Halina V. Bogatyryova

Vector singularities of the combined beams assembled from mutually incoherent orthogonally polarized components

It is shown that, for an incoherent superposition of the orthogonally polarized laser beams, the vector singularities of a specific type arise at the transversal cross section of a paraxial combined beam instead of common singularities, such as amplitude zeros or optical vortices (inherent in scalar, i.e. homogeneously polarized, fields), and C points, where polarization is circular, and L lines, along which polarization is linear (inherent in completely coherent vector, i.e. inhomogeneously polarized fields). There are U lines (closed or closing at infinity) along which the degree of polarization equals zero and the state of polarization is undetermined, and isolated P points where the degree of polarization equals unity and the state of polarization is determined by the non-vanishing component of the combined beam. U surfaces and P lines correspond to such singularities in three dimensions, by analogy with L surfaces and C lines in three-dimensional completely coherent vector fields. P lines directly reflect the snake-like distortions of a wavefront of the singular component of the combined beam. Crossing of the U line (surface) is accompanied by a step-like change of the state of polarization onto the orthogonal one. U and P singularities are adequately described in terms of the complex degree of polarization with the representation at the Stokes space, namely at and inside of the Poincare sphere. The conditions of topological stability of U and P singularities are discussed, as well as the peculiarities of the spatial distribution of the degree of polarization in the closest vicinity to such singularities. Experimental examples of reconstruction of the combined beams vector skeleton formed by U and P singularities as the extrema of the complex degree of polarization are given. Comparison with the related investigations is provided.

Optical Measurements: Polarization and Coherence of Light Fields

The Chapter is devoted to consideration of metrological aspects of intrinsically interconnected characteristics of light fields, such as intensity, polarization and coherence. Conceptually, all these quantities are derived from the Wolf’s coherency matrix [1]. However, new insight on interconnection of them is provided by the novel singular-optical approach [2, 3] predicting existence of important regularities in electromagnetic fields which were early considered as quite random ones. So, phase singularities of scalar (homogeneously polarized), polarization singularities of vector (inhomogeneously polarized) fields, as well as singularities of correlation functions of partially coherent, partially polarized fields constitute specific skeletons, i.e. “bearing” elements of a field. Knowing the loci and characteristics of such elements, one can judge on behavior of a field at its other areas, at least in qualitative manner, but quite reliably [4]. This circumstance opens quite new possibilities for metrology of optical fields and leads to prospective practical applications of new metrological techniques.

Comparative analysis of techniques for diagnostics of phase singularities

The comparative analysis of several techniques for diagnostics of phase singularities in the optical vortex beams and fields is performed. Both advantages and disadvantages in the implementation and applications of different techniques are discussed.

Reincarnations of optical singularities

In this paper, the chain of mutual transformations of optical singularities is demonstrated, including coherence singularities, polarization singularities of different kinds, and phase singularities. It is shown in what a way one can transform some type of optical singularities into another by changing one of the experimental parameters. Convenient experimental technique for diagnostics of such singularities is also described. It is shown that some of the considered singularities are generic ones, while other are non-generic, implying specific experimental conditions.

Young's diagnostics of spatial coherence phase singularities

We report the feasibilities for revealing and diagnostics of unconventional phase singularities into optical fields, namely, the singularities of spatial coherence functions into partially coherent vortex beams. It is shown that the vortices of the spatial coherence function are comprehensively diagnosed through the strip version of the Thomas Youngs interference experiment. Namely, the magnitude of a topological charge and its sign are determined, respectively, by the magnitude and the direction of bending of the Youngs interference fringes, which are produced by the edge diffraction waves from the rims of an opaque strip positioned in the vortex beam. Such experiment provides complete data on the azimuthal behavior of a phase of the spatial coherence function. On the other hand, non-localized ring singularities of the spatial coherence function and of the complex degree of coherence occurring in the radial distribution of a phase are detected through conventional Youngs interference experiment with two pinholes at an opaque screen. It is remarkable that the last of the mentioned coherence phase singularities takes place, when amplitude zeroes of the field are absent. Instead of this, the modulus of the complex degree of coherence vanishes alone.

Differentiating the phase structures of doughnut-like beams with similar intensity envelopes

