate it will rotate in the opposite direction through an angle \(6\chi\), and as a result will be rotated through an angle \(4\chi\) relative to the initial position. These doubled angles of rotation of the plane of polarization of the light will have different signs for the directions of light in the \(xz\) and \(yz\) planes. Therefore the corresponding dark points of the conoscopic pattern will all brighten to the same degree under the action of the electric field \(E_z\), and when the analyzer \(A\) is rotated in one direction, the points lying on the \(y'\) axis (Fig. 3) and \(y\) axis (Fig. 4) darken again, while those on the \(x'\) and \(x\) axes brighten to an even greater degree. When, however, the analyzer \(A\) is rotated in the other direction, the opposite change in their illumination is observed, which serves as experimental proof of the phenomenon of rotation of the plane of polarization of light along the indicated directions in a pair of crystalline plates. This phenomenon is also observed in a stack of

Fig. 3. The phenomenon of rotation of the plane of polarization of light in two crossed \(z\)-cut plates of a KDP crystal in the case where the axes \(x'\), \(y'\) make an angle of \(45^\circ\) with the vibration directions of the crossed polarizers \(P\) and \(A\). \(a\) — field absent; \(b, v, g, d, e, zh, z, i\) — changes in the conoscopic pattern as the field \(E_z\) increases; \(b', v', g', d', e', zh', z', i'\) — the corresponding conoscopic patterns when the analyzer is rotated through the angle indicated schematically by the inclined straight line, at which the brightened intersection points of the first dark ring with the \(y'\) axis are again extinguished, while with the \(x'\) axis they are brightened still more.

several \(z\)-cut plates of ADP-type crystals, identical in thickness. The positive directions of the \(z\) axes in all plates must coincide. The \(x\) axes of the odd-numbered plates must coincide in direction with the \(y\) axes of the even-numbered plates. If the stack contains an even number \((2n)\) of plates, then the greatest brightening is observed at the corresponding points on the dark—

Fig. 4. The phenomenon of rotation of the plane of polarization of light in two crossed plates of a \(z\)-cut of a KDP crystal in the case where the axes \(x, y\) coincide with the directions of oscillation in crossed polarizers, while the field is absent; \(б, в, г, д, е, ж, з, и\) — change in the conoscopic pattern as the field \(E_z\) increases; \(б', в', г', д', е', ж', з', и'\) — the corresponding conoscopic patterns when the analyzer is rotated through the angle at which the brightening points at the intersections of the first dark ring with the \(y\) axis again go dark, while with the \(x\) axis they become still brighter.

on the \(n\)-th ring of the conoscopic pattern, if counted from the center. In the case of an odd number \((2n - 1)\) of plates, their greatest brightening is observed on the dark portions of the bright rings with number \((2n - 1)\).

Institute of Crystallography
Academy of Sciences of the USSR

Received
13 IV 1964