A theoretical analysis is given of the propagation of a linearly polarized electromagnetic wave through a medium with a harmonically oscillating birefringence and a static birefringence whose principal axis is inclined to the oscillation axis. The theory is applied to the photoelastic modulator (PEM) to predict the transmitted light flux in experimental configurations of particular spectroscopic and polarimetric importance. Included is the general configuration of a modulator between two polarizers (applicable to nearly all PEM-based light-transmission experiments) and the single-polarizer configuration (characteristic of recent experiments to measure natural optical activity by light reflection). Good agreement between observed results not only provides a test of the theory but accounts for recently observed anomalies that are not explicable on the basis of the standard description of the photoelastic modulator.

Wave propagation through a medium with static and dynamic birefringence: theory of the photoelastic modulator

The measurement of natural optical activity by means of specular light reflection can provide an alternative method for spectroscopy of chiral materials that is in some cases (e.g., for thin films and opaque materials) more advantageous than current methods based on light transmission. The Fresnel amplitudes for specular reflection of light from a naturally chiral, birefringent medium are derived on the basis of a theory that takes account of spatial dispersion in both the electric and the magnetic material relations. Previous derivations neglecting the light-induced magnetization result in Fresnel amplitudes that violate the law of energy conservation (Poynting’s theorem). The differential reflection of left- and right-circularly polarized light by chiral uniaxial media is examined as a function of angle incidence and shown to peak near Brewster’s angle. The measurement of the differential circular reflection may possibly be best accomplished by photoelastic modulation of the probe-beam polarization followed by synchronous detection; the experimental prospect for achieving this is discussed.

Light reflection from a naturally optically active birefringent medium

Light propagation through an optically active Fabry–Perot interferometer, consisting of an isotropic chiral layer separating two homogeneous achiral media, is analyzed with an interest in the manifestations of chiral asymmetry in the reflected wave. It is shown that the differential reflection of circularly polarized light and the optical rotation and the ellipticity of incident linearly polarized light can be enhanced by several orders of magnitude (depending on reflection geometry, layer thickness, and optical parameters) under conditions of moderate to high levels of reflectance. This would provide a practical experimental approach to investigating chiral structure and interactions in systems not easily amenable to study, such as weakly chiral thin films and layers, both transparent and absorbing. (Previously proposed and confirmed enhancement techniques, based on multiple total external reflection, could be usefully applied only to absorbing chiral media.) Two experimental configurations of particular potential interest employ (1) total internal reflection and (2) metallic reflection at the second chiral–achiral interface. For a sufficiently thick chiral layer the reflectance of polarization orthogonal to that of the incident wave should be directly observable even under conditions of ordinary reflection. It is also shown that, in contrast to wide belief, reflection at normal incidence from an isotropic chiral medium can manifest optical activity (under appropriate circumstances when the ambient achiral media are birefringent).

Interferometric enhancement of chiral asymmetries: Ellipsometry with an optically active Fabry-Perot interferometer

Fresnel reflection amplitude coefficients (fractional amplitudes) at the surface of an isotropic, intrinsically nonmagnetic chiral medium are derived on the basis of the Drude–Condon model of optical activity The eigenvalue–eigenvector solution is obtained with use of Berreman’s 4 × 4 matrix method Self-consistent results are obtained when the calculations are based on a new 4 × 4 matrix for reflection from an isotropic chiral medium

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Reflection and refraction at the surface of an isotropic chiral medium: eigenvalue–eigenvector solution using a 4 × 4 matrix method

A multipole theory is used to describe reflection and refraction at the interface of an isotropic medium and a transparent noncentrosymmetric crystal. Both optically active and optically inactive crystals are considered. Fresnel reflection amplitudes, which satisfy the requirements of reciprocity, are obtained for the uniaxial symmetry classes when the optic axis is normal to the boundary and parallel to it. These amplitudes are related to the angle of incidence and also to macroscopic property tensors of the crystal within the electric quadrupole–magnetic dipole approximation. Experiments based on the differential reflection of orthogonal polarizations of the incident light beam are described for measuring certain crystal properties.

Reflection from noncentrosymmetric uniaxial crystals: a multipole approach

The possibility to investigate optical activity of uniaxial media by measuring the difference between the intensities of reflected electromagnetic waves (emw) of different circular polarization (reflection optical activity—ROA) is discussed. The components of the gyration tensor and the polarization of the normal emw in uniaxial media are found. The reflection of emw is studied in two cases: (a) optical axis normal to the boundary; (b) optical axis normal to the plane of incidence. Three modifications of differential spectroscopy are proposed: (1) left and right circularly polarized waves—usual reflection; (2) total reflection–circular polarization (TROA); (3) total reflection of linearly polarized waves with different azimuths of vibration. The specific features of the proposed methods (ROA and TROA) are discussed as well as the possibility of studying the optical activity induced by nondegenerate and degenerate excitations (vibrations).

A. I. Miteva

Papers

Reflection optical activity of uniaxial media