Physical significance of the determinant of a Mueller matrix

The determinant of a Mueller matrix M plays an important role in both polarization algebra and the interpretation of polarimetric measurements. While certain physical quantities encoded in M admit a direct interpretation, the understanding of the physical and geometric significance of the determinant of M (detM) requires a specific analysis, performed in this work by using the normal form of M, as well as the indices of polarimetric purity (IPP) of the canonical depolarizer associated with M. We derive an expression for detM in terms of the diattenuation, polarizance and a parameter proportional to the volume of the intrinsic ellipsoid of M. We likewise establish a relation existing between the determinant of M and the rank of the covariance matrix H associated with M, and determine the lower and upper bounds of detM for the two types of Mueller matrices by taking advantage of their geometric representation in the IPP space

Algorithm for the numerical calculation of the serial components of the normal form of depolarizing Mueller matrices

The normal form of a depolarizing Mueller matrix constitutes an important tool for the phenomenological interpretation of experimental polarimetric data. Due to its structure as a serial combination of three Mueller matrices, namely a canonical depolarizing Mueller matrix sandwiched between two pure (nondepolarizing) Mueller matrices, it overcomes the necessity of making a priori choices on the order of the polarimetric components, as this occurs in other serial decompositions. Because Mueller polarimetry addresses more and more applications in a wide range of areas in science, engineering, medicine, etc., the normal form decomposition has an enormous potential for the analysis of experimentally determined Mueller matrices. However, its systematic use has been limited to some extent because of the lack of numerical procedure for the calculation of each polarimetric component, in particular in the case of Type II Mueller matrices. In this work, an efficient algorithm applicable to the decomposition of both Type II and Type I Mueller matrices is presented

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.Agència de Gestió d'Ajuts Universitaris i de Recerca, Grant/Award Number: 2017-SGR-001500; Ministerio de Economía y Competitividad, Grant/Award Numbers: Fondos FEDER, RTI2018-097107-B-C3

Light depolarization effects in tip enhanced Raman spectroscopy of silicon (001) and gallium arsenide (001)

We report on the effects of light depolarization induced by sharp metallic tips in Tip-Enhanced Raman Spectroscopy (TERS). Experiments on Si(001) and GaAs(001) crystals show that the excitation field depolarization induces a selective enhancement of specific Raman modes, depending on their Raman tensor symmetry. A complete polarization analysis of the light backscattered from the tip confirms the TERS findings. The spatial confinement of the depolarization field is studied and its dependence on the excitation wavelength and power are explored

Experimental validation of the reverse polar decomposition of depolarizing Mueller matrices

We experimentally assess the validity of the reverse polar decomposition (R. Ossikovski et al., Opt. Lett. 32, 689 (2007)), which describes any Mueller matrix as a product of a depolarizer, a diattenuator and a retarder with the diattenuator placed after the depolarizer and not before, as in the well-known Lu and Chipman’s forward decomposition. The raw data are Mueller images of a depolarizer (dilute milk at variable concentrations), followed by two tilted glass plates as a diattenuator and a mica retardation plate. While the reverse decomposition accurately reconstructs the component matrices in all cases, the usual forward decomposition provides reasonable values only for the trace of the depolarizer matrix, the other quantities being affected by gross errors. The potential interest of this decomposition for biological samples is briefly discussed

Hydrostatic strain enhancement in laterally confined SiGe nanostripes

Strain-engineering in SiGe nanostructures is fundamental for the design of optoelectronic devices at the nanoscale. Here we explore a new strategy, where SiGe structures are laterally confined by the Si substrate, to obtain high tensile strain avoiding the use of external stressors, and thus improving the scalability. Spectro-microscopy techniques, finite element method simulations and ab initio calculations are used to investigate the strain state of laterally confined Ge-rich SiGe nano-stripes. Strain information is obtained by tip enhanced Raman spectroscopy with an unprecedented lateral resolution of ~ 30 nm. The nano-stripes exhibit a large tensile hydrostatic strain component, which is maximum at the center of the top free surface, and becomes very small at the edges. The maximum lattice deformation is larger than the typical values of thermally relaxed Ge/Si(001) layers. This strain enhancement originates from a frustrated relaxation in the out-of-plane direction, resulting from the combination of the lateral confinement induced by the substrate side walls and the plastic relaxation of the misfit strain in the (001) plane at the SiGe/Si interface. The effect of this tensile lattice deformation at the stripe surface is probed by work function mapping, performed with a spatial resolution better than 100 nm using X-ray photoelectron emission microscopy. The nano-stripes exhibit a positive work function shift with respect to a bulk SiGe alloy, quantitatively confirmed by electronic structure calculations of tensile strained configurations. The present results have a potential impact on the design of optoelectronic devices at a nanometer length scale.Comment: 40 pages, 11 figures, submitted to Physical Review

