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.

Rapid and Facile Synthesis of Gold Trisoctahedrons for Surface-Enhanced Raman Spectroscopy and Refractive Index Sensing.

Au trisoctahedrons (TOHs) with sharp tips and high-index facets have exceptional properties for diverse applications, such as plasmon-enhanced spectroscopies, catalysis, sensing, and biomedicine. However, the synthesis of Au TOHs remains challenging, and most reported synthetic methods are time-consuming or involve complex steps, hindering the exploration of their potential applications. Herein, we present a facile and fast approach to prepare Au TOHs with high uniformity and good control over the final size and shape, all within less than 10 min of synthesis, for surface-enhanced Raman spectroscopy (SERS) and refractive index sensing. The size of the Au TOHs can be easily tailored over a wide range, from 39 to 268 nm, allowing a tuning of the plasmon resonance at wavelengths from visible to near-infrared regions. The exposed facets of the Au TOHs can also be varied by controlling the growth temperatures. The wide tunability of size and exposed facets of Au TOHs can greatly broaden the range of their applications. We have also encapsulated Au TOHs with zeolite imidazolate framework (ZIF-8), obtaining core-shell hybrid structures. With the ability to tune Au TOH size, we further assessed their SERS performances in function of their size by detecting 2-NaT in solution, exhibiting enhancement factors of the order of 105 with higher values when the LSPR is blue-shifted from the laser excitation wavelength. Au TOHs have been also compared for refractive index sensing applications against Au nanospheres, revealing Au TOHs as better candidates. Overall, this facile and fast method for synthesizing Au TOHs with tunable size and exposed facets simplifies the path toward the exploration of properties and applications of this highly symmetrical and high-index nanostructure.

Impact of corpus callosum fiber tract crossing on polarimetric images of human brain histological sections: ex vivo studies in transmission configuration.

Significance: Imaging Mueller polarimetry is capable to trace in-plane orientation of brain fiber tracts by detecting the optical anisotropy of white matter of healthy brain. Brain tumor cells grow chaotically and destroy this anisotropy. Hence, the drop in scalar retardance values and randomization of the azimuth of the optical axis could serve as the optical marker for brain tumor zone delineation. Aim: The presence of underlying crossing fibers can also affect the values of scalar retardance and the azimuth of the optical axis. We studied and analyzed the impact of fiber crossing on the polarimetric images of thin histological sections of brain corpus callosum. Approach: We used the transmission Mueller microscope for imaging of two-layered stacks of thin sections of corpus callosum tissue to mimic the overlapping brain fiber tracts with different fiber orientations. The decomposition of the measured Mueller matrices was performed with differential and Lu-Chipman algorithms and completed by the statistical analysis of the maps of scalar retardance, azimuth of the optical axis, and depolarization. Results: Our results indicate the sensitivity of Mueller polarimetry to different spatial arrangement of brain fiber tracts as seen in the maps of scalar retardance and azimuth of optical axis of two-layered stacks of corpus callosum sections The depolarization varies slightly (<15%) with the orientation of the optical axes in both corpus callosum stripes, but its value increases by 2.5 to 3 times with the stack thickness. Conclusions: The crossing brain fiber tracts measured in transmission induce the drop in values of scalar retardance and randomization of the azimuth of the optical axis at optical path length of 15 µm. It suggests that the presence of nerve fibers crossing within the depth of few microns will be also detected in polarimetric maps of brain white matter measured in reflection configuration.

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.

Tailoring chiral optical properties by femtosecond laser direct writing in silica.

An object that possesses chirality, that is, having its mirror image not overlayed on itself by rotation and translation, can provide a different optical response to a left- or right-handed circular polarized light. Chiral nanostructures may exhibit polarization-selective optical properties that can be controlled for micro-to-nano optical element engineering. An attractive way to induce such complex nanostructures in three-dimension in glass is femtosecond laser direct writing. However, the mechanism of femtosecond laser induced chirality remains to be unveiled due to complex physical and chemical processes occurring during the ultrashort light-matter interaction. Here, a phenomenological model is proposed and is built on two-layers phase shifters to account for this laser-induced optical chirality in an initially achiral material (silica glass). This model is based on the observation that femtosecond laser induced nanogratings own two principal contributions to its aggregate birefringent response: a form and a stress-related one. By refining this formalism, a multilayer approach is developed to imprint on demand optical rotation. Values up to +/-60° at 550 nm within an optimal 80 µm thickness in silica glass are possible, corresponding to the highest value in a glass to date. These results provide new insights of circular-optical control in micro-nano optical manufacturing and open new opportunities for photonics applications.

