V. P. Romanov

Propagation and scattering of light in fluctuating media

Abstract The monograph deals with the problems of the propagation and scattering of light in molecular media. The explicit statistical mechanical averaging procedure for the equations of electrodynamics is developed. It permits to transform the molecular level description into the macroscopic one for the electrodynamics of the fluctuating media. In the framework of such an approach, the problems of the molecular correlation contribution into the dielectric permeability, of the calculation of the reflection coefficients with an account of surface layers and of the multiple light scattering are considered. The developed theory is applied to the description of the critical opalescence, the coherent backscattering enhancement, the light scattering depolarization phenomena and the propagation and scattering of light in anisotropic media, including the case of liquid crystals.

Crossed source–detector geometry for a novel spray diagnostic: Monte Carlo simulation and analytical results

Sprays and other industrially relevant turbid media can be quantitatively characterized by light scattering. However, current optical diagnostic techniques generate errors in the intermediate scattering regime where the average number of light scattering is too great for the single scattering to be assumed, but too few for the diffusion approximation to be applied. Within this transitional single-to-multiple scattering regime, we consider a novel crossed source-detector geometry that allows the intensity of single scattering to be measured separately from the higher scattering orders. We verify Monte Carlo calculations that include the imperfections of the experiment against analytical results. We show quantitatively the influence of the detector numerical aperture and the angle between the source and the detector on the relative intensity of the scattering orders in the intermediate single-to-multiple scattering regime. Monte Carlo and analytical calculations of double light-scattering intensity are made with small particles that exhibit isotropic scattering. The agreement between Monte Carlo and analytical techniques validates use of the Monte Carlo approach in the intermediate scattering regime. Monte Carlo calculations are then performed for typical parameters of sprays and aerosols with anisotropic (Mie) scattering in the intermediate single-to-multiple scattering regime.

Fluctuations of dielectric constant in a system of hard spheres

The correlation function for fluctuations of a dielectric constant in a latex-like suspension of spherical particles was calculated. An exact analytical expression was derived for the correlation function using the Percus-Yewick approximation for a system of hard spheres. The obtained results made it possible to calculate the indicatrix of single scattering, the extinction coefficient, and the transport mean path. It is shown that, starting with a volume content of about ten percent, the “gas” approximation becomes invalid, and optical parameters begin to depend on concentration in quite a complicated manner. In particular, the extinction length and the mean transport path, which are the basic parameters in describing the coherent effects in multiple scattering, vary nonmonotonically with concentration. It is found that there exists a range of sizes and concentrations of scattering particles in which an effect similar to the emergence of blue phase in liquid crystals can be observed.

Low-order light scattering in multiple scattering disperse media

Light scattering has been investigated in systems in which both single and higher order scattering occur. The Monte Carlo simulation technique for studying light scattering in randomly inhomogeneous, strongly scattering disperse media was employed. The reliability of the data obtained has been checked by comparing the results of the computer simulation with analytical calculations for the intensity of doubly scattered light. The first several scattering orders have been analyzed for different geometries of the optical experiment. It has been shown, in particular, that, depending on the detector aperture, the contribution of multiple scattering can vary by almost an order of magnitude.

Coherent backscattering of light in nematic liquid crystals

Multiple light scattering by director fluctuations in nematic liquid crystals is considered. A uniform director orientation is assumed to be specified by an applied magnetic field. The coherent backscattering effect, which consists in the presence of a sharp light backscattering peak, is studied. The Bethe-Salpeter equation is used to calculate the multiple scattering intensity taking into account the contributions of ladder and cyclic diagrams. An analytical expression for the angular and polarization dependences of the coherent backscattering intensity is obtained in terms of the diffusion approximation. The calculation and experimental results are compared. The developed theory is shown to qualitatively describe the elliptical shape of the backscattering cone, to explain the absence of a coherent contribution for crossed polarizations, and to calculate the relative peak height.

Light propagation in chiral media with large pitch

Light propagation in uniaxial chiral media with large pitch is studied. In these systems there are forbidden zones for extraordinary beams, which lead to effective reflection on zone boundaries and to wave damping inside the forbidden zone. We analyze the vicinities of the turning points and the transition of an extraordinary wave through the forbidden zone. Narrow forbidden zones with merging turning points are studied in detail. The transition through the forbidden zone is studied experimentally in nematic liquid crystal doped with a chiral addition. There is a good agreement between experimental results and theoretical calculations.

Simulation of the Propagation of a Light Pulse in a Randomly Inhomogeneous Medium

The propagation of a Gaussian pulse in an inhomogeneous medium is considered. The detected pulse is represented as a series in the scattering multiplicities. The developed approach enables one to describe the passage of a pulse through a randomly inhomogeneous medium in the general case, beyond the framework of the diffusion approximation. The known results of the diffusion approximation are shown to represent limiting cases of the expansion constructed in the scattering multiplicities. The calculations are performed by the Monte Carlo method for cases of singly and multiply scattering media. The agreement between the results of the theoretical analysis and the numerical simulation allows one to use the approach developed in both optical problems and investigation of propagation of waves of other nature, in particular, seismic waves.

Permittivity of a randomly inhomogeneous medium

A theory of permittivity of suspension-type systems is developed that allows one to calculate such optical parameters of inhomogeneous systems as the length of scattering and the transport length. It is shown that, in the Born approximation, which takes into account two-particle correlations in the arrangement of scattering particles, the theoretical and experimental data are in agreement only to within tens of percent. The contribution of three-particle correlations to the permittivity of a system of solid spheres is determined. It is shown that, in describing the optical properties of suspensions with a large difference between the refractive indices of the medium and the particles, it does not suffice to replace the Rayleigh-Gans form factor by the Mie form factor, even under a restriction to two-particle correlations.

Specific features of optical properties of helical liquid crystals with a large helix pitch

Light propagation in helical liquid crystals with the helix pitch considerably exceeding the light wavelength is studied. Using a multidimensional analog of the WKB method, the Green function of the electromagnetic field in such a medium is calculated. This function contains terms corresponding to ordinary and extraordinary waves. The behavior of the Green function in the far-field region is analyzed. It is shown that for the extraordinary ray there exists, on the surface of the wave vectors, a forbidden zone, which, due to periodic changes of the refractive index, corresponds to conditions of the beam turn with the formation of a flat wave channel. The extraordinary beam trajectory, both inside and outside the wave channel, determined by the ray vector, is not flat. The asymptotic behavior of the Green function inside and outside the wave channel is substantially different.

Local Dynamics of Director Reorientation under Electric Field in Helical LC Structure

The influence of an electric field on the trajectory of an extraordinary light ray in a layer of a chiral liquid crystal (LC) with a 180° turn of the director is studied. In the absence of the electric field and at a large angle of incidence the ray reflects inside the layer and return back through the surface which it entered. The applied electric field distorts the initial configuration of the director. It results in a change of the ray trajectory so that the light is propagated through the LC cell. The study of the temporal characteristics of the effect at various angles of incidence of light on the layer makes it possible to examine the local reorientation of the director inside the cell.