Search

We consider light propagation through a twisted nematic liquid crystal. At first, an expression for light transmission is obtained using a rather intuitive approach. Secondly, an accurate solution for light transmission based on Maxwell's equations is derived and compared with the previous one. Both approaches show that when changes in the orientation of the liquid crystal optical axis are small on the scale defined by the optical wavelength (Mauguin limit), the polarization of light approximately follows the optical axis. At the same time, even in this limit, the simple formula for the light transmittance mentioned in some monographs on liquid crystal displays is not necessary accurate. Conditions under which the two approaches give the same expression for the light transmission are found. In addition, two numerical methods for finding the light transmittance are considered. It is demonstrated that the Gauss-Seidel method has much faster convergence rate than the Euler method., Comment: 17 pages, 5 figures

We consider finite size effects on heat transfer between thermal reservoirs mediated by a quantum system, where the number of modes in each reservoir is finite. Our approach is based on the generalized quantum Langevin equation and the thermal reservoirs are described as ensembles of oscillators within the Drude-Ullersma model. A general expression for the heat current between the thermal reservoirs in the long-time quasi-static regime, when an observation time is of the order of $\Delta ^{-1}$ and $\Delta$ is the mode spacing constant of a thermal reservoir, is obtained. The resulting equations that govern the long-time relaxation for the mode temperatures and the average temperatures of the reservoirs are derived and approximate analytical solutions are found., Comment: Accepted for publication in Phys. Rev. E

We consider heat transfer between two thermal reservoirs mediated by a quantum system using the generalized quantum Langevin equation. The thermal reservoirs are treated as ensembles of oscillators within the framework of the Drude-Ullersma model. General expressions for the heat current and thermal conductance are obtained for arbitrary coupling strength between the reservoirs and the mediator and for different temperature regimes. As an application of these results we discuss the origin of Fourier's law in a chain of large, but finite subsystems coupled to each other by the quantum mediators. We also address a question of anomalously large heat current between the STM tip and substrate found in a recent experiment. The question of minimum thermal conductivity is revisited in the framework of scaling theory as a potential application of the developed approach., Comment: 16 pages, 6 figures

We further develop the theory of quantum finite-size effects in metallic nanoparticles, which was originally formulated by Hache, Ricard and Flytzanis [J. Opt. Soc. Am. B 3, 1647 (1986)] and (in a somewhat corrected form) by Rautian [Sov. Phys. JETP 85, 451 (1997)]. These references consider a metal nanoparticle as a degenerate Fermi gas of conduction electrons in an infinitely-high spherical potential well. This model (referred to as the HRFR model below) yields mathematical expressions for the linear and the third-order nonlinear polarizabilities of a nanoparticle in terms of infinite nested series. These series have not been evaluated numerically so far and, in the case of nonlinear polarizability, they can not be evaluated with the use of conventional computers due to the high computational complexity involved. Rautian has derived a set of remarkable analytical approximations to the series but direct numerical verification of Rautian's approximate formulas remained a formidable challenge. In this work, we derive an expression for the third-order nonlinear polarizability, which is exact within the HRFR model but amenable to numerical implementation. We then evaluate the expressions obtained by us numerically for both linear and nonlinear polarizabilities. We investigate the limits of applicability of Rautian's approximations and find that they are surprizingly accurate in a wide range of physical parameters. We also discuss the limits of small frequencies (comparable or below the Drude relaxation constant) and of large particle sizes (the bulk limit) and show that these limits are problematic for the HRFR model, irrespectively of any additional approximations used. Finally, we compare the HRFR model to the purely classical theory of nonlinear polarization of metal nanoparticles developed by us earlier [Phys. Rev. Lett. 100, 47402 (2008)]., Comment: Accepted to PRB in this form

We develop a quantum theory of electron confinement in metal nanofilms. The theory is used to compute the nonlinear response of the film to a static or low-frequency external electric field and to investigate the role of boundary conditions imposed on the metal surface. We find that the sign and magnitude of the nonlinear polarizability depends dramatically on the type of boundary condition used., Comment: Accepted to PRB in this form

We propose a method for optical nano-imaging in which the structure of a three-dimensional inhomogeneous medium may be recovered from far-field power measurements. Neither phase control of the illuminating field nor phase measurements of the scattered field are necessary. The method is based on the solution to the inverse scattering problem for a system consisting of a weakly-scattering dielectric sample and a strongly-scattering nano-particle tip. Numerical simulations are used to illustrate the results., Comment: 10 pages, 2 figures

We develop a classical theory of electron confinement in conducting nanoparticles. The theory is used to compute the nonlinear optical response of the nanoparticle to a harmonic external field., Comment: Page margins have been adjusted; otherwise, identical to the previous version

We report the first experimental test of an analytic image reconstruction algorithm for optical tomography with large data sets. Using a continuous-wave optical tomography system with 10^8 source-detector pairs, we demonstrate the reconstruction of an absorption image of a phantom consisting of a highly-scattering medium with absorbing inhomogeneities., Comment: 3 pages, 3 figures

We demonstrate that the spatial resolution of images in optical tomography is not limited to the fundamental length scale of one transport mean free path. This result is facilitated by the introduction of novel corrections to the standard integral equations of scattering theory within the diffusion approximation to the radiative transport equation., Comment: 8 pages 1 figure