"On-The-Fly" Synthesis of Self-Supported LDH Hollow Structures Through Controlled Microfluidic Reaction-Diffusion Conditions.

Layered double hydroxides (LDHs) are a class of functional materials that exhibit exceptional properties for diverse applications in areas such as heterogeneous catalysis, energy storage and conversion, and bio-medical applications, among others. Efforts have been devoted to produce millimeter-scale LDH structures for direct integration into functional devices. However, the controlled synthesis of self-supported continuous LDH materials with hierarchical structuring up to the millimeter scale through a straightforward one-pot reaction method remains unaddressed. Herein, it is shown that millimeter-scale self-supported LDH structures can be produced by means of a continuous flow microfluidic device in a rapid and reproducible one-pot process. Additionally, the microfluidic approach not only allows for an "on-the-fly" formation of unprecedented LDH composite structures, but also for the seamless integration of millimeter-scale LDH structures into functional devices. This method holds the potential to unlock the integrability of these materials, maintaining their performance and functionality, while diverging from conventional techniques like pelletization and densification that often compromise these aspects. This strategy will enable exciting advancements in LDH performance and functionality.

Spectroscopic ellipsometry of very rough surfaces.

This work expands the use of spectroscopic ellipsometry to surfaces with roughness that is similar to or larger than the wavelength of the incident light. By using a custom-built spectroscopic ellipsometer and varying the angle of incidence, we were able to differentiate between the diffusely scattered and specularly reflected components. Our findings demonstrate that measuring the diffuse component at specular angles is highly beneficial for ellipsometry analysis, as its response is equivalent to that of a smooth material. This allows for accurate determination of the optical constants in materials with extremely rough surfaces. Our results have the potential to broaden the scope and utility of the spectroscopic ellipsometry technique.

Use of complete temporal basis in polarimeters based on photoelastic modulators.

This Letter shows the advantage of applying the complete temporal basis in polarimeters based on photoelastic modulators in lieu of the commonly used truncated temporal basis that results in a discrete selection of the Fourier harmonics used for data processing. Results are numerically and experimentally illustrated for a complete Mueller-matrix-based polarimeter on four photoelastic modulators.

Complete Mueller matrix from a partial polarimetry experiment: the nine-element case: erratum.

The present erratum is intended to correct some typos as well as to complement Appendices B and C in our paper [J. Opt. Soc. Am. A36, 403 (2019)JOAOD60740-323210.1364/JOSAA.36.000403].

In situ study of chiral symmetry breaking in sodium chlorate solutions by Mueller matrix polarimetry.

This work presents a novel approach for investigating symmetry-breaking processes during crystallization using Mueller matrix polarimetry. By applying this method to the cooling process of NaClO3 solutions, we demonstrate its ability to capture not only the initial and final stages of crystallization but also the intermediate steps and dynamics of the process. This technique provides more comprehensive information and insights into the symmetry-breaking mechanisms involved in crystal formation. Overall, this study highlights the potential of Mueller matrix polarimetry for in situ statistical measurements of the optical rotation and for monitoring the evolution of enantiomeric excesses.

Optical response of media and structures exhibiting spatial dispersion.

We present a general method for redefining the permittivity and permeability tensors of a medium or structure exhibiting spatial dispersion (SD). The method effectively separates the electric and magnetic contributions that are intertwined in the traditional description of the SD-dependent permittivity tensor. The redefined material tensors are the ones to be used in the common methods for calculating the optical response of layered structures, thus enabling modeling of experiments in the presence of SD.

Model for the depolarizing retarder in Mueller matrix polarimetry.

We advance an analytical model describing the polarimetric response of a depolarizing retarder whose retardance varies spatially in magnitude or in orientation. The variation of the retarder parameters may be either of deterministic or of random nature. The model provides both the mean values and the uncertainties of the parameters. Its application is illustrated on two experimental examples, respectively covering the deterministic and the random cases.

Compact formulation of the transparent-absorbing isotropic interface electromagnetic problem.

A complete formulation of the electromagnetic problem corresponding to the light incidence from a transparent to an absorbing medium (isotropic materials) is developed. According to the standard separation in s and p polarization cases, we explicitly obtain all the relevant formulas that relate the polarization and Poynting vectors of the reflected and transmitted beams with the incident ones. Overall, the procedure is compact since it is short and complete.

