Depolarization characteristics of incompletely polarized and partially coherent laser beams in slant atmospheric turbulence

Based on the cross-spectral density function of transmission theory and the unified theory of coherence and polarization, the depolarization characteristics of incompletely polarized and partially coherent laser propagation in slant atmospheric turbulence are investigated. According to extended Huygens–Fresnel principle, the analytical expressions for intensity and degree of polarization in the slant path are derived. The effects of the wavelength, the initial spot size and the transmission distance on the intensity and degree of polarization are described. The results show that a more stable distribution of the degree of polarization at the receiver is obtained with increasing wavelength for a certain receiver height. The conclusions play an important role in optical communications and target recognition.     

Phase control algorithms for focusing light through turbid media

Light propagation in materials with microscopic inhomogeneities is affected by scattering. In scattering materials, such as powders, disordered metamaterials or biological tissue, multiple scattering on sub-wavelength particles makes light diffuse. Recently, we showed that it is possible to construct a wavefront that focuses through a solid, strongly scattering object. The focusing wavefront uniquely matches a certain configuration of the particles in the medium. To focus light through a turbid liquid or living tissue, it is necessary to dynamically adjust the wavefront as the particles in the medium move. Here we present three algorithms for constructing a wavefront that focuses through a scattering medium. We analyze the dynamic behavior of these algorithms and compare their sensitivity to measurement noise. The algorithms are compared both experimentally and using numerical simulations. The results are in good agreement with an intuitive model, which may be used to develop dynamic diffusion compensators with applications in, for example, light delivery in human tissue.     

Spectropolarised ray-tracing simulations in densely packed particulate medium

Light scattering from particulate medium is simulated using the Monte Carlo ray-tracing technique. The medium is modelled as a randomly packed medium of ellipsoidal grains with stochastically rough surfaces, with an optional thin coating. Optical properties are modelled using a wavelength-dependent complex refractive index and taking Fresnelian reflections and refractions from the interfaces. The size and shape of the grains are assumed to be large and smooth enough for geometric optics to apply reasonably well.The ray-tracing technique uses parallel, weighted rays for computing simultaneously over a wide wavelength spectrum and a small roughness range, and scaling to obtain a large range of sizes and absorbities simultaneously. Polarisation is fully accounted for. The multiobservation technique is effectively used at each scattering point. The scattering from thinner sample layers is also received as a subresult.Simulations are run for a set of model samples to study the effects and sensitivities regarding the values of certain parameters. It has been found that the size and composition of the grains affect the scattering in a unique and invertible way. The shape of the grain causes similar significant effects that must certainly be taken into account if any accuracy is required, although inverting for the shape is difficult without further constraints. The packing density has a small but observable effect. Polarisation can be used to study the composition of low-albedo objects.     

Weak localization effects in the second-harmonic light scattered by random systems of particles

We report rigorous numerical simulations that show the presence of coherent backscattering effects in the second-harmonic generation and scattering of light by random systems of two-dimensional particles. Since the medium composing the particles is assumed to be homogeneous and isotropic, the second-harmonic field is generated mainly by surface effects. For the fundamental frequency, the results present a clear enhanced backscattering peak. In contrast, the second-harmonic scattering patterns present an intensity dip in the backscattering direction.     

Applications of the expanded basis method to study the behavior of light in polaritonic photonic crystal slab with losses

We apply the expanded basis method (EBM) to investigate the behavior of light in polaritonic photonic crystal (PC) slabs with losses. The influence of losses on transmissivity is studied. It is found that the transmissivity is significantly lowered with the increase of losses, in particular, it is abruptly decreased in the vicinity of transverse-optical-phonon frequency. The electromagnetic (EM) dissipation is mainly dominated by the imaginary part of dielectric constant of PC. The larger the imaginary part of the dielectric constant, the more the EM energy depletion is. The variation of EM dissipation with the number of period layers in the PC slab is approximately linear or oscillatory increase with the number of period layers.     

Opposite Goos-Hänchen Displacements for TE- and TM-Polarized Beams Transmitting through a Slab of Indefinite Metamaterial

The Goos-Hänchen displacement of a light beam transmitting through an indefinite metamaterial slab is studied. The results indicate that the displacement would be negative or positive for different parameters, and the necessary conditions for negative or positive displacements are summarized. Due to the special anisotropic properties, the directions of displacements for different polarization beams are opposite by proper design. In addition, the simultaneously enhanced positive and negative displacements will appear at different resonant angles under consideration of the active slab. These phenomena could have convenient applications in optical devices.     

