Linear dichroism of the cornea

The dichroic properties of in vitro sheep corneas were studied with a spectrophotometer in transmission mode for several angles of incidence of light beams. Several models of corneal anisotropy have been presented in the literature. The results presented here allow us to believe that the cornea behaves as a dichroic biaxial crystal. Furthermore, this dichroism is weak when the angle of incidence on the corneal surface stays small. The mathematical model that describes these optical properties of the cornea uses Mueller matrices.     

Conditions for the Physical Realizability of Polarization Matrices Characterizing Passive Systems

Abstract

We derive conditions for the physical realizability of polarization matrices characterizing passive systems or scattering media. By physically realizable, we mean that 0  g  1 where g ≡ (output intensity/input intensity). Using the singular-value decomposition of an arbitrary 2 × 2 complex-valued matrix, we prove that a Jones matrix T _J is physically realizable if 0  det T _J ⁺ T _J  1. Consequently singular Jones matrices (i.e. det T _J = 0) completely extinguish the output intensity irrespective of the input intensity because g ≡ 0. Corresponding results are obtained for Mueller-Jones matrices (the 4 × 4 real-valued matrices which are the four-dimensional representations of the two-dimensional 2 × 2 complex-valued Jones matrices). We also study the problem for general Mueller matrices; however because of their phenomenological character they do not admit of such criteria as do the Jones and Mueller-Jones matrices. This is because g now depends upon the matrix elements of the Mueller matrix and the input Stokes parameters; whereas for the Jones and Mueller-Jones matrices, g only depends upon the matrix elements. Finally we study the problem of relating the input and output mean randomness.     

Conditions for polarization elements to be dichroic and birefringent

The polarization of light when it passes through optical media can change as a result of change in the amplitude (dichroism) or phase shift (birefringence) of the electric vector. The anisotropic properties of media can be determined from these two optical features. We derive the conditions required for polarization elements to be dichroic and birefringent. Our derivation starts from commonly accepted assumptions for dichroism and birefringence. Our main conclusions are that (i) the generalized Jones matrix for dichroic elements has in general nonorthogonal eigenpolarizations and (ii) in the general case, the birefringent and dichroic properties of polarization elements have no direct association with the corresponding phase and dichroic polar forms derived in the polar decomposition of the polarization elements' Jones matrices.     

On the Gain of a Passive Linear Depolarizing System

Abstract

Transformation of a partially polarized light by a passive linear optical system must satisfy certain physical realizability constraints imposed on the elements of the Jones operator (matrix) characterizing the system. In this note we extend earlier work by Jones, Barakat, and Azzam and Bashara and derive a set of conditions on the elements of the Jones operator which depend explicitly on the input light degree of polarization. This is accomplished by a simple and novel approach based on the Cauchy-Schwartz—Bunyakowski inequality for coherency matrices.     

Linear dichroism of the retinal nerve fiber layer expressed with Mueller matrices

An electro-optic device is used that permits the measurement of polarized absorption spectra (linear dichroism). The change of the polarization state of a light beam brought about by passage through the optic elements of a dichrograph are described mathematically by a transformation of the Stokes vector. The polarization or absorption properties of the optical elements are described by the Mueller matrices. The dichroic properties of sheep retina and cornea are studied in vitro.     

Phase calculation for image rotation in a nonplanar polarization nulling interferometer

We propose a new matrix method for calculating geometric image rotation, taking into account the effects of the geometric and dynamic phases in a nonplanar optical layout. In order to describe the propagation of light in this system, the algebra of two-dimensional Jones polarization vectors and matrices in two-dimensional space is extended to three-dimensional space. We give practical examples of nonplanar layouts of polarization nulling interferometers for application in astronomy and precision wavefront analysis.     

Polarization properties of corner-cube retroreflectors: theory and experiment

Polarization properties of the corner-cube retroreflector are discussed theoretically by use of ray tracing and analytical geometry. The Jones matrices and eigenpolarizations of the six propagation trips of the corner-cube retroreflector are derived. An experiment is also set up for the determination of the linear eigenpolarizations and the output states of polarization for incident linearly polarized light. The experimental results are consistent with theoretical expectations.     

Thermally induced birefringence in Nd:YAG slab lasers

We study thermally induced birefringence in crystalline Nd:YAG zigzag slab lasers and the associated depolarization losses. The optimum crystallographic orientation of the zigzag slab within the Nd:YAG boule and photoelastic effects in crystalline Nd:YAG slabs are briefly discussed. The depolarization is evaluated using the temperature and stress distributions, calculated using a finite element model, for realistically pumped and cooled slabs of finite dimensions. Jones matrices are then used to calculate the depolarization of the zigzag laser mode. We compare the predictions with measurements of depolarization, and suggest useful criteria for the design of the gain media for such lasers.     

Jones-matrix analysis with Pauli matrices: application to ellipsometry

The coherency matrix formalism based on Pauli matrices is applied to analyze a general ellipsometer that is described by Jones matrices. Here the Jones matrices are represented as sums of appropriate coefficients times the Pauli matrices and the identity matrix, and intensities are represented as traces of coherency matrices. This approach allows us not only to treat partial polarizations explicitly but also to take advantage of various identities to reduce to algebra the operations necessary for system analysis. A general expression is obtained for the intensity transmitted through a polarizer-sample-compensator-analyzer (PSCA) ellipsometer. This general expression is applied to an ideal PSCA ellipsometer, and then the results are reduced to describe several simpler but commonly used configurations. The results provide insight regarding general capabilities and limitations and allow us to compare different ellipsometer systems directly. Finally, this expression is extended to include artifacts, the explicit representation of which allows a complete determination of their defects.     

