We extend the T-matrix approach to light scattering by spherical particles to some simple cases in which the scatterers are optically anisotropic. Specifically we consider cases in which the spherical particles include radially and... more
We extend the T-matrix approach to light scattering by spherical particles to some simple cases in which the scatterers are optically anisotropic. Specifically we consider cases in which the spherical particles include radially and uniformly anisotropic layers. We find that in both cases the T-matrix theory can be formulated using a modified T-matrix ansatz with suitably defined modes. In a uniformly anisotropic medium we derive these modes by relating the wave packet representation and expansions of electromagnetic field over spherical harmonics. The resulting wave functions are deformed spherical harmonics that represent solutions of the Maxwell equations. We use these modes to express the equations for the T-matrix elements in terms of computationally tractable coefficient functions.
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We have used a Mie-type theory to study the light scattering from an annular anisotropic layer around a spherical colloidal particle. We have derived an exact solution of the scattering problem in the case when the distribution of the... more
We have used a Mie-type theory to study the light scattering from an annular anisotropic layer around a spherical colloidal particle. We have derived an exact solution of the scattering problem in the case when the distribution of the optical axes around the particles posses some special transformation properties under rotation and, outside of the layer, the ambient medium is isotropic. We have then calculated the dependence of the scattering cross-section on particle size, anisotropy parameter, and layer thickness for different optical axis distributions. We find that the scattering cross-section is strongly affected by the type of anisotropy. The presence of disclinations enhances scattering efficiency. We determine the region of validity of Rayleigh-Gans approximation by comparing approximate values of the scattering cross-section with the results computed from the exact solution. As an additional effect specific to anisotropic scatterer, it is found that for structures with brok...
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The method of kinetic equation is used to investigate the non-adiabatic effects induced by a strong quasi-resonant light field on relaxation processes in a single-mode vibronic system. The spectrum of absorption (amplification) of a weak... more
The method of kinetic equation is used to investigate the non-adiabatic effects induced by a strong quasi-resonant light field on relaxation processes in a single-mode vibronic system. The spectrum of absorption (amplification) of a weak probe field is calculated. Steady-state solution of the kinetic equation is discussed.
The concept of broken symmetry is used to study bifurcations of equilibria and dynamical instabilities in dynamic model of one-mode laser (nonresonant complex Lorenz model) on the basis of modified Hopf theory. It is shown that an... more
The concept of broken symmetry is used to study bifurcations of equilibria and dynamical instabilities in dynamic model of one-mode laser (nonresonant complex Lorenz model) on the basis of modified Hopf theory. It is shown that an invariant set of stationary points bifurcates into an invariant torus (doubly-periodic branching solution). Influence of the symmetry breaking on stability of branching solutions is investigated as a function of detuning. The invariant torus is found to be stable under the detuning exceeds its critical value, so that dynamically broken symmetry results in the apprearance of low-frequency Goldstone-type mode. If the detuning then goes downward and pumping is kept above the threshold, numerical analysis reveals that after a cascade of period-doublings the strange Lorenz attractor is formed at small values of detuning. It is found that there are three types of the system behavior as pumping increases depending on the detuning. Quantum counterpart of the compl...
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The magnetic moment operator of phonons for the ionic cubic crystals is constructed in the work. The vibrational magnetization induced by circular IR field is calculated. The results of different calculation methods are discussed.... more
The magnetic moment operator of phonons for the ionic cubic crystals is constructed in the work. The vibrational magnetization induced by circular IR field is calculated. The results of different calculation methods are discussed. Estimation of frequency displacement of the fundamental line in the absorption NMR spectrum which arises with excitation of vibrational magnetization in a crystal is obtained.
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The concept of broken symmetry is used to study stability of equilibrium and time doubly-periodic bifurcating solutions of the complex nonresonant Lorenz model as a function of the fre-quency detuning on the basis of modiied Hopf theory.... more
The concept of broken symmetry is used to study stability of equilibrium and time doubly-periodic bifurcating solutions of the complex nonresonant Lorenz model as a function of the fre-quency detuning on the basis of modiied Hopf theory. By contrast to the well-known real Lorenz equations, the system in question is invariant under the action of Lie group transformations (ro-tations in complex planes) and an invariant set of stationary points is found to bifurcate into an invariant torus, which is stable under the detuning exceeding its critical value. If the detuning then goes downward numerical analysis reveals that after a cascade of period-doublings the strange Lorenz attractor is formed in the vicinity of zero detuning.
