Optical Activity Of Crystals Research Articles

Poincaré and his polarization sphere.

In a text (1892) on light, Jules Henri Poincaré introduced a geometrical device for tracking the polarization of state of light interacting with matter. Poincaré first mapped all polarization ellipses onto the surface of sphere and changes of state were represented as rotations from one point to another about prescribed axes depending on linear optical properties of the medium. Here, we consider how Poincaré, the mathematician, invented his sphere. Poincaré's professional activities in the service of geodesy appear at first glance to provide a borrowed geometry for his one-to-one mapping of polarization ellipses to global lines of latitude and longitude. However, this association falls apart in the face of a close reading of Poincaré's biography and his influences, especially the research interests of his teachers from the École Polytechnique and the Écoles de Mines. The work of Tissot and Mallard on distortion ellipses in cartography and the etiology of optical activity in crystals, respectively, together with Poincaré's own study of the qualitative theory of differential equations, provide the iconography of, and motivation for, the sphere. Whether Poincaré's mentors were unwitting partners in the invention of the sphere-it is impossible to be sure-Poincaré's otherworldly geometric sensibilities carried him through isometries (rotations) on hyperbolic planes and beyond. The apparent ingenuity behind Poincaré's sphere is diminished in comparison to his fulsome achievements. Moreover, Poincaré's considerations of the psychology of invention further emphasize that sometimes great ideas arrive to those fortunate to receive them by mechanisms that resist interpretation.

The interference enhancement of light polarization conversion from structures with a quantum well

The optical activity of crystals leads to the occurrence of ellipticity at the reflection of light which is linearly polarized in the interface plane or normally to it. The effect experimentally discovered in the investigated structures with quantum wells is due to a spin-orbit interaction and birefringence. The qualitative dependence of the effect on the change in the orientation of the linear polarization of the incident light has been revealed. A sharp increase in the degree of the polarization conversion in a narrow range of incidence angles for light polarized in the incidence plane has been detected. The latter is due to the influence of the interference of the reflected wave on the structure thickness.

Specific features of optical activity in various uniaxial crystals

The influence of the antisymmetric part of the gyration pseudotensor on the characteristics of reflected and transmitted light has been considered for crystals of classes 3, 4, and 6. The results are compared with the corresponding data for crystals of classes 32, 422, and 622 with a symmetric gyration pseudotensor. Specific features of the optical activity in crystals of classes 3m, 4mm, and 6mm with an antisymmetric gyration pseudotensor have been studied. Crystals of classes \(\bar 42m\) and \(\bar 4\) with the symmetric gyration pseudotensor of an unusual form have been considered. The polarization azimuth and ellipticity of the reflected and transmitted light are calculated for these crystals at different angles of incidence.

Determination of Chirality of the Chiral Space Groups with Two-fold Screw Axis

Crystals are classified according to their symmetry operations into 230 space groups. A two-fold screw axis, 21, a symmetry operation, is frequently found in the crystal, especially non-centrosymmetric organic crystals. The two-fold screw axis shows a chiral character when molecules in the crystal tilt against the screw axis as shown in Figure. The crystals belonging to a chiral space group with two-fold screw axis such as a P21or P212121exhibit two different types with opposite chirality. However, although the two crystals are not identical in a molecular arrangement, we cannot distinguish them with the present notation of space group. Recently, the idea of determining the handedness of two-fold screw axis have been successfully proposed using hierarchical interpretation of the crystals.(I. Hisaki, T. Sasaki et al., 2012) Nevertheless, the issue on a notation to distinguish chiral crystals with two-fold screw axis still remains unsettled as far as we know. Therefore, we attempt to propose a novel notation for the crystals belonging to chiral space groups with two-fold screw axis. We focus on the relationship between the absolute structure and optical activity of the crystals. We have selected alanine crystals, which belong to P212121, as model crystals to discuss the notation. We have determined the absolute structure of the alanine crystals by X-ray diffraction and have measured their optical activity with Generalized High Accuracy Universal Polarimeter (G-HAUP).(M. Tanaka, N. Nakamura et al., 2012) G-HAUP is an apparatus that can measure simultaneously the linear birefringence, linear dichroism, circular birefringence, i.e., optical activity, and circular dichroism in any solid material. These experimental results have successfully correlated the absolute structure to the optical activity of the alanine crystals.

Optical activity and crystalline structure of crystals of the langasite family

The dependences of the refraction on the structural parameters are considered for the La3Ga5.5Nb0.5O14, La3Ga5.5Ta0.5O14, La3Ga5SiO14, Ca3Ga2Ge4O14, and Sr3Ga2Ge4O14 crystals of the langasite family. It is shown that the angle of deviation of the 1a octahedron faces that are normal to the optical axis from 60° is one of the main sources of optical activity of these crystals. The interaction of the cations belonging to the 3e dodecahedron and 1a octahedron, cations of the 3e dodecahedron and 2d tetrahedron, and the repulsion of O2− ions are believed to be the basic interactions affecting the angle value. The dependences of the angle on the crystal-chemical characteristics of the considered crystals are analyzed. The role of the relative sizes of the structural polyhedra is demonstrated.

