Extended eigenvalue calibration method for overdetermined Mueller matrix polarimeters.

The eigenvalue calibration method is a versatile approach that can be applied to any type of the Mueller matrix polarimetic setup because a precise knowledge of the optical response of the setup components is not required. The method has usually been employed in its original form to calibrate non-overdetermined polarimeters dealing with intensity data arranged in 4 × 4 matrices, but it can also be applied to calibrate overdetermined polarimeters with intensity data matrices of higher dimension. The main drawback with the original formulation of the method is its sensitivity to noise in the input data, especially if applied as it is to overdetermined intensity matrices. In the present work, we present a rigorous extension of the conventional eigenvalue calibration method to treat overdetermined data. We experimentally show that the proposed method does not enhance noise propagation, and therefore it does not degrade the quality of Mueller matrices measured with overdetermined polarimeters.

Femtosecond laser direct writing multilayer chiral waveplates with minimal linear birefringence.

Chirality transfer from femtosecond laser direct writing in achiral transparent materials mainly originates from the interplay between anisotropic nanogratings and mechanical stress with non-parallel and non-perpendicular (oblique) neutral axes. Yet, the laser fabrication simultaneously induces non-negligible linear birefringence. For precise manipulation of circular polarization properties, as well as to unlock the full functionality, we report here a geometry-inspired multilayer method for direct writing of chiral waveplates with minimal linear birefringence. We perform a theoretical analysis of both circular and linear properties response for different multilayer configurations and achieve strong circular birefringence of up to -2.25 rad with an extinction ratio of circular birefringence to total linear birefringence of up to 5.5 dB at 550 nm. Our strategy enables the precise control of circular properties and provides a facile platform for chiral device exploration with almost no linear property existence.

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.

Unraveling the physical information of depolarizers.

The link between depolarization measures and physical nature and structure of material media inducing depolarization is nowadays an open question. This article shows how the joint use of two complementary sets of depolarizing metrics, namely the Indices of polarimetric purity and the Components of purity, are sufficient to completely describe the integral depolarizing properties of a sample. Based on a collection of illustrative and representative polarimetric configurations, a clear and meaningful physical interpretation of such metrics is provided, thus extending the current tools and comprehension for the study and analysis of the depolarizing properties of material media. This study could be of interest to those users dealing with depolarization or depolarizing samples.

Polarizer calibration method for Mueller matrix polarimeters.

We advance what we believe is a novel eigenvalue-based method for calibrating Mueller matrix polarimeters employing a single calibration optical component: a polarizer. The method is potentially advantageous in high numerical aperture imaging or wide spectral range spectroscopic polarimetric configurations restricting or even prohibiting the standard use of a retarder as a second calibration component.

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.

Eigenvalue-based depolarization metric spaces for Mueller matrices.

We present a unified formal description and a detailed study of the depolarization spaces defined by various depolarization metrics based on the eigenvalues of the covariance matrix associated with a given Mueller matrix. By introducing natural generalizations of the common and Lorentz depolarization metrics, we likewise advance novel spaces appropriate for the description of extrinsic and intrinsic depolarization. We show the intimate relation existing between the depolarization spaces and the depolarization diagrams and solve the problem of the experimentally observed forbidden depolarization region. The theoretical developments are illustrated on numerical, analytical, and experimental examples of depolarizing Mueller matrices.

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.

Symmetric decomposition of experimental depolarizing Mueller matrices in the degenerate case.

We propose a detailed procedure to determine the two retardance matrix factors entering the symmetric decomposition of Mueller matrices when the depolarizer matrix is partially degenerate (i.e., two out of three of its depolarization coefficients are equal), which is a common occurrence. Thanks to a relatively simple algebraic method, we show that linear retardance, as well as its eigenaxes orientation can be determined unambiguously from each retardance matrix factor. The method, applied on both experimental Mueller matrices of an ad hoc sample, as well as on that of a biological tissue, shows its efficiency for decoupling the different polarimetric effects of retardance that occur during the propagation of light throughout a complex medium.

Extended Yeh's method for optically active anisotropic layered media.

We extend the original method of Yeh [J. Opt. Soc. Am.69, 742 (1979)JOSAAH0030-394110.1364/JOSA.69.000742] for calculating the reflection and transmission from anisotropic layered structures to media exhibiting not only dielectric, but also magnetic anisotropy, as well as optical activity. We likewise establish the relationship between the optical activity and gyration tensors from the two most used constitutive relations for optically active media and illustrate the extended Yeh's method on a practically important example.

Study of femtosecond laser-induced circular optical properties in silica by Mueller matrix spectropolarimetry.

Transmission Mueller-matrix spectroscopic ellipsometry is applied to femtosecond laser-induced modifications in silica glass in the spectral range of 450-1000 nm. Within a type II regime, the modifications exhibit not only circular dichroism, but also circular birefringence. We suggest that the laser polarization orientation with respect to pulse front tilt determines the amplitude and the sign of the circular properties. By using differential decomposition of the Mueller matrix, optical rotation is revealed for the first time, to the best of our knowledge. A maximum value of the effective optical activity of 143°/mm at 550 nm is found.

Experimental evidence for partial spatial coherence in imaging Mueller polarimetry.

We demonstrate experimentally the validity of the partial spatial coherence formalism in Mueller polarimetry and show that, in a finite spatial resolution experiment, the measured response is obtained through convolving the theoretical one with the instrument function. The reported results are of primary importance for Mueller imaging systems.

Mueller matrix polarimetry on a Young's double-slit experiment analog.

In this Letter we describe an experiment in which coherent light is sent through a calcite crystal that separates the photons by their polarization. The two beams are then let to superpose, and this recombined beam is used to measure the Mueller matrix of the system. Results are interpreted according to our recent formalism of coherent superposition in material media. This is the first experimental implementation of a Young's experiment with complete polarimetry, and it is demonstrated that our method can be used for the experimental synthesis of optical devices with on-demand optical properties.

Synthesis and characterization of depolarizing samples based on the indices of polarimetric purity.

In this work, we discuss the interest of using the indices of polarimetric purity (IPPs) as a criterion for the characterization and classification of depolarizing samples. We prove how differences in the depolarizing capability of samples, not seen by the commonly used depolarization index PΔ, are identified by the IPPs. The above-stated result is analyzed from a theoretical point of view and experimentally verified through a set of polarimetric measurements. We show how the approach presented here can be useful in easily synthetizing depolarizing samples with controlled depolarizing features, just by properly combining low-cost fully polarizing elements (such as linear retarders or polarizers).

Basic properties and classification of Mueller matrices derived from their statistical definition.

Starting from the statistical definition of the Mueller matrix, we derive the relationships between basic properties, such as the number of contact points of the characteristic ellipsoid with the Poincaré sphere and the rank of the covariance matrix. This approach enables the comprehensive classification of any experimental depolarizing Mueller matrix into one of six possible classes, thus making possible phenomenological interpretation in terms of a specific fluctuating Jones generator or of a finite sum of nondepolarizing Mueller matrices.