K. K. Konstantinov

Modern application packages for rigorous solution of problems of light propagation in anisotropic layered media: II. Optically active crystals

The matrix Δ suggested by Berreman for optically active crystals of various symmetry classes has been calculated with the use of the Mathematica-4.1 package. It is shown that the eigenvalues of this matrix are the refractive indices, whereas its eigenvectors determine the polarization states of eigenwaves propagating in the crystal. The relation between the components of the gyration tensors obtained on the basis of various constitutive equations is established. The essential differences in the optical activity described on the basis of these equations are also discussed.

Modern application packages for rigorous solution of problems of light propagation in anisotropic layered media. I. General solution of boundary problems in crystal optics

A new approach to the solution of the boundary problems of light propagation in optically active anisotropic absorbing media has been suggested. Unlike a number of already existing approaches, the new approach is based on the use of a computer mathematical system—the integrated application package Mathematica-4.1 and the method suggested by Berreman. It is shown that the special functions integrated into the package allow one to calculate the characteristics of the reflected and transmitted light for an arbitrary class of crystals and construct their dependences on various optical parameters. The examples of the application of the package Mathematica-4.1 for solving various problems of crystal optics are considered.

New concept of the origin of life on earth

A model of coupled autocatalytic reactions with allowance for the crystallization of diastereomer is considered. It is shown that the differences in the physical properties of diastereomers can be a 100% enantioselective factor, which makes it possible to obtain a significant chiral polarization even at low autocatalysis enantioselectivity. In terms of a complicated model, more complex molecules should have a higher chiral polarization than simpler ones. The calculation of the dynamics of the model under consideration shows that the presence of binomial coefficients in the reaction of pair formation from two different enantiomers (provided that diastereomers have identical properties) leads to the occurrence of an additional 100% enantioselective factor. Estimation shows that the theoretical difference between the right- and left-handed molecules (which is due to weak interaction), described in the literature, is sufficient to explain the directed symmetry breaking and construction of biological molecules from L-amino acids and D-sugars at the origin of life on earth.

Gyrotropic Absorbing Crystals of Lower Symmetries

The specific features of polarization of natural waves propagating in crystals near their optical axes have been studied successively in transparent gyrotropic, absorbing, and gyrotropic absorbing crystals of classes 222, 2, 1, m, and mm2. The dependences of the ellipticities of natural waves and the azimuth of polarization of light transmitted through a crystalline plate (the case of normal incidence) on the orientation of the optical-axis plane of the plate axes with respect to the normal to surface are calculated for these crystals. These characteristics are compared for crystals of axial and planal classes with two different orientations of the optical-axis plane with respect to the symmetry elements of crystal.

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

Optical axes in various absorbing crystals

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Total internal reflection in anisotropic crystals

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