Mueller matrix of dense polystyrene latex sphere suspensions: measurements and Monte Carlo simulation.

Mueller matrices of dense aqueous suspensions of different concentrations are measured with a phase-modulated Mueller ellipsometer as a function of the scattering angle. Different concentrations of a solution containing 404-nm-diameter polystyrene latex spheres dispersed in water were prepared. Experimental results are compared with a three-dimensional Monte Carlo simulation of the propagation of photons with the cell geometry accounted for. The Fresnel laws and the Mie theory determine the changes in direction and polarization during the propagation of the photon. Excellent agreement over the whole angular range is found between experimental and simulated Mueller matrices.

Phase-modulated mueller ellipsometry characterization of scattering by latex sphere suspensions.

Phase-modulated Mueller ellipsometry (PMME) is used to probe scattering by suspensions of polystyrene latex spheres, with particle diameters ranging from 400 nm to 3 microm. PMME allows simultaneous measurement of the 16 coefficients of the Mueller matrix. Furthermore PMME measurements can easily be carried out owing to a calibration procedure implemented in a scattering configuration. The measurements performed on low concentrations show good agreement with Mie theory. Moreover size distribution could be obtained with a least-squares method based on a genetic fit algorithm. Experimental evidence of multiple scattering on PMME measurements is also presented.

General and self-consistent method for the calibration of polarization modulators, polarimeters, and mueller-matrix ellipsometers.

Calibration of polarization-state generators (PSG's), polarimeters, and Mueller-matrix ellipsometers (MME's) is an important factor in the practical use of these instruments. A new general procedure, the eigenvalue calibration method (ECM), is presented. It can calibrate any complete MME consisting of a PSG and a polarimeter that generate and measure, respectively, all the states of polarization of light. In the ECM, the PSG and the polarimeter are described by two 4 x 4 matrices W and A, and their 32 coefficients are determined from three or four measurements performed on reference samples. Those references are smooth isotropic samples and perfect linear polarizers. Their optical characteristics are unambiguously determined during the calibration from the eigenvalues of the measured matrices. The ECM does not require accurate alignment of the various optical elements and does not involve any first-order approximation. The ECM also displays an efficient error control capability that can be used to improve the MME behavior. The ECM is illustrated by an experimental calibration, at two wavelengths (458 and 633 nm), of a MME consisting of a coupled phase modulator associated with a prism division-of-amplitude polarimeter.

Spectroellipsometric method for process monitoring semiconductor thin films and interfaces.

Real-time monitoring by multiwavelength phase-modulated ellipsometry of the growth of plasma-deposited microcrystalline silicon (muc-Si) is presented. We discuss the construction of a growth model for process monitoring, and, in particular, we treat the inhomogeneity in the muc-Si layer by using an approximation of the reflection coefficient known as the WKBJ method. By also using the Bruggeman effective medium theory to describe the optical properties of muc-Si, we demonstrate monitoring the crystallinity in the upper and the lower part of the layer together with the thickness. The inversion algorithms thus remain very fast, with calculation times within 5 s on a standard Pentium computer. This makes possible precise control of the thickness and the crystallization of both the top and the bottom interface of the layer during the elaboration of devices such as solar cells and thin-film transistors.

Broadband Division-of-Amplitude Polarimeter Based on Uncoated Prisms.

A broadband division-of-amplitude polarimeter (DOAP) is presented. It can provide the real-time measurement of any state of polarization of light, described by its Stokes vector, in large spectral windows. The light is split first into two beams by a prism and then into four beams by means of any polarizer device that will separate the two linear orthogonal states of polarization. Finally, the Stokes vector is directly deduced from the four measured intensities. To avoid interference effects, the splitting of light into four beams is induced only by refractive-index contrast effects between semi-infinite media that are weakly dependent on the wavelength. An experimental setup working from 0.4 to 2 mum is described. It provides similar sensitivities for all the states of polarization, and its characteristics are constant, on a scale of a few percent, within the spectral window. Calibrations performed at 458 and 633 nm display good agreement between theoretical and experimental values. The accuracy of the prism DOAP, evaluated by measurement of the Stokes vector produced by a rotating Glan polarizer, is better than 1%. An infrared extension of this polarimeter is also presented.

Real-time control by multiwavelength ellipsometry of plasma-deposited multilayers on glass by use of an incoherent-reflection model.

Real-time control by multiwavelength phase-modulated ellipsometry (PME) of the growth of multilayer structures deposited on transparent glass is presented. The structures consist of plasma-deposited SiO(2) and SiN(x) stacks. A model that takes into account incoherent reflection in the substrate is described and tested. A generalized feedback control method that incorporates the incoherent modeling of the transparent substrate is further applied to the growth of a Fabry-Perot and a standard quarter-wave filter. The resulting optical coatings characterized by spectroscopic PME and transmission measurements show a reproducible precision, with less than 1% error between target and measured spectral responses.