Fast and optimal broad-band Stokes/Mueller polarimeter design by the use of a genetic algorithm

A fast multichannel Stokes/Mueller polarimeter with no mechanically moving parts has been designed to have close to optimal performance from 430-2000 nm by applying a genetic algorithm. Stokes (Mueller) polarimeters are characterized by their ability to analyze the full Stokes (Mueller) vector (matrix) of the incident light. This ability is characterized by the condition number, $\kappa$, which directly influences the measurement noise in polarimetric measurements. Due to the spectral dependence of the retardance in birefringent materials, it is not trivial to design a polarimeter using dispersive components. We present here both a method to do this optimization using a genetic algorithm, as well as simulation results. Our results include fast, broad-band polarimeter designs for spectrographic use, based on 2 and 3 Ferroelectric Liquid Crystals, whose material properties are taken from measured values. The results promise to reduce the measurement noise significantly over previous designs, up to a factor of 4.5 for a Mueller polarimeter, in addition to extending the spectral range.Comment: 10 pages, 6 figures, submitted to Optics Expres

Real-time Study of the Formation of GaSb Nanopillars by Spectroscopic Mueller Matrix Ellipsometry

The formation of GaSb nanopillars have been studied in real-time by spectroscopic Mueller matrix ellipsometry. Low energy ion sputtering of GaSb leads to the formation of densely packed nanopillars on the surface. A graded anisotropic effective medium model was developed to characterize the structures from ellipsometry measurements; based on ex situ ellipsometry, atomic force microscopy, scanning electron microscopy and transmission electron microscopy. This model was applied to derive the height of the nanopillars from real-time ellipsometry measurements during sputtering. The real-time observations revealed an interesting and surprising evolution of the GaSb nanostructures. The formation could be divided into three regimes; first an initial stage with removal of oxide and some delay, followed by a second regime with a rapid and steady increase of the pillar height, and finally the formation changes to a third regime with a slow and linear increase of the pillar height. The dependence of the formation on experimental conditions, such as the temperature and the flux and energy of the ion beam, was studied. It was found that the ion flux determines the timescale of the formation, while the pillar height scale and late stage formation rate was controlled by the energy and the temperature. The real-time observations of GaSb during sputtering provide new insight into why the GaSb nanopillars are formed. Traditionally the formation of patterns on GaSb during sputtering was explained by the Bradley–Harper model, where the structures are formed by a competition between curvature dependent sputtering yield and diffusion. However, this model can not explain the observation of the three different formation regimes. Instead, the real-time observations of the nanopillar formation supports the self sustained etch masking mechanism [S. Le Roy et al. Journal of Applied Physics 106 094308 (2009)]. In this explanation, the pillars are formed due to segregation of Ga and the difference in sputtering yield between Ga and Sb. GaSb nanopillars with a height of less than 100 nm were found to have uniaxial optical properties, with the optical axis parallel to the pillar axis. For larger structures, the uniaxial effective medium model was not able to represent the optical properties of the pillars. For sputtering with an ion energy of 500 eV, nanopillars with a height up to 300 nm can be formed. By real-time Mueller matrix measurements of the formation of such pillars, it was observed that the pillars had biaxially optical properties as the height surpassed 100 nm. Fourier analysis of a scanning electron microscope image of the final nanopillars showed that the lateral anisotropy can be attributed to a direction dependent nearest neighbor distance. Each individual pillar has uniaxial symmetry; the biaxial symmetry comes from the anisotropic organization of the pillars. A commercial Mueller matrix ellipsometer was applied for the real-time measurements, based on ferroelectric liquid crystals as polarization modulating elements. Improvements of such a system were proposed by optimizing the design with a genetic algorithm. The new design promise to reduce the measurement noise significantly compared to previous designs, in addition to extending the spectral range into the infrare

Real-time in situ Mueller matrix ellipsometry of GaSb nanopillars: observation of anisotropic local alignment

The formation of GaSb nanopillars by low energy ion sputtering is studied in real-time by spectroscopic Mueller matrix ellipsometry, from the initial formation in the smooth substrate until nanopillars with a height of 200 – 300 nm are formed. As the nanopillar height increased above 100 nm, coupling between orthogonal polarization modes was observed. Ex situ angle resolved Mueller polarimetry measurements revealed a 180° azimuth rotation symmetry in the off-diagonal Mueller elements, which can be explained by a biaxial material with different dielectric functions εx and εy in a plane parallel to the substrate. This polarization coupling can be caused by a tendency for local direction dependent alignment of the pillars, and such a tendency is confirmed by scanning electron microscopy. Such observations have not been made for GaSb nanopillars shorter than 100 nm, which have optical properties that can be modeled as a uniaxial effective medium