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 recording of holograms in partially polarized recording light

A theoretical approach is considered for media whose scalar and anisotropic responses are of opposite sign. The nondiffracted beam, and the imaginary and real images formed by a polarization hologram are analyzed under these conditions. It is shown that the imaginary image has its polarization transformed compared with the object field while a pseudoscopic object field reconstructed in terms of polarization state and degree is formed in the real image. Pis’ma Zh. Tekh. Fiz. 23, 38–42 (February 12, 1997)     

Errors of Mueller matrix measurements with a partially polarized light source

The linear errors of Mueller matrix measurements, using a partially polarized light source, have been formulated for imperfections of misalignment, depolarization, and nonideal ellipsometric parameters of the polarimetric components. The error matrices for a source-polarizer system and a source-polarizer-compensator system are derived. A polarized light source, when used with an imperfect polarizer, generates extra errors in addition to those for an unpolarized source. The compensator redistributes these errors to different elements of the error matrix. The errors of the Mueller matrices for the polarizer-sample-analyzer and the polarizer-compensator-sample-analyzer systems are evaluated for a straight through case. This error analysis is applied to a Stokes method and an experiment was performed to show the errors by a polarized light source. This general analysis can be used to evaluate errors for ellipsometry and polarimetry.     

The application of non-parametric statistical techniques to an ALARA programme

For the cost-effective reduction of occupational radiation dose (ORD) at nuclear power plants, it is necessary to identify what are the processes of repetitive high ORD during maintenance and repair operations. To identify the processes, the point values such as mean and median are generally used, but they sometimes lead to misjudgment since they cannot show other important characteristics such as dose distributions and frequencies of radiation jobs. As an alternative, the non-parametric analysis method is proposed, which effectively identifies the processes of repetitive high ORD. As a case study, the method is applied to ORD data of maintenance and repair processes at Kori Units 3 and 4 that are pressurised water reactors with 950 MWe capacity and have been operating since 1986 and 1987 respectively, in Korea and the method is demonstrated to be an efficient way of analysing the data.     

Noninterferometric characterization of partially coherent scalar wave fields and application to scattered light

We report on the application of a simple propagation-based phase-space tomographic technique to the determination of characteristic projections through the mutual optical intensity and the generalized radiance of a scalar, quasi-monochromatic partially coherent wave field. This method is applied to the reconstruction of the coherence functions of an initially spatially coherent optical wave field that has propagated through a suspension of polystyrene microspheres. As anticipated, we see that the field separates into a ballistic, or unscattered, component and a scattered component with a much shorter coherence length. Good agreement is obtained between experimental results and the results of a model based on a wave-transport equation.     

Robust and accurate estimate of the orientation of partially polarized light from a camera sensor

Polarized light carries valuable information about where the light has been and the various physical parameters that have been acting upon it. Thus there are several methods in computer vision that make it possible to obtain information on the observed object by studying the polarization of light reflected on the object. Most studies using this principle are interested in the determination of the object orientation in three-dimensional space. The basis of these studies rests on the estimate of a parameter that connects the orientation of the observed surface and the polarization of the reflected light wave. This parameter is the angle of polarization phi, also called the orientation of polarization. Generally, one using these methods estimates the phi angle by observing the reflected light wave through a linear polarizing filter and grabbing multiple frames for different angular orientations of the polarizer. So, between each acquisition, the polarizer is rotated of an angle theta relative to a horizontal reference axis. The accuracy of the phi estimate is then directly related to the positioning of the polarizer. But, in practice, it is difficult to guarantee the exact value of the rotation of this polarizer. It is all the more difficult to guarantee the reliability of positioning in time. We thus propose a robust and accurate solution, based on the self-calibration principle, for measuring the orientation of partially polarized light using CCD cameras. In contrast to methods generally discussed in computer vision journals, our estimate of the angle of polarization is independent of the reliability of the polarizer positioning.     

Coherent-mode decomposition of partially polarized,partially coherent sources

It is shown that any partially polarized, partially coherent source can be expressed in terms of a suitable superposition of transverse coherent modes with orthogonal polarization states. Such modes are determined through the solution of a system of two coupled integral equations. An example, for which the modal decomposition is obtained in closed form in terms of fully linearly polarized Hermite Gaussian modes, is given.     

Beam-quality optimization of partially polarized fields

For light fields propagating through rotationally symmetric first-order optical systems, the possibility of improvement of the beam-propagation factor is shown to arise when the vectorial behavior is taken into account. For partially polarized beams, we find the optimized value of the beam-quality parameter that can be attained by using this kind of system. This value is given in terms of the beam qualities associated with the transverse polarization components of the vector field. On the basis of the so-called intensity-moment formalism, the general conditions that should be fulfilled at some plane to reach such an optimized value are determined. A procedure to experimentally get the optimization conditions is also proposed.     

