Diffractive order Mueller matrix ellipsometry for the design and manufacture of polarization beam splitting metasurfaces.

Optical metasurface technology promises an important potential for replacing bulky traditional optical components, in addition to enabling new compact and lightweight metasurface-based devices. Since even subtle imperfections in metasurface design or manufacture strongly affect their performance, there is an urgent need to develop proper and accurate protocols for their characterization, allowing for efficient control of the fabrication. We present non-destructive spectroscopic Mueller matrix ellipsometry in an uncommon off-specular configuration as a powerful tool for the characterization of orthogonal polarization beam-splitters based on a-Si:H nanopillars. Through Mueller matrix analysis, the spectroscopic polarimetric performance of the ±1 diffraction orders is experimentally demonstrated. This reveals a wavelength shift in the maximum efficiency caused by fabrication-induced conical pillars while still maintaining a polarimetric response close to ideal non-depolarizing Mueller matrices. We highlight the advantage of the spectroscopic Mueller matrix approach, which not only allows for monitoring and control of the fabrication process itself, but also verifies the initial design and produces feedback into the computational design.

Dispersion of resonant modes in patch antenna lattices.

Spectroscopic polar angle resolved Mueller matrix ellipsometry at multiple azimuthal incidences, together with a full-field model, reveal new details in the interplay between localized gap surface plasmon resonances and propagating surface plasmon polaritons (SPPs) in a rectangular array of metal-insulator-metal patches. A plane-wave expansion of the field in the insulator shows that the fundamental localized resonances are composed of oppositely propagating modes. Sharp dispersive resonances observed in p-polarization, excited near the opening of diffracted orders, are shown to be grating coupled SPPs. The SPPs show strong coupling with localized modes of similar symmetry, while they appear suppressed by modes of dissimilar symmetry.

Effects of optical activity to Mueller matrix ellipsometry of composed waveplates.

Mueller matrix ellipsometry has been used to precisely characterize quartz waveplates for demanding applications in the semiconductor industry and high precision polarimetry. We have found this experimental technique to be beneficial to use because it enables us to obtain absolute and precise measurement of retardation in a wide spectral range, waveplate orientation, and compound waveplate adjustment. In this paper, the necessity of including the optical activity in the Mueller matrix model and data treatment is demonstrated. Particularly, the optical activity of the quartz influences the adjustment of misalignment between the perpendicularly oriented waveplates of the compound biplate. We demonstrate that omitting the optical activity from the model leads to inaccurate values of the misalignment. In addition, the depolarization effects caused by a finite monochromator bandwidth is included in the model. Incorporation of the optical activity to the Mueller matrix model has required a development of rigorous theory based on appropriate constitutive equations. The generalized Yeh's matrix algebra to bianisotropic media has been used for the calculation of the eigenmodes propagation in chiral materials with reduced symmetry. Based on the applied method, the authors have proposed approximated analytical form of the Mueller matrix representing optically active waveplate and biplate and provided discussion on the analytical and numerical limits of the method.

Dispersion of polarization coupling, localized and collective plasmon modes in a metallic photonic crystal mapped by Mueller Matrix Ellipsometry.

We report a spectroscopic Mueller matrix experimental study of a plasmonic photonic crystal consisting of gold hemispheroidal particles (lateral radius 54 nm, height 25 nm) arranged on a square lattice (lattice constant 210 nm) and supported by a glass substrate. Strong polarization coupling is observed for ultraviolet wavelengths and around the surface plasmon resonance for which the off-block-diagonal Mueller matrix elements show pronounced anisotropies. Due to the Rayleigh anomalies, the block-diagonal Mueller matrix elements produce a direct image of the Brillouin Zone (BZ) boundaries of the lattice and resonances are observed at the M-point in the first and at the X-point in the second BZ. These elements show also the dispersion of the localized surface plasmon resonance.

Parametric model of the Mueller matrix of a Spectralon white reflectance standard deduced by polar decomposition techniques.

Decomposition methods have been applied to in-plane Mueller matrix ellipsometric scattering data of the Spectralon reflectance standard. Data were measured at the wavelengths 532 nm and 1500 nm, using an achromatic optimal Mueller matrix scatterometer applying a photomultiplier tube and a high gain InGaAs detector for the two wavelengths. A parametric model with physical significance was deduced through analysis of the product decomposed matrices. It is found that when the data are analyzed as a function of the scattering angle, similar to particle scattering, the matrix elements are largely independent of incidence angle. To the first order, we propose that a Guassian lineshape is appropriate to describe the polarization index, while the decomposed diagonal elements of the retardance matrix have a form resembling Rayleigh single scattering. New models are proposed for the off diagonal elements of the measured Mueller matrix.

Overdetermined broadband spectroscopic Mueller matrix polarimeter designed by genetic algorithms.

This paper reports on the design and implementation of a liquid crystal variable retarder based overdetermined spectroscopic Mueller matrix polarimeter, with parallel processing of all wavelengths. The system was designed using a modified version of a recently developed genetic algorithm [Letnes et al. Opt. Express 18, 22, 23095 (2010)]. A generalization of the eigenvalue calibration method is reported that allows the calibration of such overdetermined polarimetric systems. Out of several possible designs, one of the designs was experimentally implemented and calibrated. It is reported that the instrument demonstrated good performance, with a measurement accuracy in the range of 0.1% for the measurement of air.

Optical properties of biaxial nanopatterned gold plasmonic nanowired grid polarizer.