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.

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.

Depolarization imaging for fast and non-invasive monitoring of cervical microstructure remodeling in vivo during pregnancy.

The cervix plays a crucial role in conception, maintenance of pregnancy, and childbirth. The mechanical properties of a pregnant woman's cervix change dramatically during gestation due to a remodeling of its microstructure, necessary for delivery. However, external factors can accelerate this process and lead to prematurity, the primary cause of perinatal mortality worldwide, due to the inefficiency of existing diagnostic methods. This study shows that polarized light is a powerful tool to probe the cervical microstructure during pregnancy. A wide-field multispectral polarimetric imaging system was fabricated to explore in vivo the cervix of full-term pregnant women. The polarimetric properties of the cervix change significantly with pregnancy progression. In particular, a set of several depolarization parameters (intrinsic and extrinsic) showed a strong linear correlation with gestational age in the red part of the visible spectral range. This trend can be attributed, among other things, to a decrease in collagen density and an increase in hydration of cervical connective tissue. Wide field depolarization imaging is a very promising tool for rapid and non-invasive analysis of cervical tissue in vivo to monitor the steady progression of pregnancy, providing the practitioner with useful information to improve the detection of preterm birth.

Comparing Commercial Metal-Coated AFM Tips and Home-Made Bulk Gold Tips for Tip-Enhanced Raman Spectroscopy of Polymer Functionalized Multiwalled Carbon Nanotubes.

Tip-enhanced Raman spectroscopy (TERS) combines the high specificity and sensitivity of plasmon-enhanced Raman spectroscopy with the high spatial resolution of scanning probe microscopy. TERS has gained a lot of attention from many nanoscience fields, since this technique can provide chemical and structural information of surfaces and interfaces with nanometric spatial resolution. Multiwalled carbon nanotubes (MWCNTs) are very versatile nanostructures that can be dispersed in organic solvents or polymeric matrices, giving rise to new nanocomposite materials, showing improved mechanical, electrical and thermal properties. Moreover, MWCNTs can be easily functionalized with polymers in order to be employed as specific chemical sensors. In this context, TERS is strategic, since it can provide useful information on the cooperation of the two components at the nanoscale for the optimization of the macroscopic properties of the hybrid material. Nevertheless, efficient TERS characterization relies on the geometrical features and material composition of the plasmonic tip used. In this work, after comparing the TERS performance of commercial Ag coated nanotips and home-made bulk Au tips on bare MWCNTs, we show how TERS can be exploited for characterizing MWCNTs mixed with conjugated fluorene copolymers, thus contributing to the understanding of the polymer/CNT interaction process at the local scale.

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.

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.

Polarization and depolarization metrics as optical markers in support to histopathology of ex vivo colon tissue.

Tissue polarimetry holds great promise to improve the effectiveness of conventional cancer diagnostics and staging, being a fast, minimally invasive, and low-cost optical technique. We introduce an enhanced diagnostic method for ex vivo colon specimens assessment by utilizing Stokes and Mueller matrix polarimetry. The proposed method makes use of experimental Mueller matrices, measured from healthy and tumor zones of a colon specimen, as input data for post-processing algorithms that include physical realisability filtering, symmetric decomposition and estimation of various polarization and depolarization metrics for colon specimen diagnostics. We validated our results with the gold standard histological diagnostics provided by pathologists. It was found that the Stokes-Mueller matrix polarimetry, combined with the appropriate filtering, decomposition algorithms and polarization/depolarization metrics calculations provides relevant optical markers of the colon tissue pathological conditions (healthy versus cancer), as confirmed by histopathology analysis. This approach potentially provides physicians with valuable and complementary information that holds promises in helping with the diagnostics of colon tissue specimens.

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.

Depolarization metric spaces for biological tissues classification.

