Kullback relative entropy and characterization of partially polarized optical waves

Different properties of partially polarized light are discussed using the Kullback relative entropy, which provides a physically meaningful measure of proximity between probability density functions (PDFs). For optical waves with a Gaussian PDF, the standard degree of polarization is a simple function of the Kullback relative entropy between the considered optical light and a totally depolarized light of the same intensity. It is shown that the Kullback relative entropies between different PDFs allow one to define other properties such as a degree of anisotropy and a degree of non-Gaussianity. It is also demonstrated that, in dimension three, the Kullback relative entropy between a partially polarized light and a totally depolarized light can lead to natural definitions of two degrees of polarization needed to characterize the polarization state. These analyses enlighten the physical meaning of partial polarization of light waves in terms of a measure of disorder provided by the Shannon entropy.     

Shannon entropy of partially polarized and partially coherent light with Gaussian fluctuations

We propose to analyze Shannon entropy properties of partially coherent and partially polarized light with Gaussian probability distributions. It is shown that the Shannon entropy is a sum of simple functions of the intensity, of the degrees of polarization, and of the intrinsic degrees of coherence that have been recently introduced. This analysis clearly demonstrates the contribution of partial polarization and of partial coherence to the characterization of disorder of the light provided by the Shannon entropy, which is a standard measure of randomness. We illustrate these results on two simple examples.     

Polarization changes in a partially coherent radially polarized doughnut beam through turbulent ocean

On the basis of the extended Huygens–Fresnel integral principle and unified theory of coherence and polarization of light, we studied the effects of oceanic turbulence on polarization properties of a partially coherent radially polarized doughnut (PCRPD) beam. The ocean-induced fluctuations in the refractive index are assumed be driven by temperature and salinity fluctuations. Numerical examples of changes in polarization properties, such as the degree of polarization, the degree of ellipticity, and the orientation angle in the oceanic turbulence for the PCRPD beam, are given. Our analysis demonstrates how polarization of the PCRPD beam is affected by statistical properties of the source and by several parameters of oceanic turbulence. We find that the propagation of the PCRPD beam is different from that of stochastic beams in oceanic turbulence. The degree of polarization for the PCRPD beam approaches a certain steady value, and the elliptical polarized state of the fully polarized portion of the beam will become fully linear in the far field.     

Some current trends of correlation optics metrology of coherence and polarization

New feasibilities for metrology of coherence and polarization of light fields provided by correlation optics approaches are considered. This paper shows these approaches are fruitful in measuring the field parameters that are critical for optical diagnostics using the data on the degree of coherence and the state and the degree of polarization of partially coherent and inhomogeneously polarized fields.     

Partial spatial coherence and partial polarization in random evanescent fields on lossless interfaces

We consider partial spatial coherence and partial polarization of purely evanescent optical fields generated in total internal reflection at an interface of two dielectric (lossless) media. Making use of the electromagnetic degree of coherence, we show that, in such fields, the coherence length can be notably shorter than the light's vacuum wavelength, especially at a high-index-contrast interface. Physical explanation for this behavior, analogous to the generation of incoherent light in a multimode laser, is provided. We also analyze the degree of polarization by using a recent three-dimensional formulation and show that the field may be partially polarized at a subwavelength distance from the surface even though it is fully polarized farther away. The degree of polarization can assume values unattainable by beamlike fields, indicating that electromagnetic evanescent waves generally are genuine three-dimensional fields. The results can find applications in near-field optics and nanophotonics.     

Entropy of partially polarized light and application to statistical processing techniques

We have analyzed entropy properties of coherent and partially polarized light in an arbitrary number of spatial dimensions. We show that for Gaussian fields, the Shannon entropy is a simple function of the intensity and of the Barakat degree of polarization. In particular, we provide a probabilistic interpretation of this definition of the degree of polarization. Using information theory results, we also deduce some physical properties of partially polarized light such as additivity of the entropy and depolarization effects induced by mixing partially polarized states of light. Finally, we demonstrate that entropy measures can play an important role in segmentation and detection tasks.     

Influence of polarization orientation of violet light on the diffraction efficiency of bacteriorhodopsin

When a grating is recorded in a bacteriorhodopsin film by two linear parallel polarized beams together with an auxiliary violet light, the diffraction efficiency has a dependence on the polarization orientation of the violet light as well as its intensity. A method for calculating the diffraction efficiency of gratings in bacteriorhodopsin is proposed based on the two-state photochromic model, considering the saturation effect and the polarization status of all the involved lights. It is found that the polarization orientation of the violet light produces an approximate-cosine and an approximate-sine modulation on the steady-state diffraction efficiency separately at low and high intensities, respectively. The parallel polarized violet light can improve the steady-state diffraction efficiency to a larger degree than the perpendicularly polarized violet light when both are at their optimal intensities. The optimal intensity for the parallel polarized violet light is lower than that of the perpendicular polarized one. Thus, the improvement of the steady-state diffraction efficiency is less sensitive to the intensity of perpendicular polarized violet light than to that of parallel polarized violet light.     

