We describe experimental results exposing the possibilities of optical crystals, especially anisotropic and birefringent, for creation, control, and diagnostics of structured light fields with singular and extraordinary properties. The efficiency of birefringent media is demonstrated for purposeful generation of optical beams with phase singularities (optical vortices) and desirable patterns of internal energy flows, in both the mono- and polychromatic light. On the other hand, anisotropic micro-objects can be used as probing bodies for investigation of the peculiar features of internal energy flows and corresponding momentum and angular momentum distributions in structured light fields. In particular, the specific mechanical action of light fields, formed under the total-reflection conditions, has been detected that confirms the existence of “extraordinary” dynamical characteristics of evanescent light waves predicted theoretically: the “transverse” momentum and “vertical” spin and their dependence on the incident beam polarization. The results can be useful for the optical trapping and micromanipulation techniques, including the biomedical and pharmaceutical applications.

The review describes general principles and characteristics of inhomogeneously polarized paraxial optical fields and, especially, the polarization singularities (PSs). Main parameters of the optical vector waves are discussed, with the emphasis on the physical relevance and topological distinctiveness of the PSs. Special features of the stochastic vector fields are considered in the context of the PSs’ genericity and structural stability. A detailed attention is paid to interrelations between the PSs and the phase singularities of scalar fields formed by the orthogonal polarization projections of the total field, and their derivatives (complex Stokes fields, phase-difference fields, etc.). On this base, the practical approaches are discussed for the experimental PS identification and characterization. A particular examination of the internal energy flows associated with the PSs, and accompanying distributions of the optical momentum and angular momentum, reveals meaningful dynamical features of PSs and supplies additional physically transparent and informative means for their studies and characterization.

Over the past 30 years, physical optics has been enriched by the appearance of singular optics as a new branch approved in scientific classifiers. This review briefly outlines the main concepts of the singular optics, their role in physical research and applications, and prospects of further development. The wave singularities are considered as a sort of structured-light elements and analyzed based on the generic example of screw wavefront dislocation (optical vortex). Their specific topological and mechanical properties associated with the transverse energy circulation are discussed. Peculiar features of the non-linear optical phenomena with singular fields are exhibited, with the special attention to generation of multidimensional entangled quantum states of photons. Optical fields with multiple singularities, especially, the stochastic speckle fields, are discussed in the context of optical diagnostics of random scattering objects. The exact and approximate correspondences between characteristic parameters of the optical-field intensity and phase distributions are analyzed with the aim of recovering phase information from the intensity measurements (“phase problem” solution). Rational singularity-based approaches to informative measurements of the scattered-field distribution are discussed, as well as their employment for the objects’ diagnostics. In particular, the practical instruments are described for the high-precision rough-surface testing. Possible enhancements of the singular-optics ideas and concepts in a wider context, including the transformation optics, near-field optics (surface waves), partially-coherent fields, and wave fields of other physical nature, are briefly exposed.

SignificanceThe interference-holographic method of phase scanning of fields of scattered laser radiation is proposed. The effectiveness of this method for the selection of variously dispersed components is demonstrated. This method made it possible to obtain polarization maps of biological tissues at a high level of depolarized background. The scale-selective analysis of such maps was used to determine necrotic changes in the optically anisotropic architectonics of biological tissues.ObjectiveDevelopment and experimental approbation of layered phase polarimetry of repeatedly scattered fields in diffuse layers of biological tissues. Application of scale-selective processing of the found coordinate distributions of polarization states in various phase sections of object fields. Determination of criteria (markers) for histological differential diagnosis of the causes of necrotic changes in optical anisotropy of biological tissues.ApproachWe used a synthesis of three instrumental and analytical methods. Polarization-interference registration of laser radiation scattered by a sample of biological tissue. Digital holographic reconstruction and layered phase scanning of distributions of complex amplitudes of the object field. Analytical determination of polarization maps of various phase cross-sections of repeatedly scattered radiation. Application of wavelet analysis of the distributions of polarization states in the phase plane of a single scattered component of an object field. Determination of criteria (markers) for differential diagnosis of necrotic changes in biological tissues with different morphological structure. Two cases are considered. The first case is the myocardium of those who died as a result of coronary heart disease and acute coronary insufficiency. The second case is lung tissue samples of deceased with bronchial asthma and fibrosis.ResultsA method of polarization-interference mapping of diffuse object fields of biological tissues has been developed and experimentally implemented. With the help of digital holographic reconstruction of the distributions of complex amplitudes, polarization maps in various phase sections of a diffuse object field are found. The wavelet analysis of azimuth and ellipticity distributions of polarization in the phase plane of a single scattered component of laser radiation is used. Scenarios for changing the amplitude of the wavelet coefficients for different scales of the scanning salt-like MHAT function are determined. Statistical moments of the first to fourth orders are determined for the distributions of the amplitudes of the wavelet coefficients of the azimuth maps and the ellipticity of polarization. As a result, diagnostic markers of necrotic changes in the myocardium and lung tissue were determined. The statistical criteria found are the basis for determining the accuracy of their differential diagnosis of various necrotic states of biological tissues.ConclusionsNecrotic changes caused by “coronary artery disease–acute coronary insufficiency” and “asthma–pulmonary fibrosis” were demonstrated by the method of wavelet differentiation with polarization interference with excellent accuracy.