Spectrally modulated polarimetry with wavelength domain analysis.

Spectrally modulated Stokes polarimeters use a pair of high-order crystal retarders to generate a spectrally dependent modulation of the polarization of light. In these systems, the detected intensity versus wavenumber spectrum is usually referred to as a channeled spectrum, and the Fourier inversion of this spectrum allows the determination of Stokes parameters of light without needing any other mechanical or active device for polarization control. This work proposes a spectrally modulated polarimeter beyond the concept of a channeled wavenumber spectrum, so effectively detaching the spectral modulation from the Fourier analysis technique. The wavelength domain analysis we use is best suited for dispersive spectrometers offering intensity versus wavelength measurements. The technique is illustrated with the measurement of very small optical rotations produced by sucrose solutions. The proposed technique is easily extendable to spectrally modulated Mueller polarimeters.

Mueller matrix imaging with a polarization camera: application to microscopy.

In this work, we describe the design and implementation of a Mueller matrix imaging polarimeter that uses a polarization camera as a detector. This camera simultaneously measures the first three Stokes components, allowing for the top three rows of the Mueller matrix to be determined after only N = 4 measurements using a single rotating compensator, which is sufficient to fully characterize nondepolarizing samples. This setup provides the polarimetric analysis with micrometric resolution in about 3 seconds and can also perform live birefringence imaging at the camera frame rate by fixing the compensator at a static 45° angle. To further improve the conditioning of the setup, we also give the first experimental demonstration of an optimal elliptical retarder design.

Optimal elliptical retarder in rotating compensator imaging polarimetry.

In this Letter, we present a new, to the best of our knowledge, design for elliptical retarders based on two quarter-wave retarders with an angle offset, which is particularly well suited for polarimetric measurements based on rotating compensator systems. We show that this simple elliptical retarder design offers the minimum condition number achieved by traditionally optimal polarimeter setups and can be used to further improve the accuracy of polarimetric imaging measurements in the presence of error sources, with the advantage that it only requires common quarter-wave retarders.

Mueller matrix ellipsometer based on discrete-angle rotating Fresnel rhomb compensators.

A spectroscopic Mueller matrix ellipsometer based on two rotating Fresnel rhomb compensators with a nearly achromatic response and optimal retardance is described. In this instrument, the compensators rotate in a discrete manner instead of continuously rotating, and this allows for a well-conditioned measurement even for low intensity samples. Moreover, in this configuration, the exposure time of the CCD detector can be varied within orders of magnitude without interfering with the dynamics of the compensator rotation. An optimization algorithm determines the optimal set of discrete angles that allows the determination of the Mueller matrix in the presence of noise. The calibration of the instrument is discussed, and examples of experimentally determined Mueller matrices are provided.

Dielectric function of vanadium oxide thin films by thermal annealing.

The dielectric function of ${{\rm{VO}}_x}$ and ${{\rm{V}}_2}{{\rm{O}}_5}$ thin films is determined with the use of a spectroscopic Mueller matrix ellipsometer from 1.5 to 5.0 eV. The complex dielectric function of the films is calculated using the measured Mueller matrices filtered with the Cloude decomposition. ${{\rm{VO}}_x}$ shows high absorption in the UV region, a Tauc-Lorentz gap around 2.4 eV, and non-vanishing absorption in the visible. ${{\rm{V}}_2}{{\rm{O}}_5}$ shows a high absorption band centered at 2.87 eV, an indirect optical band gap at 1.95 eV, and a direct optical band gap at 2.33 eV. The ellipsometric characterization is supported by Raman, x-ray photoelectron, and photoluminescence spectroscopy.

Polymorphic chiral squaraine crystallites in textured thin films.

An enantiomerically pure (R)-2-methylpyrrolidine-based anilino squaraine crystallizes in two chiral polymorphs adopting a monoclinic C2 and an orthorhombic P21 21 21 structure, respectively. By various thin-film preparation techniques, a control of the polymorph formation is targeted. The local texture of the resulting textured thin films is connected to the corresponding optical properties. Special attention is paid to an unusual Davydov splitting, the anisotropic chiroptical response arising from preferred out-of-plane orientation of the crystallites, and the impact of the polymorph specific excitonic coupling.