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We consider director configurations of cholesteric liquid crystal (CLC) cells with two plane confining substrates. Exact solutions of the Euler-Lagrange equations for out-of-plane orientations of the easy axes that correspond to... more
We consider director configurations of cholesteric liquid crystal (CLC) cells with two plane confining substrates. Exact solutions of the Euler-Lagrange equations for out-of-plane orientations of the easy axes that correspond to inhomogeneous conical structures of CLC director are derived. We study dependence of the CLC twist wavenumber on the free twisting number assuming that anchoring energies at the substrates are either equal or different. In both cases this dependence is found to be generally discontinuous with hysteresis loops and bistability effects involved. For CLC cells with identical substrates and planar anchoring conditions the jump-like behaviour only disappears in the weak anchoring limit. Contrastingly, when the anchoring strengths are different, there is the finite value of anchoring below which the dependence becomes continuous. Another effect is the appearance of the gap between the adjacent twist wavenumber intervals representing locally stable director configur...
In order to explore electric-field-induced transformations of polarization singularities in the polarization-resolved angular (conoscopic) patterns emerging after deformed-helix ferroelectric liquid crystal (DHFLC) cells with... more
In order to explore electric-field-induced transformations of polarization singularities in the polarization-resolved angular (conoscopic) patterns emerging after deformed-helix ferroelectric liquid crystal (DHFLC) cells with subwavelength helix pitch, we combine the transfer matrix formalism with the results for the effective dielectric tensor of biaxial FLCs evaluated using an improved technique of averaging over distorted helical structures. Within the framework of the transfer matrix method, we deduce a number of symmetry relations and show that the symmetry axis of L lines (curves of linear polarization) is directed along the major in-plane optical axis which rotates under the action of the electric field. When the angle between this axis and the polarization plane of incident linearly polarized light is above its critical value, the C points (points of circular polarization) appear in the form of symmetrically arranged chains of densely packed star-monstar pairs. We also empha...
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ABSTRACT In this paper we consider nematic liquid crystal (NLC) confined to a cylindrical cavity under the anchoring conditions of various type. The influence of the saddle-splay and splay-bend terms (the K24-term and the K13-term) on the... more
ABSTRACT In this paper we consider nematic liquid crystal (NLC) confined to a cylindrical cavity under the anchoring conditions of various type. The influence of the saddle-splay and splay-bend terms (the K24-term and the K13-term) on the axial director configuration stability is investigated. By using the Fourier expansion of director fluctuations over azimuth angle our analytical method of attack enables the stability conditions to be found in terms of the stability to each fluctuation mode. Two ways to stabilize the structure are explored: the stabilization by magnetic field and by the action of the boundary conditions. We get the restrictions imposed on the constant values to make the stabilization possible. The dependence of the resultant stability threshold on the surfacelike elastic constant values is calculated. We discuss in detail experimentally detectable effects due to the presence of the K13-term. It is shown that the escaped-radial director structure exhibits some special features induced by the K13-term.
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We describe the method to extend the generalized Mie approach to the case of light scattering by uniformly anisotropic spherical particles by relating the wave packet representation and expansions for electromagnetic field over spherical... more
We describe the method to extend the generalized Mie approach to the case of light scattering by uniformly anisotropic spherical particles by relating the wave packet representation and expansions for electromagnetic field over spherical harmonics. As a result, we define quasi-spherical modes in anisotropic medium. For radially anisotropic layer we determine the region of validity of Rayleigh-Gans approximation by comparing approximate values of the scattering cross-section with the results computed from the exact solution. We study the relative error for the scattering cross section as a function of the particle size, the anisotropy parameter and the layer thickness.
