Orientation of optical axes in absorptive crystals with arbitrary permittivity tensors

The direct relation has been established between the orientations of the optical axes and the components of the inverse complex permittivity tensor of an absorptive crystal possessing an arbitrary symmetry. The particular forms of the general relationships for triclinic crystals, characterized by an arbitrary degree of absorption, are obtained for crystals of all the other symmetry systems. The relationships obtained acquire a substantially simplified form for weakly absorptive crystals. The consideration is based on the relationship established for the components of the inverse permittivity tensor in the Cartesian coordinates and the diadic form of this tensor, which is related to the directions of the optical axes.     

Optical Properties of Cholesteric Liquid Crystals at Oblique Incidence

The optical properties of a periodic structure characterized by a uniform rotation of the dielectric tensor about a given axis are theoretically analyzed. The electromagnetic wave is described as a superposition of elementary modes having the form of Bloch waves. Each elementary mode is represented by a sum of plane waves elliptically polarized, whose wavevectors are the solutions of a characteristic equation. This equation, presented in a preceding paper, is furtherly analyzed, in order to obtain the wave vectors in terms of a power series of a small parameter δ, representing the anisotropy of the dielectric tensor. The coefficients of the series up to terms containing δ⁶ are explicitly given, and the corresponding truncation errors computed. The spectral composition and the polarization states of the Bloch waves are also analyzed and discussed for different values of the incidence angle in the frequency range containing the lower reflection bands. In particular it is shown that in the regions between the reflection bands both the wave functions and the wavevectors can be evaluated with very good approximation by simple analytic expressions, while for an accurate evaluation of the reflection properties of the structure more involved expressions are needed.     

Optical axes in various absorbing crystals

Analytical expressions have been derived for the components of the complex permittivity tensor as a function of the number of optical axes existing in an absorbing monoclinic crystal. Some specific features of the orientation of these axes are considered. The ellipticities of natural waves are calculated for these crystals, as well as the ellipticities of transmitted light for right- or left-hand circularly polarized waves normally incident on a crystal. A significant difference of particular cases of absorbing monoclinic crystals from the general case of crystal with four circular axes is demonstrated.     

Low‐temperature elastic and dielectric properties of K3Na(SO4)2 crystals

Elastic and dielectric properties of glaserite K₃Na(SO₄)₂ single crystal were examined using the method of composite oscillators, Brillouin light scattering methods and dielectric spectroscopy. Measurements were performed in the temperature range from 18 K to 300 K. Anomalies in the temperature dependencies of Brillouin shift and dielectric permittivity at about 70 K confirmed the earlier predicted phase transition at 75 ± 25 K. Temperature dependences of the resonance frequency of the vibrating composite oscillator, Brillouin shift measured in the [110] direction, components of dielectric permittivity tensor reveal an anomaly at about 50 K. Moreover, thermal hysteresis of the dielectric permittivity suggested the presence of an incommensurate state between T ₁ = 50 K and T ₂ = 70 K. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spectrum of natural electromagnetic waves in a periodic ferromagnet-dielectric structure

The specific features of propagation of natural TE waves in a periodic ferromagnet-dielectric structure are investigated in the following geometry: a bias magnetic field is parallel to the ferromagnet/dielectric interface and perpendicular to the wave propagation direction. The transformation matrix for the period of the structure, the dispersion relation, and the energy reflection coefficient are obtained for the case of normal incidence of a wave on a semi-infinite periodic medium by solving the boundary-value problem. It is shown that an external field can be used to control the spectrum and characteristics of reflected waves.     