Method of error analysis for phase-measuring algorithms applied to photoelasticity

We present a method of error analysis that can be applied for phase-measuring algorithms applied to photoelasticity. We calculate the contributions to the measurement error of the different elements of a circular polariscope as perturbations of the Jones matrices associated with each element. The Jones matrix of the real polariscope can then be calculated as a sum of the nominal matrix and a series of contributions that depend on the errors associated with each element separately. We apply this method to the analysis of phase-measuring algorithms for the determination of isoclinics and isochromatics, including comparisons with real measurements.     

Operator expansions for polarization mode dispersion analysis and compensation

We present analytic third- and fourth-order expansions of the Jones matrix as products of exponentials of individual matrices. In our first formalism, these are polarization mode dispersion (PMD) matrices of definite orders. We then discuss an alternative procedure that instead employs exponentials of general skew-Hermitian matrices with a low-order dependence on the deviation of the optical frequency from a central reference frequency. Our expressions correspond to PMD compensators formed from a succession of relatively simple optical components each of which has the frequency response of a single operator in the product.     

Investigation of the polarization optics of the living human cornea and lens with purkinje images

We present what to our knowledge is a new method for assessing the polarization optics of the cornea and lens, by examining the state of polarization of the first, second, and fourth Purkinje images. When linearly polarized light is incident on the cornea at 70 degrees to the line of gaze along the horizontal meridian, and then traverses the cornea, or the cornea and the lens, the emergent light is elliptically polarized. The degree of ellipticity varies widely between subjects. The results indicate that both the cornea and the lens may be optically active and to our knowledge are the first to suggest that the cornea may exhibit circular birefringence.     

Transmitted and reflected scattering matrices from an English oak leaf

The complete Mueller matrix for an English oak (Quercus robur) leaf for a fixed azimuth angle (90 degrees) was determined immediately after plucking and a day following exposure to normal room temperature and pressures. The Mueller matrices were determined for transmitted light at observation angles ranging from 0 degrees to 24 degrees and for reflected backscattering angles from 153 degrees to 170 degrees. All the measurements were taken with a He-Ne laser light source at 0.63 microm. Since positive eigenvalues were obtained for the coherence matrix, the polarimetric measurements were physically realizable. The anisotropy parameters were determined from the Jones matrices by use of the decomposition theorem. From the M33 and M44 components of the Mueller matrices, it was found that nonspherical structures within the leaf were primarily responsible for observed transmitted light scatter, and spherical structures were mostly responsible for observed backscatter. Variations in backscatter Mueller matrix elements from a fresh leaf to a second day of observation were assumed because of changes to water vapor concentration in the leaf.     

Scattering matrices for large ice crystal particles

The problem of light scattering by ice crystal particles whose sizes are essentially larger than the incident wavelength is divided into two parts. First, the scattered field is represented as a set of plane-parallel outgoing beams in the near zone of the particle. Then, in the far zone the scattered field is represented as a result of both diffraction and interference of these beams within the framework of physical optics. A proper ray-tracing algorithm for calculation of the amplitude (Jones) scattering matrix is developed and applied. For large particles, a number of reduced Mueller matrices are introduced and discussed, since the pure Mueller matrix obtained from the Jones matrix becomes a rather cumbersome and quickly oscillating value. Backscattering by hexagonal ice crystals, including polarization properties, is considered in detail.     

Color modulation properties of a liquid-crystal device

The color modulation properties of a twisted-nematic liquid-crystal device are studied based on the Jones calculus. The usefulness of Jones calculus is demonstrated for the blue mode of a supertwisted birefringent liquid-crystal device, after which some experimental results of the color modulation effect for a twisted-nematic liquid-crystal television are presented. We investigated the color dependence of the transmitted light on the applied voltage by using a chromaticity diagram. Most of the experimental results are well explained by the theory derived from the Jones calculus.     

Spectral analysis of the device operators in polarization dynamics

Abstract

The spectral analysis of the device (instrument) operators, as an alternative approach to the dynamical polarization phenomena, is presented by means of an example of a classical time-varying optical device, the electrooptical modulator with longitudinal effect in crystals of KDP type. The polarization-spectral structure of the modulated light is analysed on this basis, both in terms of spectral Jones vectors and of spectral polarization matrices. Some experimental results are presented.     

Simple expressions for transmission and reflection matrix elements of a biaxial thin layer at normal incidence

The extended Jones matrix method is applied for determination of the transmission and reflection matrices for a normally incident plane wave upon an homogeneous and lossless biaxial thin layer. The elements of these matrices are expressed by simple analytical relations. By using these relations one can express analytically the polarization-dependent optical parameters to be determined by generalized ellipsometry.     

Modeling of scattering and depolarizing electro-optic devices. I. Characterization of lanthanum-modified lead zirconate titanate

We describe a new method of modeling electro-optic (EO) devices, such as lanthanum-modified lead zirconate titanate polarization modulators, that resolves two deficiencies of current methods: (i) the inclusion of depolarization effects resulting from scattering and (ii) saturation of the EO response at strong electric-field strengths. Our approach to modeling depolarization is based on describing the transmitted optical field by superposition of a deterministic polarized wave and a scattered, randomly polarized, stochastic wave. Corresponding Jones matrices are used to derive a Mueller matrix to describe the wave propagation in scattering and depolarizing EO media accurately. A few simple optical measurements can be used to find the nonlinear behavior of the EO phase function, which is shown to describe accurately the material's EO behavior for weak and strong applied electric fields.