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In this paper, using the full security framework for continuous variable quantum key distribution (CV-QKD), we provide a composable security proof for the CV-QKD system in a realistic implementation. We take into account equipment losses and contributions from various components of excess noise and evaluate performance against collective and coherent attacks assuming trusted hardware noise. The calculation showed that the system remains operable at channel losses up to 10.2 dB in the presence of collective attacks and up to 7.5 dB in the presence of coherent ones., Comment: 28 pages, 5 figures

We employ the transfer matrix approach combined with the Green's function method to theoretically study polarization resolved far-field angular distributions of photoluminescence from quantum nanorods (NRs) embedded in an anisotropic polymer film. The emission and excitation properties of NRs are described by the emission and excitation anisotropy tensors. These tensors and the solution of the emission problem expressed in terms of the evolution operators are used to derive the orientationally averaged coherency matrix of the emitted wavefield. For the case of in-plane alignment and unpolarized excitation, we estimate the emission anisotropy parameter and compute the angular profiles for the photoluminescence polarization parameter such as the degree of linear polarization, the Stokes parameter $s_1$, the ellipticity and the polarization azimuth. We show that the alignment order parameter has a profound effect on the angular profiles., Comment: revtex4-1, 25 pages, 13 figures, corrected version

We theoretically analyze the waveguide regime of light propagation in a cylindrical pore of a polymer matrix filled with liquid crystals assuming that the effective radial optical anisotropy is biaxial. From numerical analysis of the dispersion relations, the waveguide modes are found to be sensitive to the field-induced changes of the anisotropy. The electro-optic properties of the polymer porous polyethylene terephthalate (PET) films filled with the nematic liquid crystal 5CB are studied experimentally and the experimental results are compared with the results of the theoretical investigation., Comment: 15 pages, 10 figures, revtex4-1

In our investigation into the effects of the degree of polarization in modulation of partially polarized light we assume general settings of the interferometry of partially polarized lightwaves and perform theoretical analysis of the Uhlmann and the interferometric phases. We introduce the relative Uhlmann phase determined by the Uhlmann holonomies of interfering beams and show that the interferometric phase generalized to the case of nonunitary evolution can, similar to the Uhlmann phase, be cast into the holonomy defined form. By using the technique based on a two-arm Mach-Zehnder interferometer, two different dynamical regimes of light modulation are experimentally studied: (a) modulation of the input light by the rotating quarter-wave plate (QWP); and (b) modulation of the testing beam by a birefringent plate with electrically controlled anisotropy represented by the deformed-helix ferroelectric liquid crystal (DHFLC) cell. In the setup with the rotating QWP, the interferometric phase is found to be equal to the relative Uhlmann phase. Experimental and theoretical results being in excellent agreement both show that this phase is an oscillating function of the QWP angle and increases with the degree of polarization. For modulation by the DHFLC cell, the data derived from our electro-optic measurements are fitted using the theory of the orientational Kerr effect in FLCs. This theory in combination with the results of fitting is used to evaluate electric field dependencies of the interferometric and the Uhlmann phases., Comment: revtex 4.1, 19 pages, 12 figures (published version)

We study the electro-optic properties of subwavelength-pitch deformed-helix ferroelectric liquid crystals (DHFLC) illuminated with unpolarized light. In the experimental setup based on the Mach-Zehnder interferometer, it was observed that the reference and the sample beams being both unpolarized produce the interference pattern which is insensitive to rotation of in-plane optical axes of the DHFLC cell. We find that the field-induced shift of the interference fringes can be described in terms of the electrically dependent Pancharatnam relative phase determined by the averaged phase shift, whereas the visibility of the fringes is solely dictated by the phase retardation., Comment: 8 pages, 7 figures, revised version. arXiv admin note: text overlap with arXiv:1508.04964