Gold nanoparticles deposited on self-organized nano-ripple quartz substrates have been studied by spectroscopic Mueller matrix ellipsometry. The surface was found to have biaxial anisotropic optical properties. For electric field components normal to the ripples the periodic and disconnected nature of the in plane nanowires gives rise to an optical response dominated by the localized plasmon resonance. In the direction parallel to the ripples the gold nanoparticles are aligned closely leading to localized plasmon resonances in the infrared. As Au was deposited at an angle oblique to the surface normal, the gold nanoparticles were formed on the side of the ripples facing the incoming evaporation flux. This makes the gold particles slightly inclined, correspondingly the principal coordinate system of the biaxial dielectric tensor results tilted. The anisotropic plasmonic optical response results in a strong polarizing effect, making it suitable as a plasmonic nanowired grid polarizer.

Mueller matrix measurements and modeling pertaining to Spectralon white reflectance standards.

The full Mueller matrix for a Spectralon white reflectance standard was measured in the incidence plane, to obtain the polarization state of the scattered light for different angles of illumination. The experimental setup was a Mueller matrix ellipsometer, by which measurements were performed for scattering angles measured relative to the normal of the Spectralon surface from -90° to 90° sampled at every 2.5° for an illumination wavelength of 532 nm. Previously, the polarization of light scattered from Spectralon white reflectance standards was measured only for four of the elements of the Muller matrix. As in previous investigations, the reflection properties of the Spectralon white reflectance standard was found to be close to those of a Lambertian surface for small scattering and illumination angles. At large scattering and illumination angles, all elements of the Mueller matrix were found to deviate from those of a Lambertian surface. A simple empirical model with only two parameters, was developed, and used to simulate the measured results with fairly good accuracy.

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.

Bidirectional reflectance distribution function of Spectralon white reflectance standard illuminated by incoherent unpolarized and plane-polarized light.

A Lambert surface would appear equally bright from all observation directions regardless of the illumination direction. However, the reflection from a randomly scattering object generally has directional variation, which can be described in terms of the bidirectional reflectance distribution function (BRDF). We measured the BRDF of a Spectralon white reflectance standard for incoherent illumination at 405 and 680 nm with unpolarized and plane-polarized light from different directions of incidence. Our measurements show deviations of the BRDF for the Spectralon white reflectance standard from that of a Lambertian reflector that depend both on the angle of incidence and the polarization states of the incident light and detected light. The non-Lambertian reflection characteristics were found to increase more toward the direction of specular reflection as the angle of incidence gets larger.

Mueller matrix measurements of algae with different shape and size distributions.

The full Mueller matrix was measured to obtain the polarization state of the scattered light for a variety of algae with different shapes, wall compositions, sizes, and refractive indices. The experimental setup was a multiple laser Mueller matrix ellipsometer, by which measurements were performed for scattering angles from 16° to 160° sampled at every second degree for wavelengths of 473 nm and 532 nm. Previously, the polarization of light scattered from microalgae was investigated only for a few species, and the Mueller matrix was found to have little variation between the species. In our work a total of 11 algal species were investigated, representing diatoms, dinoflagellates, coccolithophorids, green algae, and a cryptophyte. The selection of species was made to obtain high variability in shape, size, cell wall, and refractive index. As in previous investigations, very small variations were found between species for most of the Mueller matrix elements, but noticeable variations were found for M(11), (M(12)+M(21))/2 and (M(33)+M(44))/2.

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 (sample). This ability is characterized by the condition number, κ, 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.

Combined imaging of oxidative stress and microscopic structure reveals new features in human atherosclerotic plaques.

Human atherosclerotic samples collected by carotid endarterectomy were investigated using electronic paramagnetic resonance imaging (EPRI) for visualization of reactive oxygen species, and nonlinear optical microscopy (NLOM) to study structural features. Regions of strong EPRI signal, indicating a higher concentration of reactive oxygen species and increased inflammation, were found to colocalize with regions dense in cholesterol crystals as revealed by NLOM.

Mueller matrix three-dimensional directional imaging of collagen fibers.

A method for measuring three-dimensional (3-D) direction images of collagen fibers in biological tissue is presented. Images of the 3-D directions are derived from the measured transmission Mueller matrix images (MMIs), acquired at different incidence angles, by taking advantage of the form birefringence of the collagen fibers. The MMIs are decomposed using the recently developed differential decomposition, which is more suited to biological tissue samples than the common polar decomposition method. Validation of the 3-D direction images was performed by comparing them with images from second-harmonic generation microscopy. The comparison found a good agreement between the two methods. It is envisaged that 3-D directional imaging could become a useful tool for understanding the collagen framework for fibers smaller than the diffraction limit.

Quantitative characterization of articular cartilage using Mueller matrix imaging and multiphoton microscopy.

The collagen meshwork in articular cartilage of chicken knee is characterized using Mueller matrix imaging and multiphoton microscopy. Direction and degree of dispersion of the collagen fibers in the superficial layer are found using a Fourier transform image-analysis technique of the second-harmonic generated image. Mueller matrix images are used to acquire structural data from the intermediate layer of articular cartilage where the collagen fibers are too small to be resolved by optical microscopy, providing a powerful multimodal measurement technique. Furthermore, we show that Mueller matrix imaging provides more information about the tissue compared to standard polarization microscopy. The combination of these techniques can find use in improved diagnosis of diseases in articular cartilage, improved histopathology, and additional information for accurate biomechanical modeling of cartilage.