Stokes-parameter analysis of the polarization of light transmitted through a chiral nematic liquid-crystal cell

A spectroscopic Stokes polarimeter is used to directly measure the linearly, circularly, and randomly polarized components of light obtained on transmission of unpolarized light through thick chiral nematic liquid-crystal cells in the stop band. The Stokes parameters are simulated to fit the experimental data by use of the Berreman 4 x 4 transfer matrix by means of the Jones and Stokes vectors and taking into account multiple reflections at the interfaces of the cell. Excellent agreement is obtained. The transmitted light through a commercial cell is mainly circularly polarized at normal incidence, but a significant linearly polarized component is also observed. The model shows that this results from refractive-index mismatching at the liquid-crystal-alignment-layer interface, but a small linearly polarized component remains even with optimized index matching. An improved device configuration incorporating random defects at the exit boundary of the liquid crystal gives a highly circularly polarized output with virtually no linear or unpolarized components.     

Estimation of the degree of polarization of coherent light in the presence of uniform and nonuniform illumination

We address estimation of the degree of polarization (DOP) in active images acquired under coherent light when the coherency matrix of the backscattered light is diagonal. We consider cases when the illumination intensity is uniform on the scene and when it is not, and we take into account different parametrizations of the DOP. In all cases, we determine the maximum-likelihood (ML) estimators and compare their variances with the Cramer-Rao lower bound for unbiased estimation. When illumination is not uniform, the ML estimators are solutions of equations that have to be solved numerically. We show that simpler estimators based on the trimmed mean make it possible to approach performance of ML estimators at lower computational cost.     

Theoretical analysis of polarization patterns from incoherent backscattering of light

Anisotropy in the polarization of the backscattered light from a polarized laser beam incident upon a scattering medium has been observed experimentally. When the beam is viewed through an oriented polarizer, characteristic patterns in the backscattered light are observed. We present here a simple explanation of these patterns, using the theory of incoherent scattering of light by spheres. It appears that the major contribution to the observed patterns comes from the double scattering of light.     

Depolarization index and the average degree of polarization

Two single number metrics for depolarization of samples are contrasted: (1) the average degree of polarization of the exiting light averaged over the Poincaré sphere and (2) the depolarization index of Gill and Berbenau [Opt. Acta 32, 259-261 (1985); 33, 185-189 (1986)1. The depolarization index is a geometric measure that varies from 0 for the ideal depolarizer to 1 for nondepolarizing Mueller matrices. The average degree of polarization also varies from 0 to 1 and characterizes the typical level of depolarization. Although the depolarization index is very often close to the average degree of polarization, these two metrics can differ by more than 0.5 for certain Mueller matrices.     

Scattering-induced changes in the degree of polarization of a stochastic electromagnetic plane-wave pulse

The scattering of a stochastic electromagnetic plane-wave pulse on a deterministic spherical medium is investigated. An analytical formula for the degree of polarization (DOP) of the scattered field in the far zone is derived. Letting pulse duration T(0) → ∞, our formula can be applied to study the scattering of a stationary stochastic electromagnetic light wave. Numerical results show that the DOP of the far zone field is closely determined by the size of the spherical medium when the incident field is a stochastic electromagnetic plane-wave pulse. This is much different from the case when the incident field is a stationary stochastic electromagnetic light wave, where the DOP of the far zone field is independent of the size of the medium. One may obtain the information of the spherical medium by measuring the scattering-induced changes in the DOP of a stochastic electromagnetic plane-wave pulse.     

Precision of moment-based estimation of the degree of polarization in coherent imagery without polarization device

We propose and analyze a statistical method to estimate the degree of polarization of light from a single speckle intensity image by analyzing the statistical distribution of the light intensity. The optimal precision of such an estimation method is evaluated by computing the Cramer-Rao bounds for several speckle degrees. Two moment-based estimators of the square degree of polarization are introduced and characterized. For the first time to our knowledge, it is shown theoretically and through simulations that the estimators are almost efficient for high orders of speckle. The robustness of the method is discussed for the case when the intensity fluctuations do not follow the standard speckle model.     

Soft-x-ray polarimeter with multilayer optics: complete analysis of the polarization state of light

The design of a versatile high-precision eight-axis ultrahigh-vacuum-compatible polarimeter is presented. This multipurpose instrument can be used as a self-calibrating polarization detector for linearly and circularly polarized UV and soft-x-ray light. It can also be used for the characterization of reflection or transmission properties (reflectometer) or polarizing and phase-retarding properties (ellipsometer) of any optical element. The polarization properties of Mo/Si, Cr/C, Cr/Sc, and Ni/Ti multilayers used in this polarimeter as polarizers in transmission and as analyzers in reflection have been investigated theoretically and experimentally. In the soft-x-ray range, close to the p edges of Sc, Ti, and Cr, resonantly enhanced phase retardation of the transmission polarizers of as much as 18 degrees has been measured. With these newly developed optical elements the complete polarization analysis of soft-x-ray synchrotron radiation can be extended to the water-window range from 300 to 600 eV.     

A device for the light polarization selection

The properties of defect modes in chiral photonic crystals with anisotropic defects are considered, and changes in these properties caused by variations of the position of a defect layer in the system are analyzed. It is shown that, for certain thicknesses of a defect layer, a change in its position leads to a change in the ellipticity of the transmitted (reflected) light. This phenomenon can be used to create a device capable of selecting the polarization of light by changing the position of a defect layer. Such a device can also operate as a light modulator, a purely optical diode, or a bidirectional asymmetric switch. In a certain wavelength range, this light polarization selector can produce controlled rotation of the polarization plane.     