Fast spectrally encoded Mueller optical scanning microscopy

Mueller microscopes enable imaging of the optical anisotropic properties of biological or non-biological samples, in phase and amplitude, at sub-micrometre scale. However, the development of Mueller microscopes poses an instrumental challenge: the production of polarimetric parameters must be sufficiently quick to ensure fast imaging, so that the evolution of these parameters can be visualised in real-time, allowing the operator to adjust the microscope while constantly monitoring them. In this report, a full Mueller scanning microscope based on spectral encoding of polarization is presented. The spectrum, collected every 10 μs for each position of the optical beam on the specimen, incorporates all the information needed to produce the full Mueller matrix, which allows simultaneous display of all the polarimetric parameters, at the unequalled rate of 1.5 Hz (for an image of 256 × 256 pixels). The design of the optical blocks allows for the real-time display of linear birefringent images which serve as guidance for the operator. In addition, the instrument has the capability to easily switch its functionality from a Mueller to a Second Harmonic Generation (SHG) microscope, providing a pixel-to-pixel matching of the images produced by the two modalities. The device performance is illustrated by imaging various unstained biological specimens

Complementary analysis of Mueller-matrix images of optically anisotropic highly scattering biological tissues

Background: Using optical techniques for tissue diagnostics (so-called ‘optical biopsy’) has been a subject of extensive research for many years. Various groups have been exploring different spectral and/or imaging modalities (e.g. diffuse reflectance spectroscopy, autofluorescence, Raman spectroscopy, optical coherence tomography (OCT), polarized light microscopy, etc.) for biomedical applications. In this paper, we report on using multi-wavelength imaging Mueller polarimetry combined with an appropriated image post-processing for the detection of tissue malignancy. Methods: We investigate a possibility of complementary analysis of Mueller matrix images obtained for turbid tissue-like scattering phantoms and excised human normal and cancerous colorectal tissue samples embedded in paraffin. Combined application of correlation, fractal and statistical analysis was employed to assess quantitatively the polarization-inhomogeneous scattered fields observed at the surface of tissue samples. Results: The combined analysis of the polarimetric images of paraffin-embedded tissue blocks has proved to be an efficient tool for the unambiguous detection of tissue malignant transformation. A fractal structure was clearly observed at spatial distributions of depolarization of light scattered in healthy tissues in a visible range of spectrum, while corresponding distributions for cancerous tissues did not show such dependence. We demonstrate that paraffin does not destroy a fractal structure of spatial distribution of depolarization. Thus, the loss of fractality in spatial distributions of depolarization for cancerous tissue is related to the structural changes in the tissue sample induced by cancer itself and, therefore, may serve as a marker of the disease. Conclusion: The obtained results emphasize that a combined use of statistical, correlation and fractal analysis for the Mueller-matrix image post-processing is an effective approach for an assessment of variations of optical properties in turbid tissue-like scattering media and biological tissues, with a high potential to be transferred to clinical practice for screening cancerous tissue samples

Phonon driven transport in amorphous semiconductors: Transition probabilities

Inspired by Holstein's work on small polaron hopping, the evolution equations of localized states and extended states in presence of atomic vibrations are derived for an amorphous semiconductor. The transition probabilities are obtained for four types of transitions: from one localized state to another localized state, from a localized state to an extended state, from an extended state to a localized state, and from one extended state to another extended state. At a temperature not too low, any process involving localized state is activated. The computed mobility of the transitions between localized states agrees with the observed `hopping mobility'. We suggest that the observed `drift mobility' originates from the transitions from localized states to extended states. Analysis of the transition probability from an extended state to a localized state suggests that there exists a short-lifetime belt of extended states inside conduction band or valence band. It agrees with the fact that photoluminescence lifetime decreases with frequency in a-Si/SiO$_{2}$ quantum well while photoluminescence lifetime is not sensitive to frequency in c-Si/SiO$_{2}$ structure.Comment: 41 pages, 3 figures, submitted to Phys. Rev.