Selective optical properties of a multilayered periodic gyrotropic structure at an arbitrary angle of incidence of waves

A multilayered periodic gyrotropic structure consisting of an arbitrary number of unit cells is considered. The gyrotropic properties of this multilayered structure are due to the external magnetic field. A matrix is calculated on the basis of the boundary conditions for waves in each layer, which relates a wave incident at an arbitrary angle with the transmitted and reflected waves. The complex amplitude transmittance and reflectance are found for the entire multilayered structure from the calculated matrix elements. The optimal parameters of a structure consisting of layers of potassium dihydrogen phosphate and europium-doped glass are calculated. The dependences of the intensity, ellipticity, and the angle of rotation of the major axis of the polarization ellipse of reflected and transmitted waves on the number of cells, light frequency, and magnetic field at an arbitrary angle of incidence of waves are obtained in graphical form. The structure considered is characterized by selective reflection of electromagnetic waves and can be used as a polarization converter controlled by a magnetic field.     

Experimental Solution of the Local Field Problem in Uniaxial Liquid Crystals†

A method of experimental determination of the Lorentz-factor tensor in uniaxial liquid crystals is suggested. The specific features of the local field tensor of the light wave in a nematic liquid crystal with low optical anisotropy have been investigated experimentally. Anisotropy of the local field and Lorentz-factor tensors has been found to decrease with the decreasing optical and molecular-optical anisotropies. These results appear to contradict the existing polarization theories of liquid crystals. The local field problem in cholesteric liquid crystals has been considered. A new approach to the local field problem in uniaxial liquid crystals with arbitrary optical anisotropy is developed and the experimental results are explained.     

Resonance excitation of polaritons by bulk electromagnetic waves in the layered systems with anisotropic substrates

The possible resonance excitation of surface electromagnetic waves by the bulk waves at the interface between a positive transparent uniaxial crystal and an isotropic medium has been predicted. The existence of the surface waves is provided by anisotropy of one of the boundary media. The tensor relation between the vector amplitudes of an exciting bulk electromagnetic wave and the excited surface wave is established. The ratio of the moduli of the tangential components of these amplitudes is analyzed as a function of the angle of incidence and the polarization of the bulk wave. The numerical calculations are performed for the surface waves at the interface between paratellurite TeO₂ and a KRS-6 (TlBr 30%-TlCl 70%) crystal.     

Coherent and incoherent reflection and transmission of light in anisotropic layer structures

Reflection and transmission of light in anisotropic planar structures consisting of layers coherently and incoherently interacting with light have been considered. The reflection and transmission matrices for mul-tilayered structures are obtained for the general case of an arbitrary incidence angle. The optical characteristics of the structure are studied as functions of its parameters for the particular case of a magneto-gyrotropic film on the substrate.     

Electrostatic model of the LiТаO<Subscript>3</Subscript> ferroelectric

Possible combinations of the electronic polarizability tensor components for oxygen and tantalum ions have been established based on the analysis of the refraction coefficients of LiТаO₃ crystal in the far-IR region. The local electric field on structurally nonequivalent ions in the LiТаO₃ unit cell was calculated within the modified point-multipole model. A combination of the electronic polarizability tensor components for oxygen and tantalum ions and their effective charges is established, which provides a good correspondence of the calculation results with the experimental data on LiТаO₃ crystals obtained by ⁷Li nuclear magnetic resonance and ¹⁸¹Та nuclear quadrupole resonance and with the known value of the crystal spontaneous polarization.     

Electrostatic model of the α-LiIO<Subscript>3</Subscript> pyroelectric

The range of possible combinations of the components of the electronic-polarizability tensors of oxygen and iodine ions and the effective charges of these ions is established on the basis of the experimental study of the parameters of the electric-field gradient tensor at ⁷Li nuclei in an α-LiIO₃ crystal and the calculation of the electric-field gradient from the classical electrostatic model. The I-O bonds in α-LiIO₃ are shown to be mixed ionic-covalent bonds with low ionicity. Spontaneous polarization of the crystal is estimated.     