Geometric approach to the degree of polarization for arbitrary fields

Abstract

The eigenvalue decomposition of the polarization matrix is employed to find out the geometric interpretation of the traditional degree of polarization and, in particular, of the degree of polarization for arbitrary electromagnetic fields put forward recently by Setälä et al. [2002, Phys. Rev. Lett., 88, 123902]. It is shown that both measures have similar geometric meaning as a measure for the purity of the polarization state. Possible extensions to the analysis are discussed.     

Coherent quantum measurement for the direct determination of the degree of polarization and polarization mode dispersion compensation

Abstract

An example of a coherent measurement for the direct evaluation of the degree of polarization of a single-mode optical beam is presented. It is applied to the case of great practical importance where depolarization is caused by polarization mode dispersion. It is demonstrated that coherent measurement has the potential of significantly increasing the information gain, compared to standard incoherent measurements.     

Strain mapping by measurement of the degree of polarization of photoluminescence

A technique is described for the simultaneous measurement of the difference in the normal components of strain and of the shear strain in luminescent III-V material from the degree of polarization (DOP) of photoluminescence. This technique for the measurement of shear strain and of the difference in the normal components of strain in InP was calibrated by applying known external loads on the bars of InP with V grooves etched into the bars and by fitting the experimental results to two-dimensional finite-element simulations. Fits to the difference in the normal components of strain (as opposed to stress) yielded significantly smaller residues. On this basis we conclude that the DOP of luminescence is proportional to the difference in the normal components of strain.     

Two-dimensional polarization encoding with a phase-only liquid-crystal spatial light modulator

We show how to two dimensionally encode the polarization state of an incident light beam using a parallel-aligned liquid-crystal spatial light modulator (LCSLM). Each pixel of the LCSLM acts as a voltage-controlled wave plate and can be programmed over a 2pi phase range at a wavelength of 514.5 nm. Techniques are reviewed for either rotating the major axis of elliptically polarized light or for converting an input linearly polarized beam into an arbitrary elliptically polarized beam. Experimental results are demonstrated in which we generate various two-dimensional spatial patterns of polarized light. Several potential applications are suggested. We also report an unexpected edge-enhancement effect that might be useful in image processing applications.     

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.     

Coding and decoding in a point-to-point communication using the polarization of the light beam

A new technique for coding and decoding of optical signals through the use of polarization is described. In this technique the concept of coding is translated to polarization. In other words, coding is done in such a way that each code represents a unique polarization. This is done by implementing a binary pattern on a spatial light modulator in such a way that the reflected light has the required polarization. Decoding is done by the detection of the received beam's polarization. By linking the concept of coding to polarization we can use each of these concepts in measuring the other one, attaining some gains. In this paper the construction of a simple point-to-point communication where coding and decoding is done through polarization will be discussed.     

Three-dimensional polarization states of monochromatic light fields

The 3×1 generalized Jones vectors (GJVs) [E(x) E(y) E(z)](t) (t indicates the transpose) that describe the linear, circular, and elliptical polarization states of an arbitrary three-dimensional (3-D) monochromatic light field are determined in terms of the geometrical parameters of the 3-D vibration of the time-harmonic electric field. In three dimensions, there are as many distinct linear polarization states as there are points on the surface of a hemisphere, and the number of distinct 3-D circular polarization states equals that of all two-dimensional (2-D) polarization states on the Poincaré sphere, of which only two are circular states. The subset of 3-D polarization states that results from the superposition of three mutually orthogonal x, y, and z field components of equal amplitude is considered as a function of their relative phases. Interesting contours of equal ellipticity and equal inclination of the normal to the polarization ellipse with respect to the x axis are obtained in 2-D phase space. Finally, the 3×3 generalized Jones calculus, in which elastic scattering (e.g., by a nano-object in the near field) is characterized by the 3-D linear transformation E(s)=T E(i), is briefly introduced. In such a matrix transformation, E(i) and E(s) are the 3×1 GJVs of the incident and scattered waves and T is the 3×3 generalized Jones matrix of the scatterer at a given frequency and for given directions of incidence and scattering.     

Contour mapping of the spatiotemporal state of polarization of light

A novel interferometric polarimeter capable of mapping a spatiotemporal change in the state of polarization (SOP) of light is described. The polarimeter has a reference beam of light with two orthogonal linearly polarized components that interfere with the counterpart components of an elliptically polarized signal beam. The resultant interference pattern is recorded by a computer by the use of a wideband metal-oxide semiconductor video camera. The interference pattern reduces to the ellipticity and azimuth of the ellipse at an instant of time, by which the spatiotemporal change in the SOP is mapped. No optical elements are used for the control of polarization in the polarimeter, and this allows for the mapping of a rapid change in the SOP. Successful experiments are demonstrated by generating an elliptically polarized beam whose SOP varies in space and time.     

Limiting degree of polarization of a nonmonochromatic radiation propagating in a fiber guide with random inhomogeneities

It is shown that the mean degree of polarization of a nonmonochromatic radiation propagating in a fiber guide with random inhomogeneities tends to zero as the fiber length tends to infinity.     

Scattering and polarization of light by magnetic fluids

Expression for the intensity and the degree of polarization of light scattered by a magnetic colloid are derived. Experimental results obtained by earlier investigators are discussed on the basis of these expressions.     

Changes in the spectrum, in the spectral degree of polarization, and in the spectral degree of coherence of a partially coherent beam propagating through a gradient-index fiber

Expressions are derived for the cross-spectral density matrix of an electromagnetic Gaussian Schell-model beam propagating through a paraxial ABCD system. Using the recently developed unified theory of coherence and polarization of electromagnetic beams and the ABCD matrix for gradient-index fibers, we study the changes of the spectral density, of the spectral degree of polarization, and of the spectral degree of coherence of such a beam as it travels through the fiber. Effects of material dispersion are also considered.