We theoretically study electro-optic light modulation based on the quantum model where the linear electro-optic effect and the externally applied microwave field result in the interaction between optical cavity modes. The model assumes that the number of interacting modes is finite and effects of the mode overlapping coefficient on the strength of the intermode interaction can be taken into account through dependence of the coupling coefficient on the mode characteristics. We show that, under certain conditions, the model is exactly solvable and, in the semiclassical approximation where the microwave field is treated as a classical mode, can be analyzed using the technique of the Jordan mappings for the su(2) Lie algebra. Analytical results are applied to study effects of light modulation on the frequency dependence of the photon counting rate. We also establish the conditions of validity of the semiclassical approximation by applying the methods of polynomially deformed Lie algebras for analysis of the model with quantized microwave field., Comment: 13 pages; 7 figures, revised version

We use the T-matrix formalism in combination with the method of far-field matching to evaluate the optical force exerted by Laguerre-Gaussian (LG) light beams on a spherical (Mie) particle. For both non-vortex and optical vortex LG beams, the theoretical results are used to analyze the optical-force-induced dynamics of the scatterer near the trapping points represented by the equilibrium (zero-force) positions. The regimes of linearized dynamics are described in terms of the stiffness matrix spectrum and the damping constant of the ambient medium. For the purely azimuthal LG beams, the dynamics is found to be locally non-conservative and is characterized by the presence of conditionally stable equilibria (unstable zero-force points that can be stabilized by the ambient damping). The effects related to the Mie resonances that under certain conditions manifest themselves as the points changing the trapping properties of the particles are discussed., Comment: 29 pages, 17 figures. corrected and expanded version; a continuation of our study arXiv:1401.7585

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, azimuthal angle of the in-plane optical axis and electrically controlled parts of the principal in-plane refractive indices were 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 FLC are used to fit the experimental data. 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 phase and amplitude modulation of light in the DHFLC cell. We demonstrate that, if the thickness of the DHFLC layer is about 50 $\mu$m, the detrimental effect of field-induced rotation of the in-plane optical axes on the characteristics of an axicon designed using the DHFLC spatial light modulator in the reflective mode is negligible., Comment: 14 pages, 11 figures

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 emphasize the role of phase singularities of a different kind and discuss the enhanced electro-optic response of DHFLCs near the exceptional point where the condition of zero-field isotropy is fulfilled., Comment: 36 pages, 14 figures

We study Mie scattering of Laguerre-Gaussian (LG) light beams remodelled using the method of far-field matching. The theoretical results are used to analyze the optical field in the near-field region for purely azimuthal LG beams characterized by a nonzero azimuthal mode number $m_{LG}$. The mode number $m_{LG}$ is found to have a profound effect on the morphology of photonic nanojets and the near-field structure of optical vortices associated with the components of the electric field., Comment: 22 pages, 7 figures

We disclose the vertically aligned deformed helix ferroelectric liquid crystal (VADHFLC) whose Kerr constant ($K_{\mathrm{kerr}}\approx 130$~nm/V$^2$ at $\lambda=543$~nm) is one order of magnitude higher than any other value previously reported for liquid crystalline structures. Under certain conditions, the phase modulation with ellipticity less than 0.05 over the range of continuous and hysteresis free electric adjustment of the phase shift from zero to 2$\pi$ have been obtained at sub-kilohertz frequency., Comment: revtex4-1, 4 pages, 5 figures

We experimentally study how the cholesteric pitch, $P$, depends on the equilibrium one, $P_0$, in planar liquid crystal (LC) cells with both strong and semistrong anchoring conditions. The cholesteric phase was induced by dissolution in the nematic LC the right-handed chiral dopant 7-DHC (7-dehydrocholesterol, provitamin $D_3$) which transforms to left-handed tachysterol under the action of UV irradiation at the wavelength of 254 nm. By using the model of photoreaction kinetics we obtain dependencies of isomers concentrations and thus the equilibrium pitch on UV irradiation dose. The cholesteric pitch was measured as a function of irradiation time using the polarimetry method. In this method, the pitch is estimated from the experimental data on the irradiation time dependence of the ellipticity of light transmitted through the LC cells. It is found that the resulting dependence of the twist parameter, $2 D/P$ ($D$ is the cell thickness), on the free twisting number parameter, $2 D/P_0$, shows the jump-like behaviour and agrees well with the known theoretical results for the anchoring potential of the Rapini-Papoular form., Comment: 21 pages, 9 figures, published paper with extended Appendix