Quality improvement of partially polarized beams

Improvement of the beam-quality parameter of partially polarized beams is investigated. We focus on the use of a Mach-Zehnder-type interferometric arrangement with crossed polarizers. The analysis has been carried out within the framework of the intensity moment formalism. Conditions are given under which the beam-quality parameter is optimized.     

Dove prisms and polarized light

Abstract

A Dove prism inverts the transmitted image and, when rotated, rotates the image at twice the rotation frequency of the prism. However, although the image is rotated, for a wide range of design parameters the polarization state of the transmitted light is not rotated. This has important implications when using Dove prisms within laser cavities, interferometers and other optical experiments.     

Anisotropic pure-phase plates for quality improvement of partially coherent,partially polarized beams

From a theoretical point of view, the use of anisotropic pure-phase plates (APP) is considered in order to improve the quality parameter of certain partially coherent, partially polarized beams. It is shown that, to optimize the beam-quality parameter, the phases of the two Cartesian components of the field at the output of the APP plate should be identical and should exhibit a quadratic dependence on the radial polar coordinate.     

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.     

Pauli algebraic analysis of polarized light modulation

The modification of the polarization and spectral structure of light by electro-optic modulation with longitudinal effect in crystals of class 42 m is analyzed in the frame of a Pauli algebraic and Poincaré geometric approach. The results are generalized, in a vectorial Pauli algebraic form, for any birefringent time-varying device.     

Propagation of polarized light through textile material

In this paper a detailed investigation, based on simulations and experiments of polarized light propagation through textile material, is presented. The fibers in textile material are generally anisotropic with axisymmetric structure. The formalism of anisotropic fiber scattering (AFS) at oblique incidence is first deduced and then, based on this formalism and considered multiscattering, a polarization-dependent Monte Carlo method is employed to simulate the propagation of polarized light in textile material. Taking cotton fiber assemblies as samples, the forward-scattering Mueller matrices are calculated theoretically through the AFS-based simulations and measured experimentally by an improved Mueller matrix polarimeter. Their variations according to sample thickness are discussed primarily. With these matrices polar-decomposed, a further discussion on the optical polarization properties of cotton fiber assemblies (i.e., depolarization Δ, diattenuation D, optical rotation ψ and linear retardance δ) versus the thickness is held. Simultaneously, a meaningful comparison of both the matrices and their polar decomposition, generated from the simulations based on isotropic fiber scattering (IFS), with those simulated based on AFS is made. Results show that the IFS-derived values are strikingly different from those that are AFS-derived due to ignoring the fiber anisotropy. Furthermore, all the AFS-derived results are perfectly consistent with those obtained experimentally, which suggests that the Monte Carlo simulation based on AFS has potential applications for light scattering and propagation in textile material.     

Observation and modeling of polarized light from scarab beetles

The light reflected from scarab beetles illuminated with unpolarized white light is analyzed ellipsometrically and displayed as the sum of an elliptically polarized spectrum I(p) and an unpolarized spectrum I(u). A chirped stack of chiral resonators, each with a characteristic Bragg wavelength and partial realignment of birefringent material to a fixed axis, is proposed as a model for simulation of both reflection and polarization spectra. Possible mechanisms that effectively eliminate impedance mismatch at the air-elytron interface and allow some beetles to exhibit nearly perfect circularly polarized reflections are discussed. Results are presented for three representative beetles, Ischiosopha bifasciata, which is shown to be a narrowband left-circular polarizer; Chrysophora chrysochlora, a broadband left-circular polarizer; and Chrysina woodi, an elliptical polarizer. The methods that are developed are applicable to the more general problem of synthesis of reflectors with prescribed reflection and polarization spectra.     

Interaction of polarized light with comb-shaped metal-coated nanostructures

We have studied metal-coated (20-nm-thick gold) periodic grating structures (period T = 350 nm) with a rectangular profile formed on the surface of a GaAs substrate. The spectra of reflection of a linearly polarized light from these gratings have been measured in a wavelength range of 600–1200 nm. A sharp (more than 20-fold) maximum in the polarization contrast has been observed at 720–760 nm. The dependence of this peak on the angle of sample rotation is approximately described by a cos⁶θ function. The formation of contrast and its features are related to the excitation of surface plasmons at the metal-air interface on vertical walls of the grating structure.     

Multipole theory for tight focusing of polarized light, including radially polarized and other special cases

A multipole expansion, based on spherical harmonics, provides an efficient method for calculating the field in the focal region of a lens for radially polarized illumination, or other illumination polarization and phase distributions, including vortex beams. The multipole approach also has the benefit of providing a simple measure of the purity of the longitudinal field mode. The method is also convenient for calculation of fields scattered by particles and calculation of optical trapping forces.     

Holographic recording and reconstruction of polarized light with dyed plastic

Recording and reconstruction of the polarization state of the object beam is achieved by using dyed red plastic as a holographic material. Holographic characteristics are presented of dyed red plastic involving beam powers ranging between 3 and 120 mW/cm2 and exposure times in the order of minutes. It is also shown that the resulting modulation becomes photostationary under continuous exposure.