Propagation of a stochastic electromagnetic Gaussian Schell-model beam through an optical system in turbulent atmosphere

A generalized diffraction integral formula for stochastic electromagnetic beams propagating through an optical system in turbulent atmosphere is derived with the help of tensor method. Some analyses are illustrated by a numerical example relating to changes in the average intensity and the degree of polarization of an electromagnetic Gaussian Schell-model beam propagating through a double-lenses system. It is shown that the optical system has strong influence on the propagation properties of the beam. The method used in this paper can be widely applied to the propagation of astigmatic beams through an optical system in turbulent atmosphere.     

A Monte Carlo study of penetration depth and sampling volume of polarized light in turbid media

Detection depth and sampling volume of polarized light in highly turbid, cylindrically-shaped samples are estimated using pathlength distributions calculated from a polarization-sensitive Monte Carlo model. Due to defined ranges of the polarized light pathlength distribution, the estimated penetration depth and the interrogated volume of the polarization-maintaining photon subpopulation are smaller than those of the whole collected photon population, the latter exhibiting a wider pathlength distribution resulting from multiple scattering. It is also demonstrated that the spatial interrogation extent of polarized light in turbid media is greatly affected by the experimental detection geometry.     

Link between the laws of geometrical optics and the radiative transfer equation in media with a spatially varying refractive index

We proposed in a previous paper [J.-M. Tualle, E. Tinet, Opt. Commun. 228 (2003) 33] a modified radiative transfer equation to describe radiative transfer in a medium with a spatially varying refractive index. The present paper is devoted to the demonstration that this equation perfectly works in the non-absorbing/non-scattering limit, what was contested by Martí-López and coworkers [L. Martí-López, J. Bouza-Domínguez, R.A. Martínez-Celorio, J.C. Hebden, Opt. Commun. 266 (2006) 44]. The assertion that this equation would imply a zero divergence of the rays is also commented.     

Stochastic electromagnetic beams for LIDAR systems operating through turbulent atmosphere

With the help of the generalized Huygens–Fresnel integral and the ABCD matrix approach a bistatic LIDAR system involving a rough target at a distant location in a turbulent atmosphere is modeled. The system operates by means of an optical beam which has arbitrary spectral composition, and states of coherence and polarization. The rough target is modeled as a combination of a Gaussian mirror and a thin phase screen which induces phase perturbations of the components of the electric field. The analytical form of the cross-spectral density matrix of the returned beam is determined, from which the effect of the rough target on the spectral density (intensity) and polarization of the returned wave is analyzed. E. Watson’s work performed while assigned to the Ladar and Optical Communications Institute, University of Dayton, Dayton, OH 45469, USA.     

Polarization Changes of Partially Coherent Electromagnetic Vortex Beams Propagating in Turbulent Atmosphere

We investigate the polarization change of partially coherent electromagnetic vortex beams propagating in turbulent atmosphere. It is shown that the polarization of the beams will experience changes, and the changes of the polarization are dependent on the spatial coherence, topological charges of the beams, and the degree of polarization of the source plane and the atmospheric turbulence. The results obtained may have applications in space optical communication.     

Change in degree of coherence of partially coherent electromagnetic beams propagating through atmospheric turbulence

We study the change in the degree of coherence of partially coherent electromagnetic beam (so called electromagnetic Gaussian Schell-model beam). It is shown analytically that with a fixed set of source parameters and under a particular atmospheric turbulence model, an electromagnetic Gaussian Schell-model beam propagating through atmospheric turbulence reaches its maximum value of coherence after the beam propagates a particular distance, and the effective width of the spectral degree of coherence also has its maximum value. This phenomenon is independent of the used turbulence model. The results are illustrated by numerical curves.     

Changes in the coherence of quasi-monochromatic electromagnetic Gaussian Schell-model beams propagating through turbulent atmosphere

Based on the extended Huygens-Fresnel principle, the mutual coherence function of quasi-monochromatic electromagnetic Gaussian Schell-model (EGSM) beams propagating through turbulent atmosphere is derived analytically. By employing the lateral and the longitudinal coherence length of EGSM beams to characterize the spatial and the temporal coherence of the beams, the behavior of changes in the spatial and the temporal coherence of those beams is studied. The results show that with a fixed set of beam parameters and under particular atmospheric turbulence model, the lateral coherence of an EGSM beam reaches its maximum value as the beam propagates a certain distance in the turbulent atmosphere, then it begins degrading and keeps decreasing along with the further distance. However, the longitudinal coherence length of an EGSM beam keeps unchanging in this propagation. Lastly, a qualitative explanation is given to these results.     

