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.

Experimental studies of the transmission of light through low-coverage regular or random arrays of silica micropillars supported by a glass substrate.

The transmission of light through low-coverage regular and random arrays of glass-supported silica micropillars of diameters 10-40 µm and height 10 µm is studied experimentally. Angle-resolved measurements of the transmitted intensity are performed at visible wavelengths by either a goniospectrophotometer or a multimodal imaging (Mueller) polarimetric microscope. It is demonstrated that for the regular arrays, the angle-resolved measurements are capable of resolving many of the densely packed diffraction orders that are expected for periodic structures of lattice constants 20-80 µm, but they also display features ("halos" and fringes) that are due to the scattering and guiding of light in individual micropillars or in the supporting glass slides. These latter features are also found in angle-resolved measurements on random arrays of micropillars of the same surface coverage. Finally, we perform a comparison of direct measurements of haze in transmission for our patterned glass samples with what can be calculated from the angle-resolved transmitted intensity measurements. Good agreement between the two types of results is found, which testifies to the accuracy of the angle-resolved measurements that we report.

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).

On the equivalence between Young's double-slit and crystal double-refraction interference experiments.

We show, both analytically and experimentally, that under common experimental conditions the interference pattern produced in a classic Young's double-slit experiment is indistinguishable from that generated by means of a doubly refracting uniaxial crystal whose optic axis makes a skew angle with the light propagation direction. The equivalence between diffraction and crystal optics interference experiments, taken for granted by Arago and Fresnel in their pioneering research on the interference of polarized light beams, is thus rigorously proven.

Comparative study of SiO2, Si3N4 and TiO2 thin films as passivation layers for quantum cascade lasers.

The aim of this article is to determine the best dielectric between SiO2, Si3N4 and TiO2 for quantum cascade laser (QCL) passivation layers depending on the operation wavelength. It relies on both Mueller ellipsometry measurement to accurately determine the optical constants (the refractive index n and the extinction coefficient k) of the three dielectrics, and optical simulations to determine the mode overlap with the dielectric and furthermore the modal losses in the passivation layer. The impact of dielectric thermal conductivities are taken into account and shown to be not critical on the laser performances.

Explicit expressions for the elementary polarization properties of a weakly anisotropic, homogeneous medium.

We derive the relationships between the elementary polarization properties describing a homogeneous medium within the framework of the differential Jones and Mueller formalisms from transmission polarimetry, and the permittivity tensor of the medium, assumed to be weakly anisotropic. The expressions are illustrated on selected examples and allowed to physically interpret experimental polarimetry data.

Sum regression decomposition of spectral and angle-resolved Mueller matrices from biological reflectors.

We show spectroscopic Mueller-matrix data measured at multiple incidence angles of the scarab beetle C. aurata. A method of regression decomposition can decompose the Mueller matrix into a set of two matrices representing one polarizer and one dielectric reflector. We also report on a tentative decomposition of the beetle C. argenteola using the same method.

Use of optical spacers to enhance infrared Mueller ellipsometry sensitivity: application to the characterization of organic thin films.

Mueller ellipsometry in the mid-infrared (IR) spectral range can be used to obtain information about chemical composition through the vibrational spectra of samples. In the case of very thin films (<100 nm), the ellipsometric spectral features due to vibrational absorption are in general quite weak, and sometimes they are hidden by the noise in the measured data. In this work, we present one method based on the use of optical spacers as a tool to enhance the sensitivity of IR Mueller ellipsometry. An optical spacer is a thin film made of a known material which is between the substrate and the layer of interest. We show that, when the thickness of the two layers fulfills a given condition, the spectral features due to vibrational absorptions are enhanced. We explain the enhancement effect in terms of the Airy formula. The theoretical discussion is illustrated with two examples. We analyzed polystyrene thin films deposited on silicon wafers. Some of the wafers were covered by a thin film of thermal silicon dioxide (SiO2), which was used as a spacer. The results show the suitability of the proposed technique to overcome the lack of sensitivity in ellipsometric measurements when it comes to working with either very thin films or materials with low absorption.

Spatial evolution of depolarization in homogeneous turbid media within the differential Mueller matrix formalism.

We show, through visible-range Mueller polarimetry, as well as numerical simulations, that the depolarization in a homogeneous turbid medium consisting of submicron spherical particles follows a parabolic law with the path-length traveled by light through the medium. This result is in full agreement with the phenomenological theory of the fluctuating medium within the framework of the differential Mueller matrix formalism. We further found that the standard deviations of the fluctuating elementary polarization properties of the medium depend linearly on the concentration of particles. These findings are believed to be useful for the phenomenological interpretation of polarimetric experiments, with special emphasis on biomedical applications.

Elementary polarization properties in the backscattering configuration.

In the normal incidence backscattering configuration, a polarimetric measurement always preserves the reciprocal symmetry. For a reciprocal Jones matrix, the number of elementary polarization properties is reduced from six to four. In this work, the physical interpretation of these properties is examined and they are compared with the equivalent polarization properties in transmission. It is found that, with the exception of natural optical activity, a polarimetric backreflection experiment can essentially provide the same type of information about the anisotropy of a medium as a transmission analysis, although transmission and backreflection information comes in a completely different form. Experimental examples are provided to illustrate the discussion.