Comparison of the Spectral Characteristics of Chromium-Containing Crystals of the Calcium Gallogermanate Type with Their Structural Features

The molecular refractions and characteristics of the circular dichroism spectra of unactivated and chromium_activated La3Ga5.5Ta0.5O14, La3Ga5.5Nb0.5O14, La3Ga5GeO14, La3Ga5SiO14, Sr3Ga2Ge4O14, and Ca3Ga2Ge4O14crystals are compared with their structural parameters. Correlations between the molecular refractions and the structural distortions responsible for the optical activity of crystals and correlations between the characteristics of circular dichroism bands of defects and chromium ions and the interatomic distances in polyhedra and their distortions are found. The calcium gallogermanate structures exhibit a unique correspondence between the electronic configuration of host ions and the local symmetry.

Coexistence of ordinary gyration and weak optical activity in crystals: eigen waves of a new type

Abstract We present the results of analysis for the refractive indices and the ellipticity of eigen waves under the conditions of coexisting gyration and weak optical activ-ity. Quantitative relations describing the appropriate parameters are derived. It is shown that the ellipticities of eigen waves become different and one of that waves acquires a complicated (longitudinally-transverse) elliptical polarisation state. This represents a new type of electromagnetic eigen waves in crystals. Keywords: weak optical activity, gyration, spatial dispersion, refraction, polarisation PACS: 78.20.Ek UDC: 535.56 1. Introduction Optical activity is described with taking into consideration an inhomogeneity of the elec-tric displacement D j of an optical wave propagating through a medium: 0 jiijj ijkk DEBD ix γ∂=+∂, (1) where E i denotes electric field, 0 B ij the optical-frequency impermeability tensor without accounting for spatial dispersion effects, γ ijk the third-rank antisymmetric polar tensor (γγ

Determination of the components of the gyration tensor of quartz by oblique incidence transmission two-modulator generalized ellipsometry

The two independent components of the gyration tensor of quartz, g(11) and g(33), have been spectroscopically measured using a transmission two-modulator generalized ellipsometer. The method is used to determine the optical activity in crystals in directions other than the optic axis, where the linear birefringence is much larger than the optical activity.

The Electrogyration Effect

Almost 200 years have passed since Arago observed optical activity in crystals, and it’s been more than 30 years since researchers have induced a spatial dispersion effect with an electric field—a phenomenon now known as electrogyration.

Manifestation of optical activity in crystals of different symmetry classes

Specific features of manifestation of optical activity in cubic, uniaxial, and biaxial crystals are described. The effect of optical activity on characteristics of transmitted light is considered as a function of the wavelength of incident light, temperature, and the orientation the optical axis. The results of the investigation of crystals of different symmetry classes are reported.

Optical Activity of the KDP Group Crystals

The temperature dependencies (from 295 K to melting temperatures) of optical activity for the KDP group crystals (KH 2(1−x) D2x PO4, NH 4 H 2 PO 4 , RbH 2 PO 4 , and CsH 2(1−x) D 2x AsO 4 ) for wavelengths λ = 633 nm are measured. The experimental technique related to the HAUP is used. Insignificant influence of deuteration on the optical activity of these crystals is detected.

Gyration Waves in Optical Crystals

The optical activity of crystals can be explained by energy transfer from radiation incident on the crystal into the radiation mode (gyration wave) propagating in the incident wave direction but having the polarization plane perpendicular to that of incident radiation.

Effect of multiple reflections of light on the optical characteristics of crystals

Using the Jones calculus technique, the interference phenomena which are associated with multiple internal reflections of light in crystal plates characterized by both the refraction and the absorption anisotropy are described for a practical case of weak optical anisotropy. The corrections for the multiple reflections arising in the frame of commonly used techniques for determining the absorption coefficient, the birefringence and the optical activity of crystals are obtained. The effect of the multiple reflections on the crystal optical parameters is experimentally studied for a number of crystals. The comparison of those results with the theoretical predictions confirms the validity of the approach.

High-accuracy universal polarimeter measurement of optical activity and birefringence of α-quartz in the presence of multiple reflections

The high-accuracy universal polarimeter (HAUP) method for simultaneous measurement of birefringence and optical activity in crystals is used when multiple reflections at the plate faces cause modulated variation of the optical parameters. We applied the HAUP method to obtain the birefringence and gyration tensors of α-quartz as a function of temperature in the range 25–100 °C at λ=632.8 nm. Results for birefringence Δn= ne-no and nonnull gyration tensor components g11,g22=g11, and g33, with samples cut in different crystallography planes, are consistent with crystal symmetry and in good agreement with other reported values. For example, the temperature coefficient d(Δn)/dt for a cut perpendicular to the optical axis is -1.06× 10-6 (°C)-1,g11=(5.9±0.4)×10-5, and g33=-(10.1±0.2)×10-5 at 24 °C.