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The problem of light scattering from an anisotropic layer with a spherically symmetric distribution of the optical axis is solved exactly. The dependence of the scattering efficiency on the particle size, the anisotropy parameter, and the... more
The problem of light scattering from an anisotropic layer with a spherically symmetric distribution of the optical axis is solved exactly. The dependence of the scattering efficiency on the particle size, the anisotropy parameter, and the layer thickness is studied numerically for various anisotropy types. It is shown that the scattering cross section is strongly affected by the type of
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We study both experimentally and theoretically modulation of light in a planar aligned deformed-helix ferroelectric liquid crystal (DHFLC) cell with subwavelength helix pitch, which is also known as a short-pitch DHFLC. In our... more
We study both experimentally and theoretically modulation of light in a planar aligned deformed-helix ferroelectric liquid crystal (DHFLC) cell with subwavelength helix pitch, which is also known as a short-pitch DHFLC. In our experiments, the azimuthal angle of the in-plane optical axis and electrically controlled parts of the principal in-plane refractive indices are measured as a function of voltage applied across the cell. Theoretical results giving the effective optical tensor of a short-pitch DHFLC expressed in terms of the smectic tilt angle and the refractive indices of the ferroelectric liquid crystal (FLC) are used to fit the experimental data. The optical anisotropy of the FLC material is found to be weakly biaxial. For both the transmissive and reflective modes, the results of fitting are applied to model the phase and amplitude modulation of light in the DHFLC cell. We demonstrate that if the thickness of the DHFLC layer is about 50μm, the detrimental effect of field-in...
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We study the kinetics of photoinduced ordering in the azo-dye SD1 photoaligning layers and present the results of modeling performed using two different phenomenological approaches. A phenomenological two state model is deduced from the... more
We study the kinetics of photoinduced ordering in the azo-dye SD1 photoaligning layers and present the results of modeling performed using two different phenomenological approaches. A phenomenological two state model is deduced from the master equation for an ensemble of two-level molecular systems. Using an alternative approach, we formulate the two-dimensional (2D) diffusion model as the free energy Fokker-Planck equation simplified for the limiting regime of purely in-plane reorientation. The models are employed to interpret the irradiation time dependence of the absorption order parameters extracted from the available experimental data by using the exact solution to the light transmission problem for a biaxially anisotropic absorbing layer. The transient photoinduced structures are found to be biaxially anisotropic whereas the photosteady and the initial states are uniaxial.
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The photoinduced 3D orientational structures in the films of liquid crystalline polyester, containing azobenzene side groups, are studied both experimentally and theoretically. By using the null ellipsometry and the UV absorption methods,... more
The photoinduced 3D orientational structures in the films of liquid crystalline polyester, containing azobenzene side groups, are studied both experimentally and theoretically. By using the null ellipsometry and the UV absorption methods, preferential in-plane alignment of the azobenzene fragments and in-plane reorientation under irradiation with polarized UV light are established. The uniaxial and biaxial orientational configurations of the azobenzene chromophores are detected. The biaxiality is observed in the intermediate stages of irradiation, whereas the uniaxial structure is maintained in the photosaturated state. The components of the order parameter tensor of the azobenzene fragments are estimated for the initial state and after different doses of irradiation. The proposed theory takes into account biaxiality of the induced structures. Numerical analysis of the master equations for the order parameter tensor is found to yield the results that are in good agreement with the experimental dependencies of the order parameter components on the illumination time.
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Stochastic dynamics in the energy representation is employed as a method to study non-equilibrium Brownian-like systems. It is shown that the equation of motion for the energy of such systems can be taken in the form of the Langevin... more
Stochastic dynamics in the energy representation is employed as a method to study non-equilibrium Brownian-like systems. It is shown that the equation of motion for the energy of such systems can be taken in the form of the Langevin equation with multiplicative noise. Properties of the steady states are examined by solving the Fokker-Planck equation for the energy distribution functions. The generalized integral fluctuation theorem is deduced for the systems characterized by the shifted probability flux operator. There are a number of entropy and fluctuation relations such as the Hatano-Sasa identity and the Jarzynski's equality that follow from this theorem. Comment: revtex4-1, 18 pages, extended discussion, references added