Simplified calibration procedure for Mueller polarimeter in transmission configuration.

We address calibration of Mueller polarimeters in transmission configuration and in the presence of noise. By comparing the maximum likelihood (ML) method and the extended eigenvalue calibration method, it is found that the ML method yields higher precision in the presence of noise. Moreover, we show that by employing the ML method together with simple constraints on the calibration matrices, it is possible to perform the calibration without using a retarder, and with only polarizers. This result is of great interest for the calibration of multispectral polarimeters.

Application of the arbitrary decomposition to finite spot size Mueller matrix measurements.

Finite spot size Mueller matrix polarimetric measurements whereby the light spot impinges on two different areas of the sample, e.g., a grating and a substrate, are relatively frequently met in practice. It has been shown that if the Mueller matrix of one of the areas (the substrate) is known from an additional measurement then the Mueller matrix of the remaining medium (the grating) can be obtained from the (substrate-grating) overall response by the polarimetric subtraction method. We show that, provided a specific condition is fulfilled, the individual polarimetric responses of the two areas can be retrieved from the finite spot size measurement by using a special form of the arbitrary decomposition even if none of the individual responses is known a priori. The decomposition method is illustrated on a microelectronics grating structure and its accuracy, as well as limits of applicability, is discussed.

Maximum likelihood method for calibration of Mueller polarimeters in reflection configuration.

We address calibration of Mueller polarimeters in the presence of noise. We compare an extension of the eigenvalue calibration method (ECM) and a maximum likelihood (ML) method. The performances of these two calibration methods are investigated with numerical simulations and real experiments on a broadband infrared polarimeter. It is found that the ML method is superior to the extended ECM in terms of calibration precision and can be used at lower signal-to-noise ratio.

Experimental validation of Mueller matrix differential decomposition.

Mueller matrix differential decomposition is a novel method for retrieving the polarimetric properties of general depolarizing anisotropic media [N. Ortega-Quijano and J. L. Arce-Diego, Opt. Lett. 36, 1942 (2011), R. Ossikovski, Opt. Lett. 36, 2330 (2011)]. The method has been verified for Mueller matrices available in the literature. We experimentally validate the decomposition for five different experimental setups with different commutation properties and controlled optical parameters, comparing the differential decomposition with the forward and reverse polar decompositions. The results enable to verify the method and to highlight its advantages for certain experimental applications of high interest.

Quantification of surface charging memory effect in ionization wave dynamics.

The dynamics of ionization waves (IWs) in atmospheric pressure discharges is fundamentally determined by the electric polarity (positive or negative) at which they are generated and by the presence of memory effects, i.e. leftover charges and reactive species that influence subsequent IWs. This work examines and compares positive and negative IWs in pulsed plasma jets (1 [Formula: see text]s on-time), showing the difference in their nature and the different resulting interaction with a dielectric BSO target. For the first time, it is shown that a surface charging memory effect is produced, i.e. that a significant amount of surface charges and electric field remain in the target in between discharge pulses (200 [Formula: see text]s off-time). This memory effect directly impacts IW dynamics and is especially important when using negative electric polarity. The results suggest that the remainder of surface charges is due to the lack of charged particles in the plasma near the target, which avoids a full neutralization of the target. This demonstration and the quantification of the memory effect are possible for the first time by using an unique approach, assessing the electric field inside a dielectric material through the combination of an advanced experimental technique called Mueller polarimetry and state-of-the-art numerical simulations.

Anisotropy coefficients of a Mueller matrix.

Anisotropy coefficients α, ß, and γ that describe the type and the relative amount of the three kinds of anisotropy generally present in a Mueller matrix are introduced. Their derivation, algebraic properties, and physical interpretation are discussed. In particular, they are shown to permit a geometrical representation for the anisotropy and polarizing characteristics of a Mueller matrix. Illustrative experimental examples are provided.

In-situ monitoring of an organic sample with electric field determination during cold plasma jet exposure.

Pockels-based Mueller polarimetry is presented as a novel diagnostic technique for studying time and space-resolved and in-situ the interaction between an organic sample (a layer of onion cells) and non-thermal atmospheric pressure plasma. The effect of plasma is complex, as it delivers electric field, radicals, (UV) radiation, non-uniform in time nor in space. This work shows for the first time that the plasma-surface interaction can be characterized through the induced electric field in an electro-optic crystal (birefringence caused by the Pockels effect) while at the same moment the surface evolution of the targeted sample is monitored (depolarization) which is attached to the crystal. As Mueller polarimetry allows for separate detection of depolarization and birefringence, it is possible to decouple the entangled effects of the plasma. In the sample three spatial regions are identified where the surface evolution of the sample differs. This directly relates to the spatial in-homogeneity of the plasma at the surface characterized through the detected electric field. The method can be applied in the future to investigate plasma-surface interactions for various targets ranging from bio-films, to catalytic surfaces and plastics/polymers.