Some new aspects about the elimination of systematical errors in HAUP measurements

In recent years the HAUP method, which allows determination of simultaneously occurring birefringence and optical activity of crystals, has extensively been applied in order to answer the question of whether there is an optical activity in the incommensurate phase of -type crystals or not. Especially in the case of tetramethylammonium tetrachlorozincate (TMAZC), which was investigated most thoroughly, several authors reported contradictory results. In order to establish possible causes of these discrepancies we performed HAUP measurements on several test samples of quartz and . The results revealed an essential influence of sample preparation and gave us a better insight into the systematical errors, primarily the so-called error, the parasitic ellipticities of polarizer and analyser, and a further parameter representing the ellipticity induced by the sample's surfaces. This made it possible to understand some of the reasons for the diverging results published for -type crystals so far.

Light propagation in cubic and other anisotropic crystals

A consistent multipole theory is presented to describe light propagation in non-absorbing non-magnetic crystals. Although valid for the 32 crystal classes, the theory is applied here to all except the five members of the triclinic and monoclinic systems. To account for the birefringence that has been observed in certain cubic crystals and also for the predicted Jones birefringence, the theory has to allow for electric octopoles and magnetic quadrupoles induced by the light wave. At the earlier stage of electric quadrupoles and magnetic dipoles, it is able to describe optical activity in crystals. An expression for this is derived which, when electric quadrupole contributions are omitted, yields the familiar Nye result. As a criterion for the correct inclusion in the theory of all relevant induced multipole moments, tensor expressions for observables are shown to be independent of the choice of origin. Finally, the concepts of O-ray and E-ray are found to break down beyond the electric dipole approximation and alternatives are proposed.

Mechanisms and dispersion of crystalline optical activity

A lattice-dynamical calculation applicable to crystals of any structural complexity and any symmetry (that permits optical activity) reveals three mechanisms causing optical activity in crystals: electric-dipole–magnetic-dipole interference, electric-dipole–electric-quadrupole interference, and first-order wave-vector dispersion of the bonding forces. Only the last mechanism was found by Born and Huang from lattice dynamics, while quantum-mechanical derivations have produced only the other two. Thus the present derivation removes a discrepancy between these two approaches, which, since they deal with a long-wavelength phenomenon, should produce closely comparable formulas. The first two mechanisms give terms in the rotatory power proportional to ω2/(ωi2 − ω2), whereas the third mechanism gives terms proportional to ω2/(ωi2 − ω2) (ωj2 − ω2). Both types of term have been shown to be necessary to fit frequency dispersion in particular crystals. Thus the present theory produces all the known mechanisms along with the needed dispersion from a general, unified, basic approach.

Theory and computation of optical rotatory power in inorganic crystals

The classical polarizability theory of optical activity in crystals is elaborated and a method of calculating rotatory power from crystal structure data is described. By varying the polarizabilities of the atoms within reasonable limits, optical rotatory powers are computed for crystals of α-quartz, AlPO4, cinnabar, Bi12SiO20, Bi12GeO20, α-LiIO3, NaClO3 and NaBrO3. In general, the agreement between theory and experiment is excellent. As expected, considerable variability in polarizabilities is required in different structures in order to obtain satisfactory fits to the observed refractive indices and rotatory powers. The orientations of anisotropic polarizability ellipsoids derived in the course of the calculation are compared with those suggested earlier by Glazer & Stadnicka [J. Appl. Cryst. (1986), 19, 108-122].

A New Method for Measuring Optical Activity in Crystals and Its Application to Quartz

This report describes a theoretical study of a convenient method for measuring the optical activity in crystals in which birefringence and optical activity coexist. The method was applied to right-handed quartz. The gyrations in the [100] direction and at 45° from the optical axis were measured. The gyration tensor component g33 calculated from the gyrations measured in these two directions was found to be in good agreement with the value of g33 measured by other workers in the direction of the c-axis (the optical axis) by conventional methods.

Physical Mechanisms of Nonlinear Optical Activity in Crystals

Possible mechanisms of nonlinear optical activity (NLOA) in crystals connected with electronic nonlinearities are considered in this work. Relations are obtained that describe nonlinear changes in the structure of light polarization in a medium having weak, arbitrary nonlinearity. It is shown that in media with third-order nonlinearity, NLOA may be linked either with the distribution of nonlinearity in the medium or with the anisotropy of nonlinear absorption-so-called absorptive and dispersive NLOA.