The experimental validation of methods for the digital holographic 3D layer-by-layer reconstruction of complex amplitude distributions in different phase planes of diffuse biological tissue histological section microscopic images with a subsequent reconstruction of azimuth and ellipticity polarization maps is presented. Polarization dependencies of the integral and layer-by-layer vector structure of the laser object field azimuth and ellipticity distributions in two types of biological layer samples—the fibrous myocardium and parenchymal liver—have been investigated. Scenarios and dynamics of changes in the values of statistical moments of the first to fourth orders, which characterize the integral and layer-by-layer polarization maps of diffuse biological tissue histological section microscopic images with different morphological structures, have been determined. Criteria for selecting the polarization components of the object field that are formed by acts of scattering of different multiplicities have been identified. An example of biomedical application in cancer detection of biological tissues is provided.

This study focuses on the topographic structure of optical anisotropy maps (theziograms) of dehydrated blood plasma films (facies) to identify and utilize markers for diagnosing self-similarity (multifractality) in the birefringence parameters of supramolecular protein networks. The research is based on the Jones-matrix analytical framework, which describes the formation of polarization-structural speckle fields in polycrystalline blood plasma facies. In the proposed model, algorithms were developed to relate the real and imaginary parts of the complex elements of the Jones matrix to the theziograms of linear and circular birefringence. To experimentally implement these algorithms, a novel optical technology was introduced for polarization-interference registration and phase scanning of the laser speckle field of blood plasma facies. The laser-based Jones-matrix layer-by-layer theziography relies on polarization filtration and the digital recording of interference patterns from microscopic images of blood plasma facies. This process includes digital 2D Fourier reconstruction and phase-by-phase scanning of the object field of complex amplitudes, enabling the acquisition of phase sections of laser polarization-structural speckle field components scattered with varying multiplicities. Jones-matrix images of supramolecular networks, along with their corresponding theziograms of linear and circular birefringence, were obtained for each phase plane. The experimental data derived from laser layer-by-layer Jones-matrix theziography were quantitatively analyzed using two complementary approaches: statistical analysis (central moments of the 1st to 4th orders) and multifractal analysis (spectra of fractal dimension distributions). As a result, the most sensitive markers—namely asymmetry and kurtosis—were identified, highlighting changes in the statistical and scale self-similar structures of the theziograms of linear and circular birefringence in blood plasma facies. The practical aspect of this work is to evaluate the diagnostic potential of the Jones-matrix theziography method for identifying and differentiating changes in the birefringence of supramolecular networks in blood plasma facies caused by the long-term effects of COVID-19. For this purpose, a control group (healthy donors) and three experimental groups of patients, confirmed to have had COVID-19 one-to-three years prior, were formed. Within the framework of evidence-based medicine, the operational characteristics of the method—sensitivity, specificity, and accuracy—were assessed. The method demonstrated excellent accuracy in the differential diagnosis of the long-term effects of COVID-19. This was achieved by statistically analyzing the spectra of fractal dimensions of Jones-matrix theziograms reconstructed in the phase plane of single scattering within the volume of blood plasma facies.