Polarization changes at Lyot depolarizer output for different types of input beams

Lyot depolarizers are optical devices made of birefringent materials used for producing unpolarized beams from totally polarized incident light. The depolarization is produced for polychromatic input beams due to the different phase introduced by the Lyot depolarizer for each wavelength. The effect of this device on other types of incident fields is investigated. In particular two cases are analyzed: (i) monochromatic and nonuniformly polarized incident beams and (ii) incident light synthesized by superposition of two monochromatic orthogonally polarized beams with different wavelengths. In the last case, it is theoretically and experimentally shown that the Lyot depolarizer increases the degree of polarization instead of depolarizes.     

Invariant polarimetric contrast parameters of coherent light

Many applications use an active coherent illumination and analyze the variation of the polarization state of optical signals. However, as a result of the use of coherent light, these signals are generally strongly perturbed with speckle noise. This is the case, for example, for active polarimetric imaging systems that are useful for enhancing contrast between different elements in a scene. We propose a rigorous definition of the minimal set of parameters that characterize the difference between two coherent and partially polarized states. Indeed, two states of partially polarized light are a priori defined by eight parameters, for example, their two Stokes vectors. We demonstrate that the processing performance for such signal processing tasks as detection, localization, or segmentation of spatial or temporal polarization variations is uniquely determined by two scalar functions of these eight parameters. These two scalar functions are the invariant parameters that define the polarimetric contrast between two polarized states of coherent light. Different polarization configurations with the same invariant contrast parameters will necessarily lead to the same performance for a given task, which is a desirable quality for a rigorous contrast measure. The definition of these polarimetric contrast parameters simplifies the analysis and the specification of processing techniques for coherent polarimetric signals.     

Invariant polarimetric contrast parameters of light with Gaussian fluctuations in three dimensions

We propose a rigorous definition of the minimal set of parameters that characterize the difference between two partially polarized states of light whose electric fields vary in three dimensions with Gaussian fluctuations. Although two such states are a priori defined by eighteen parameters, we demonstrate that the performance of processing tasks such as detection, localization, or segmentation of spatial or temporal polarization variations is uniquely determined by three scalar functions of these parameters. These functions define a "polarimetric contrast" that simplifies the analysis and the specification of processing techniques on polarimetric signals and images. This result can also be used to analyze the definition of the degree of polarization of a three-dimensional state of light with Gaussian fluctuations in comparison, with respect to its polarimetric contrast parameters, with a totally depolarized light. We show that these contrast parameters are a simple function of the degrees of polarization previously proposed by Barakat [Opt. Acta 30, 1171 (1983)] and Set?l? et al. [Phys. Rev. Lett. 88, 123902 (2002)]. Finally, we analyze the dimension of the set of contrast parameters in different particular situations.     

Propagation properties of partially coherent radially polarized beam in a turbulent atmosphere

Based on the Huygens–Fresnel principle and the unified theory of coherence and polarization of partially coherent beams, we investigate the propagation characteristics of a partially coherent radially polarized doughnut (PCRPD) beam in a turbulent atmosphere. It is found that, after propagating through a turbulent atmosphere, the doughnut beam spot is changed into a circular Gaussian beam. Moreover, the degree of coherence, the degree of polarization and the degree of cross-polarization of the beam will change on propagation, and this change is dependent upon the degree of coherence of the source and atmospheric turbulence.     

Radiation efficiency of partially coherent electromagnetic beams.

We present a general definition of the radiation efficiency of stationary electromagnetic fields and prove that it is bounded between zero and unity for beams of any state of coherence and polarization. The radiation efficiency may be interpreted as a measure of how directed the radiated fields are, and therefore it can be used to assess the allowed spatial coherence and intensity variations across a beam. We consider a class of partially coherent electromagnetic fields that were recently introduced in the literature and evaluate the radiation efficiencies for two particular examples, namely, the azimuthally polarized symmetric beams and the dipolar beams that are nearly linearly polarized in the central region. The results show that the radiation efficiency is fairly insensitive to the state of polarization and that it differs appreciably from unity for only small values of source and correlation widths.     

Optical heterodyne detection of random electromagnetic beams

Abstract

In this paper we present a general analysis for the optical heterodyne detection of random electromagnetic beams. To describe the ensemble of quasimonochromatic beams which are partially polarized and partially coherent, we use a recently developed matrix treatment. We derive an expression for the signal-to-noise ratio (SNR) in terms of the beam coherence polarization matrices of the beams on the detector surface. Numerical examples are given for the SNR variation in the case of partially polarized Gaussian Schell model beams and the optimum detection is discussed in terms of beam parameters of the local oscillator.     

