Decomposition of Jones and Mueller matrices in terms of four basic polarization responses.

A simple new method is introduced to analyze the polarization of light by media. This method decomposes a Jones matrix into a linear combination of four basic matrices that represent different polarization responses. The Mueller matrix expressed in terms of the response coefficients of the basic matrices demonstrates a highly symmetric form that spells out the physical origins of each matrix element. Randomness in the response coefficients gives rise to depolarization that appears only in the diagonal elements of a Mueller matrix. The decomposition of a Mueller matrix gives both the depolarization and polarization characteristics relating directly to the anisotropic optical properties.

Optical scattering depolarization in a biomedium with anisotropic biomolecules.

The depolarization property of a biomedium with anisotropic biomolecule optical scattering is investigated theoretically. By using a simple ellipsoid model of a single biomolecule, the scattering fields and Mueller matrices are derived from fundamental electromagnetism theory. The biomedium is modeled as a system of uncorrelated anisotropic molecules. On the basis of a statistical model of anisotropic molecular distribution, the scattering depolarization of the biomedium is investigated. Simulated results of the molecular shape and orientation dependent single scattering depolarization D(1) and the double scattering depolarization D(2) are reported. The D(2) contribution is found to be more important for higher-density scattering media. The depolarizations of the forward single and double scattering of a model cell membrane are simulated and discussed. The fitting to a single tetra-methylrhodamine-labeled lipid molecule's anisotropic imaging experiment has demonstrated that large depolarization arises for the membrane to which the fluorescence emitting molecule is attached. This theory can provide a simulation analysis tool for investigating the scattering polarization/depolarization effect and the photon density wave transport property of a highly scattering biomedium.

Degrees of polarization and coherence of paired linear polarized laser beam by scattering glass plates measured using optical coherent ellipsometer.

An accurate optical coherent ellipsometer (OCE) is proposed and setup in which a two-frequency paired linear polarized laser beam is integrated with a common-path heterodyne interferometer. This OCE is able to precisely measure the optical properties of scattering specimen by measuring ellipsometric parameters (Psi, Delta). In the mean time the degree of polarization P, and degree of coherence Chi of incident two-frequency linear polarized laser beam are measured too. In the experiment, both smooth and ground BK7 glass plates were tested in which the optical parameters (Psi, Delta, P, Chi ) were obtained precisely. Comparing with conventional ellipsometers, OCE can characterize scattering specimen precisely and excludes the scattering effect.

Scattering polarization by anisotropic biomolecules.

The full polarization properties of anisotropic biomolecule optical scattering are investigated theoretically. By using a simple ellipsoid model of a single biomolecule, the scattering fields and Mueller matrices are derived from fundamental electromagnetism theory. The energy of scattered photons is not necessarily equal to that of the incident laser beam. This theory can be generally applied to the experiments of fluorescence, Raman scattering, and second-harmonic generation. Fitting of a single tetramethylrhodamine-labeled lipid molecule's anisotropic imaging experiment is demonstrated. This theory has provided a fundamental simulation analysis tool of understanding and developing the optical polarimetric sensing science and technology of the anisotropic biomolecules and biomedium. The medium dielectric constant of the model ellipsoid provides a theoretic background for correlating the optical polarization properties of a biomolecule to its microscopic electronic structure.

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.

Polarization of transmission scattering simulated by using a multiple-facets model.

A Mueller matrix for scattering by a rough plane surface of a glass hemisphere was simulated by using a micro-facet model. The algorithms are formulated in vector representation in terms of the input and output directions. The single-facet scattering simulation used the results of the Kirchhoff integral for medium rough surfaces with exponential height distribution. Scatterings by two or more facets were also simulated. For a fixed angle between the incident and the detection directions, the transmission scattering and its polarization properties were symmetric when plotted against the off-specular incident angle. The single-facet model generated no depolarization or polarization change. When double-facet scattering was included, polarizations were changed appreciably while depolarization was still very small. Depolarization increased appreciably when scattering by higher orders was included. The simulated results that include all orders of scattering fit excellently to the measured scattering transmittance and its polarization and depolarization.

Polarization of holographic grating diffraction. I. General theory.

The full polarization property of volume holographic grating diffraction is investigated theoretically. With a simple volume grating model, the diffracted fields and Mueller matrices are first derived from Maxwell's equations by using the Green's function algorithms. The formalism is derived for the general case that the diffraction beam and the grating wave vector are not in the plane of incidence, where s waves and p waves are not decoupled. The derived photon-momentum relations determine the Bragg angle selectivity. The parameters of diffraction strength related to the hologram-writing process and material are defined and are not necessarily small in general. The diffracted-beam profiles are analytically calculated by using the known grating shape function. This theory has provided a fundamental understanding of the polarization phenomena of a real holographic diffraction grating device. The derived algorithm would provide a simulation-analysis tool for the engineering design of real holographic beam combiner/splitter devices.

Polarization of holographic grating diffraction. II. Experiment.

The transmittance, ellipsometric parameters, and depolarization of transmission, diffraction, and reflection of two volume holographic gratings (VHGs) are measured at a wavelength of 632.8 nm. The measured data are in good agreement with the theoretical simulated results, which demonstrated the correlation between the diffraction strength and the polarization properties of a VHG. Vector electromagnetic theory and polarization characterization are necessary for complete interpretation of the diffraction property of a VHG. The diffraction efficiency is measured at 532 nm in a polarization-sensing experiment. The measured data and theoretical simulation have demonstrated the potential application of the holographic beam splitter for polarization-sensor technology.

Ultrafast holographic Stokesmeter for polarization imaging in real time.

We propose an ultrafast holographic Stokesmeter using a volume holographic substrate with two sets of two orthogonal gratings to identify all four Stokes parameters of the input beam. We derive the Mueller matrix of the proposed architecture and determine the constraints necessary for reconstructing the complete Stokes vector. The speed of this device is determined primarily by the channel spectral bandwidth (typically 100 GHz), corresponding to a few picoseconds.

Error analysis for Mueller matrix measurement.

The linear errors of Mueller matrix measurements are formulated for misalignment, depolarization, and incorrect retardation of the polarimetric components. The measured errors of a Mueller matrix depend not only on the imperfections of the measuring system but also on the Mueller matrix itself. The error matrices for different polarimetric systems are derived and also evaluated for the straight-through case. The error matrix for a polarizer-sample-analyzer system is much simpler than those for more complicated systems. The general error matrix is applied to null ellipsometry, and the obtained errors in ellipsometric parameters psi and delta are identical to the errors specifically derived for null ellipsometry with depolarization.