We study both theoretically and experimentally the electro-optical properties of vertically aligned deformed helix ferroelectric liquid crystals (VADHFLC) with subwavelength pitch that are governed by the electrically induced optical biaxiality of the smectic helical structure. The key theoretical result is that the principal refractive indices of homogenized VADHFLC cells exhibit the quadratic nonlinearity and such behavior might be interpreted as the orientational "Kerr effect" caused by the electric-field-induced orientational distortions of the FLC helix. In our experiments, it has been observed that, for sufficiently weak electric fields, the magnitude of biaxiality is proportional to the square of electric field in good agreement with our theoretical results for the effective dielectric tensor of VADHFLCs. Under certain conditions, the 2$\pi$ phase modulation of light, which is caused by one of the induced refractive indices, is observed without changes in ellipticity of incident light., Comment: revtex4-1, 8 pages, 6 figures

Electro-optical properties of deformed helix ferroelectric liquid crystal (DHFLC) cells are studied by using a general theoretical approach to polarization gratings in which the transmission and reflection matrices of diffraction orders are explicitly related to the evolution operator of equations for the Floquet harmonics. In the short-pitch approximation, a DHFLC cell is shown to be optically equivalent to a uniformly anisotropic biaxial layer where one of the optical axes is normal to the substrates. For in-plane anisotropy, orientation of the optical axes and birefringence are both determined by the voltage applied across the cell and represent the parameters that govern the transmittance of normally incident light passing through crossed polarizers. We calculate the transmittance as a function of the applied voltage and compare the computed curves with the experimental data. The theoretical and experimental results are found to be in good agreement., Comment: 26 pages, 8 figures, revtex 4.1

We theoretically investigate into the effects of the incidence angles in light transmission of cholesteric liquid crystal two-layer sandwich structures with twist defects created by rotation of the one layer about the helical axis.The conoscopic images and polarization resolved patterns are obtained for thick layers by computing the intensity and the polarization parameters as a function of the incidence angles.In addition to the defect angle induced rotation of the pictures as a whole, the rings of defect mode resonances are found to shrink to the origin and disappear as the defect twist angle varies from zero to its limiting value and beyond., Comment: revtex4, 7 pages, 4 figures

We study the angular structure of polarization of light transmitted through a nematic liquid crystal (NLC) cell by analyzing the polarization state as a function of the incidence angles and the polarization of the incident wave. The polarization resolved angular patterns emerging after the NLC cell illuminated by the convergent light beam are described in terms of the polarization singularities such as C-points (points of circular polarization) and L-lines (lines of linear polarization). For the homeotropically aligned cell, the Stokes polarimetry technique is used to measure the polarization resolved conoscopic patterns at different values of the ellipticity of the incident light impinging onto the cell. Using the exact analytical expressions for the transfer matrix we show that variations of the ellipticity induce transformations of the angular pattern exhibiting the effect of avoided L-line crossings and characterized by topological events such as creation and annihilation of the C-points. The predictions of the theory are found to be in good agreement with the experimental results., Comment: revtex4, 29 pages, 10 figures

We study the angular structure of polarization of light transmitted through a nematic liquid crystal (NLC) cell by theoretically analyzing the polarization state as a function of the incidence angles. For a uniformly aligned NLC cell, the $4\times 4$ matrix formalism and the orthogonality relations are used to derive the analytical expressions for the transmission and reflection matrices. The polarization resolved angular patterns in the two-dimensional projection plane are characterized in terms of the polarization singularities: C points (points of circular polarization) and L lines (lines of linear polarization). In the case of linearly polarized plane waves incident on the homeotropically aligned cell, we present the results of detailed theoretical analysis describing the structure of the polarization singularities. We apply the theory to compute the polarization patterns for various orientational structures in the NLC cell and discuss the effects induced by the director orientation and biaxiality., Comment: pdflatex, rextex4, 22 pages, 7 figures (jpeg)

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 complex Lorenz model is discussed., Comment: 23 pages (LaTeX), 8 figures, uses epsf.sty (submitted to J. of Phys. A)