Polarization properties of inversely twisted nematic liquid-crystal gratings

Based on the Jones matrix representation of twisted nematic liquid crystals (LC's), we have carried out a theoretical analysis of the polarization properties of inversely twisted nematic (ITN) LC gratings. Some interesting polarization behaviors are expected in the ITN LC grating. When a linearly polarized light parallel or perpendicular to the grating direction is incident on the ITN LC grating, the diffracted light in the 0th order is linearly polarized with the same polarization direction of incident light, while the diffracted light in high orders is linearly polarized perpendicular to that of incident light. Using a multirubbing alignment technique, we have practically prepared an ITN LC grating with ?45 degrees inversely twisted structures. The experimental investigations of the optical characteristics of the ITN LC grating demonstrate agreement with theoretical expectations.     

Polarization-sensitive speckle spectroscopy of scattering media beyond the diffusion limit

A scattering-media-characterization method that uses partially coherent radiation and polarization discrimination of multiply scattered light is described. The method is based on an analysis of the dependence of speckle contrast on the coherence length of the probe light. Polarization discrimination of detected speckles makes it possible to select scattered-light components that propagate in the probed medium at different distances. A theoretical analysis of the polarization-dependent speckle contrast as influenced by the probe-light coherence and parameters of the probed medium is presented. Experimental results obtained with various nondiffuse scattering samples are presented.     

A three-dimensional degree of polarization based on Rayleigh scattering

A measure of the degree of polarization for the three-dimensional polarization matrix (coherence matrix) of an electromagnetic field is proposed, based on Rayleigh scattering. The degree of polarization at a point is defined as an average, over all scattering directions, of an imagined dipole scattering of the three-dimensional state of polarization. This gives a well-defined purity measure, which, unlike other proposed measures of the three-dimensional degree of polarization, is not a unitary invariant of the matrix. This is demonstrated and discussed for several examples, including a partially polarized transverse beam.     

Optical Transmission in Polycrystals

Optical transmission in a polycrystalline aggregate consisting of randomly oriented anisotropic transparent crystals has been worked using Mueller matrices. The interesting results are: (1) A completely polarized beam of light emerges as partially polarized light. (2) The completely polarized part of the emergent beam is in the same state of polarization as the incident light for optically inactive crystallites. (3) The intensity of the completely polarized part not only depends on the optical and the geometrical parameters of the crystallite but also on the polarization state of the incident light. (4) For optically active crystallites the medium behaves as an isotropic optically active solid with a rotatory power equal to the mean rotatory power of the single crystal. This helps one in extracting most of the gyration tensor components in enantiomorphic optically active crystals.     

Light scattering by an infinite circular cylinder immersed in an absorbing medium

Analytic solutions are developed for the single-scattering properties of an infinite dielectric cylinder embedded in an absorbing medium with normal incidence, which include extinction, scattering and absorption efficiencies, the scattering phase function, and the asymmetry factor. The extinction and scattering efficiencies are derived by the near-field solutions at the surface of the particle. The normalized scattering phase function is obtained by use of the far-field approximation. Computational results show that, although the absorbing medium significantly reduces the scattering efficiency, it has little effect on absorption efficiency. The absorbing medium can significantly change the conventional phase function. The absorbing medium also strongly affects the polarization of the scattered light. However, for large absorbing particles the degrees of polarization change little with the medium's absorption. This implies that, if the transmitting lights are strongly weakened inside the particle, the scattered polarized lights can be used to identify objects even when the absorption property of the host medium is unknown, which is important for both active and passive remote sensing.     

Imaging objects hidden in scattering media with fluorescence polarization preservation of contrast agents

A method for fluorescence polarization difference imaging is demonstrated for enhancing the image quality of a luminous object embedded in a random medium. The polarization preservation of light propagating in the scattering medium leads to partially polarized light emission by a contrast-agent dye located inside the object. Subtraction of the images of the luminous object detected at two orthogonal polarization directions improves the image resolution compared with a conventional optical imaging approach.     

Deformed chiral-nematic networks obtained by polarized excitation of a dichroic photoinitiator

Photo-initiated polymerization of chiral-nematic monomers leads to helicoidal networks with well-defined and stable reflection bands. Exposure of the monomer mixtures to polarized UV light in the presence of a dichroic photoinitiator causes photo-induced diffusion simultaneously with the polymerization process. The diffusion is on a length scale equal to half of the cholesteric pitch and deforms the chiral-nematic helix. The films that are produced exhibit extraordinary optical properties such as in-plane birefringence, polarization conversion and polarization dependent higher order reflections. When combined with photo-induced diffusion on the length scale of the film thickness, wideband polarizing reflectors are obtained that transmit linearly polarized light rather than circularly polarized light as is the case for conventional chiral-nematic networks.