Depolarization of light in the pulse transmission through the medium with large inhomogeneities

A theoretical approach to the calculation of the time profile of the degree of polarization in an ultrashort pulse of polarized light is developed in the approximation of the basic polarization modes. It is demonstrated that the degree of polarization of linearly polarized light differs from zero at the initial time interval that is on the order of transport mean free time. In the medium with large inhomogeneities, the circular polarization exhibits slower decay on the time scale that is on the order of the interval between depolarizing collisions. The results are in agreement with the results of numerical calculations and experiments.     

Vector statistics of multiply scattered light in a random medium with large inhomogeneities

The distribution function of the scattered radiation intensity is calculated in the approximation of the basic polarization modes. In such an approximation, the distribution function is represented in terms of the degree of polarization of the initially circularly and linearly polarized waves transmitted by the sample. The effect of the difference of the decay rates for the circular and linear polarization modes on the statistics of the light waves that are multiply scattered in the medium with large inhomogeneities is analyzed.     

Multiply scattered component of lidar returns

The results of statistical simulation of the spatiotemporal structure of the multiply scattered component of lidar returns by the Monte Carlo method are discussed for the case of monostatic sensing geometry. The spatial characteristics of the region of the medium where occurs the last scattering of photon before arriving at the reciever. This region of the medium is called the instantaneous brightness body of multiply scattered radiation. It is demonstrated that the instantaneous brightness body of multiply scattered radiation that propagates toward the receiver may occupy a large volume that does not necessarily coincide with the region of formation of the singly scattered component. The main factors influencing the spatial and brightness characteristics of this volume source are established. The effect of scattering order on the spatiotemporal structure of lidar returns is analyzed for the case of sensing of aerosol haze and advective and radiative fogs with optical thickness 2<τ<8. Received: 2 August 2001 / Revised version: 7 January 2002 / Published online: 25 September 2002 RID="*" ID="*"Corresponding author. Fax: +7-38/2225-8026, E-mail: belov@iao.ru     

Statistical properties of correlated radial stochastic electromagnetic array beams on propagation

A kind of array beam named the correlated radial stochastic electromagnetic array beam that is generated by an electromagnetic Gaussian Schell-model source is introduced by use of tensor method. The analytical expression for the cross-spectral density matrix of this array beam propagating through the turbulent atmosphere and in free space is obtained after performing vector integration. Some typical numerical calculations are illustrated for the changes in the spectral density, spectral degree of polarization, and spectral degree of coherence of the beam on propagation. We find that the atmospheric turbulence can destroy the correlated effect among the beamlets.     

A temporal-coherence anisotropy of unpolarized light

We analyze the anisotropic behavior of unpolarized, temporally partially coherent light. We demonstrate that unpolarized light with different intrinsic degrees of coherence can present an anisotropic behavior which is experimentally observable while it is not the case if both intrinsic degrees are equal. This behavior is analyzed in comparison with the standard anisotropy property of partially polarized light.     

Frequency Response of Multilayer Media Comprised of Double-Negative and Double-Positive Slabs

We present the interactions of the electromagnetic waves with multilayer media formed by double-negative and double-positive slabs to find the frequency response of the structure. The double-negative slabs are analytically realized by using the frequency dispersive cold plasma medium. Numerical examples are performed using an in-house developed simulation programme code. The variation of the reflectance and the transmittance with the emphasis on the plasma frequencies is observed in these examples.     

Illustration of a bimodal system in Intralipid-20% by polarized light scattering: experiments and modeling

Intralipid suspensions behave like phantoms of human tissues concerning their light scattering properties. We present experimental measurements of the angular distribution of polarized light scattering at various incidence angles on Intralipid-20%. A comparison of the absolute values of these measurements with simulations using a vector radiative transfer model (N-flux) developed for multilayered media demonstrates a stratified structure of the samples with a double distribution of the size of scatterers. This result is confirmed by polarimetry imaging.