Classification of tissues is an important problem in biomedicine. An efficient tissue classification protocol allows, for instance, the guided-recognition of structures through treated images or discriminating between healthy and unhealthy regions (e.g., early detection of cancer). In this framework, we study the potential of some polarimetric metrics, the so-called depolarization spaces, for the classification of biological tissues. The analysis is performed using 120 biological ex vivo samples of three different tissues types. Based on these data collection, we provide for the first time a comparison between these depolarization spaces, as well as with most commonly used depolarization metrics, in terms of biological samples discrimination. The results illustrate the way to determine the set of depolarization metrics which optimizes tissue classification efficiencies. In that sense, the results show the interest of the method which is general, and which can be applied to study multiple types of biological samples, including of course human tissues. The latter can be useful for instance, to improve and to boost applications related to optical biopsy.

Colon cancer detection by using Poincaré sphere and 2D polarimetric mapping of ex vivo colon samples.

This work is dedicated to the diagnosis and grading of colon cancer by a combined use of Poincaré sphere and 2D Stokes vector polarimetry mapping approaches. The major challenge consists in exploring the applicability of polarized light for noninvasive screening of the histological abnormalities within the samples of biological tissues. Experimental studies were conducted in ex vivo colon sample, excised after surgical procedure for colon tumor removal of G2-adenocarcinoma lesion. Polarimetric measurements in linear and circular regime were carried via personally developed polarimetric, optical set-up, using supercontinuous fiber laser with irradiation fixed at 635 nm. We apply the Poincaré sphere and two-dimensional Stokes vector scanning approach for screening the corresponding tissue samples. A comparison between linear and circular polarization states is made both for quantitative and qualitative evaluations. It is shown that circular polarization has better diagnostic capabilities than linear polarization, with higher dynamic ranges of the polarimetric parameters and better values of the diagnostic quantities. In addition to the standard polarimetry parameters, utilized as essential diagnostic markers, we apply statistical analysis to obtain more detailed information in frame of the applied diagnostic approach.

A Comparison between Nanogratings-Based and Stress-Engineered Waveplates Written by Femtosecond Laser in Silica.

This paper compares anisotropic linear optical properties (linear birefringence, linear dichroism, degree of polarization) and performances (absorption coefficient, thermal stability) of two types of birefringent waveplates fabricated in silica glass by femtosecond laser direct writing. The first type of waveplate is based on birefringence induced by self-organized nanogratings imprinted in the glass. One the other hand, the second design is based on birefringence originating from the stress-field formed around the aforementioned nanogratings. In addition to the provided comparison, the manufacturing of stress-engineered half waveplates in the UV-Visible range, and with mm-size clear aperture and negligible excess losses, is reported. Such results contrast with waveplates made of nanogratings, as the later exhibit significantly higher scattering losses and depolarization effects in the UV-Visible range.

Analysis of tissue microstructure with Mueller microscopy: logarithmic decomposition and Monte Carlo modeling.

Significance: Definitive diagnostics of many diseases is based on the histological analysis of thin tissue cuts with optical white light microscopy. Extra information on tissue structural properties obtained with polarized light would help the pathologist to improve the accuracy of his diagnosis.

Aim: We report on using Mueller matrix microscopy data, logarithmic decomposition, and polarized Monte Carlo (MC) modeling for qualitative and quantitative analysis of thin tissue cuts to extract the information on tissue microstructure that is not available with a conventional white light microscopy.

Large-scale patterning of π-conjugated materials by meniscus guided coating methods.

Printed organic electronics has attracted considerable interest in recent years as it enables the fabrication of large-scale, low-cost electronic devices, and thus offers significant possibilities in terms of developing new applications in various fields. Easy processing is a prerequisite for the development of low-cost, flexible and printed plastics electronics. Among processing techniques, meniscus guided coating methods are considered simple, efficient, and low-cost methods to fabricate electronic devices in industry. One of the major challenges is the control of thin film morphology, molecular orientations and directional alignment of polymer films during coating processes. Herein, the recent progress of emerging field of meniscus guided printing organic semiconductor materials is discussed. The first part of this report briefly summarizes recent advances in meniscus guided coating techniques. The second part discusses periodic deposits and patterned deposition at moving contact lines, where the mass-transport influences film morphology due to convection at the triple contact line. The last section summarizes our strategy to fabricate large-scale patterning of π-conjugated polymers using meniscus guided method.

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.