Kinetics of protein crystal nucleation and growth in the batch method

We have applied the Johnson–Mehl–Avrami–Kolomogorov (JMAK) theory of crystal nucleation and growth to the problem of protein crystallization in the batch method. Without integrating the JMAK equation explicitly, we use dimensional analysis to derive a general formula for the half-life for decay of the protein supersaturation. This formula includes a dimensioned group and an arbitrary dimensionless function. We integrate the JMAK equation exactly for the special case where the growth rate is independent of the supersaturation and the nucleation rate is proportional to its square. This gives an equation for the time decay of the supersaturation and a formula for the half-life in which all arbitrary dimensionless functions are evaluated. The results are consistent not only with Von Weimarn's rule, which asserts that the average size of a crystal increases as the supersaturation decreases, but also with our experimental results for crystallization of lysozyme, in which the half-life at fixed pH decreases with increasing ionic strength and decreasing temperature.     

Accurate Modelling of Liquid Crystal-Based Microwave Devices

Liquid crystal substrates have been shown to provide the means to develop low-cost, reconfigurable, adaptive and tuneable microwave devices for mobile and wireless communication systems. In order to take maximum advantage of the possibilities that these materials offer and to design LC-based devices appropriately, techniques for the characterisation of the liquid crystal dielectric properties are needed. Similarly, appropriate modelling methods are required to simulate accurately the switching behaviour of the liquid crystal and the characteristics of the wave propagation through the devices, taking full consideration of the point-by-point variation of the material tensor permittivity.     

Investigation of shallow strain distributions in silicon single crystals with X-ray bragg reflection

The use of X-ray double crystal diffractometry in Bragg case reflection for the determination of shallow strain distributions is investigated. Based on the theory of Takagi-Taupin theoretical calculations of reflection curves of silicon crystals with diffusion induced strain profiles are carried out for different wave lengths and reflections. Possibilities for an optimal choise of reflections are discussed and the limits of detectibility are estimated. Experimental results of boron diffused silicon crystals confirm the theoretical results. Triple crystal diffractometry of (+n, –n, +n) setting is discussed as one possibility to increase the sensibility.     

晶体和准晶旋声性质的旋转不变性

依据群论原理对计算张量的群论方法作了改进,采用非对称化基函数取代对称化基函数,以便于编程.用MATLAB编制了用于计算属于SO(2)群各阶张量的软件.借助于该软件得到了具有SO(2)群对称性的旋声张量的形式.指出晶体中属于六角系的6、6 mm和622晶类和准晶中属于五角系的5、52、5 m晶类的旋声性质具有围绕晶体或准晶中唯一高次轴的任意旋转不变性.该结果对于旋声性的应用有重要意义.     

Nonlinear optical properties of lithium sulfate monohydrate

In this paper, all eight tensor components of the nonlinear optical susceptibility tensor for second harmonic generation were determined for monoclinic non‐centrosymmetric lithium sulfate monohydrate, Li₂SO₄·H₂O, using the Maker fringe technique at the wavelength λ=1064 nm. The largest component of the nonlinear optical susceptibility tensor was 0.34 pm/V. This crystal has the maximum effective value 0.13 pm/V along the phase matching directions at type I and 0.10 pm/V at type II. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite element analysis of dislocation density during bulk single crystal growth (effect of doping atoms in InP single crystal)

A computer code for simulation of dislocation density in a bulk single crystal during liquid encapsulated Czochralski (LEC) or Czochralski (CZ) growth process. In this computer code, the shape of crystal–melt interface and the temperature in a crystal at an arbitrary time were determined by linear interpolation of the results that were discretely obtained by heat conduction analysis of a CZ single crystal growth system. A dislocation kinetics model called Haasen–Sumino model was used as a constitutive equation. In this model, creep strain rate is related to dislocation density, and this model extended to multiaxial stress state was incorporated into a finite element elastic creep analysis program for axisymmetric bodies. Dislocation density simulations were performed using this computer code for InP bulk single crystals with about 8″ in diameter. In the analysis, the effect of dopant atoms on the dislocation density was examined. In the case of a low doped InP single crystal, dislocations are distributed in the whole of the crystal. On the other hand, in the case of a highly doped InP single crystal, dislocations are localized at both the central and peripheral regions of the crystal.