We represent the straightforward techniques for differentiation of the phase structures of light beams of various origin but having similar intensity envelopes using doughnut-like beams as an example. Namely, we compare the phase structure of the set of beams: (i) a ring beam with smooth (vortexless) wavefront but with artificially introduced central amplitude zero, with Gaussian radial intensity distribution; (ii) Laguerre-Gaussian mode LG10+1 with the central vortex; (iii) combined beam assembled from uncorrelated weighed Laguerre-Gaussian modes LG10 and LG11 with the central screw dislocation and with the ring edge dislocation of the spatial coherence function; (iv) combined beam assembled from uncorrelated Hermite-Gaussian modes HG10 and HG10 ; (v) combined beam assembled from correlated but orthogonal in polarization Hermite-Gaussian modes HG10 and HG10 ; (vi) combined beam assembled from uncorrelated and orthogonal in polarization Hermite-Gaussian modes HG10 and HG10 . Experimental analysis and comparison of the phase structures (i) and (ii) can be performed using a common interference technique with off-axis reference wave. Other mentioned cases cannot be analyzed by applying this technique. To differentiate the corresponding phase structures and associated singularities, we attract the united technique based on edge diffraction and use of an opaque strip screen placed at the analyzed beam. In cases (v) and (vi), this technique is added by 2D Stokes polarimetry. The proposed techniques provide reliable diagnostics of common optical vortices, vortices of the spatial correlation functions, polarization singularities of completely (but inhomegeneously) polarized light beams, and the singularities of the complex degree of polarization from typical bending or a half-period shift of the Young’s interference fringes at the shadow of the strip screen.

Non-generated on wave length double phase conjugation based on second-order static holograms

We represent the double phase conjugation technique for uncorrelated complex optical signals at arbitrarily different (incommensurable) wave lengths for implementation of long-term (archive) storage, i.e. coupling and mutual associative reconstruction of such signals. The essence of the proposed approach consists in exploiting natural recording nonlinearity of a static hologram that results in formation of the combined (summation) pseudogratings corresponding to the quadratic component of the amplitude response of a static nonlinearly recorded hologram. In contrast to earlier (real-time holography) version of the double phase conjugation using photorefractive crystals, we use for the each signal wave collimated (plane) reference wave, so that the wave vectors of two reference waves are strictly opposite to each other. It is shown that under these conditions nonlinear mixing of two sets of cross-gratings results in formation of the complete set of pseudogratings constituting a second-order hologram defined, following H.J. Caulfield, as ‘a hologram between two (linear) holograms’. Being read out by any of two stored signals or its incomplete/distorted version (in absence of the reference waves, just as in a photorefractive prototype), a hologram reconstructs the phase-conjugate replica of the second signal (heteroassociative response) at the wavelength of the readout beam, with predictable on the wavelength ratio scaling and angular shift from the nominal position. Especial attention is paid to determination of the experimental conditions for providing the combination pseudogratings to be thin (by applying the Klein’s parameter), if even the partial cross-gratings are thick (volume), by proper choice of the angular conditions of the experiment. If this condition is violated, the Bragg selectivity can hinder heteroassociative reconstruction.

Graph-analytic technique for data routing in nonlinear holographic associative memories

We derive the graph-analytic representation of influence of the higher-order nonlinearities (including the third and fourth ones) of holographic recording on the associative properties of second-order holograms defined as ‘holograms between two holograms’. It is shown that the higher-order nonlinearities of the amplitude response of a hologram do not only cause the noise contribution into conjugate associative response, but in some scenarios of formation of the second-order hologram just predetermine reconstruction of this response. Using the proposed technique, we analyze various cases of imposed (sequential) record of partial signals within the framework of the model of multiple diffraction at hologram structure. We discuss the cases when reconstruction of the conjugate associative response is provided by the presence of the hierarchy of combination pseudogratings, rather than by the ‘direct’ interference mechanism that lies in the base of conventional holographic associative storage, using ghost-image holograms. The represented results expand considerably functional feasibilities of the phase-conjugation associative memories on the base of static holograms.

Autocorrelation diagnostics of phase singularities in diffracted optical fields

The autocorrelation technique applied to diagnostics of phase singularities arising in diffraction patterns is presented for the first time. The proposed technique is based on the Young-Rubinowicz model of diffraction phenomena (model of the edge diffraction wave) and consists in analysis of bending or shift of interference fringes, which are produced by the waves from two edges of narrow opaque strip placed in the beam. This original approach has been applied previously for detection and diagnostics of optical vortices in Laguerre-Gaussian beams, in combined partially coherent/ partially polarized beams as well as in speckle fields. Here we show applicability of the same experimental approach for detecting another type of optical singularities, viz. edge (rather than screw) dislocations of optical wave fronts. Such technique is of especial importance when the use of separate reference wave (cross-correlation approach) is hampered due to incomplete spatial coherence of the analyzed beam or its complex polarization structure. We demonstrate practicability of the proposed technique with instructive examples of typical diffraction patters both in Fraunhofer and Fresnel zones. Besides, our experiments show structural stability of edge dislocations in diffraction patterns. Namely, if even amplitude zeroes are ‘hidden’, then autocorrelation technique provides detecting at least component singularity.

Scattering-induced spectral changes

The model of intermediately rough surface as the specific anti-reflection layer is presented for explaining the coloring of the regular component of a white-light beam forward scattered by a colorless glass with such surface. It is shown that this model predicts the sequence of colors of the forward scattered component of a white-light beam that is observed in practice. New experimental arguments supported this approach are provided.