Model-free determination of the birefringence and dichroism in c-cut crystals from transmission ellipsometry measurements.

In this work, we derive closed-form expressions for determination of the linear birefringence and linear dichroism of uniaxial crystals utilizing transmission ellipsometry measurements at small angles of incidence in $ c $c-cut crystal substrates. The model-free method we use is an algebraic generalization of the method reported in Appl. Opt.44, 3153 (2005).APOPAI0003-693510.1364/AO.44.003153 The optical anisotropy of substrates of sapphire, 4H-SiC, and 6H-SiC single crystals is measured for illustration.

Stern-Gerlach experiment with light: separating photons by spin with the method of A. Fresnel.

In 1822 A. Fresnel described an experiment to separate a beam of light into its right- and left-circular polarization components using chiral interfaces. Fresnel's experiment combined three crystalline quartz prisms of alternating handedness to achieve a visible macroscopic separation between the two circular components. Such quartz polyprisms were rather popular optical components in XIXth century but today remain as very little known optical devices. This work shows the analogy between Fresnel's experiment and Stern-Gerlach experiment from quantum mechanics since both experiments produce selective deflection of particles (photons in case of Fresnel's method) according to their spin angular momentum. We have studied a historical quartz polyprism with eight chiral interfaces producing a large spatial separation of light by spin. We have also constructed a modified Fresnel biprism to produce smaller separations and we have examined the analogy with Stern-Gerlach apparatus for both strong and weak measurements. The polarimetric analysis of a Fresnel polyprism reveals that it acts as a spin angular momentum analyzer.

Snapshot circular dichroism measurements.

Two coherent waves carrying orthogonal polarizations do not interfere when they superpose, but an interference pattern is generated when the two waves share a common polarization. This well-known principle of coherence and polarization is exploited for the experimental demonstration of a novel method for performing circular dichroism measurements whereby the visibility of the interference fringes is proportional to the circular dichroism of the sample. Our proof-of-concept experiment is based upon an analog of Young's double-slit experiment that continuously modulates the polarization of the probing beam in space, unlike the time modulation used in common circular dichroism measurement techniques. The method demonstrates an accurate and sensitive circular dichroism measurement from a single camera snapshot, making it compatible with real-time spectroscopy.

Complete Mueller matrix from a partial polarimetry experiment: the nine-element case.

We show that an incomplete, nine-element Mueller matrix with a row and a column missing, obtained in a partial polarimetry experiment, can be completed to a full, 16-element Mueller matrix, provided depolarization is absent experimentally. There exist exactly two solutions for the missing row and column, differing from one another only by the signs of the respective row and column elements. To select the correct solution, additional information on the sample properties, such as weak anisotropy or special symmetry, is needed. We provide analytical and numerical procedures for completing the partial Mueller matrix for the cases of practical interest and illustrate the approach on an experimental example.

Complete Mueller matrix from a partial polarimetry experiment: the 12-element case.

Conventional generalized ellipsometry instrumentation is capable of measuring 12 out of the 16 elements of the Mueller matrix of the sample. The missing column (or row) of the experimental partial Mueller matrix can be analytically determined under additional assumptions. We identify the conditions necessary for completing the partial Mueller matrix to a full one. More specifically, such a completion is always possible if the sample is nondepolarizing; the fulfillment of additional conditions, such as the Mueller matrix exhibiting symmetries or being of a special two-component structure, are necessary if the sample is depolarizing. We report both algebraic and numerical procedures for completing the partial 12-element Mueller matrix in all tractable cases and validate them on experimental examples.

Quaternion algebra for Stokes-Mueller formalism.

In this paper, we show that the Stokes-Mueller formalism can be reformulated in terms of quaternions and that the quaternion algebra is a suitable alternative presentation of the formalism of Mueller-Jones states that we have recently described [J. Opt. Soc. Am. A34, 80 (2017)JOAOD60740-323210.1364/JOSAA.34.000080]. The vector and matrix states associated with the Mueller matrices of nondepolarizing optical systems are different representations that are isomorphic to the same quaternion state, and this quaternion state turns out to be the rotator of the Stokes quaternion. In this work, we study the properties of this general quaternion state and its application to the calculus of polarization effects. We also show that the coherent linear combination of nondepolarizing optical media states and depolarization phenomena can be reformulated in terms of quaternion states.