Peter V. Polyanskii

Partially coherent vortex beams with a separable phase

We propose and experimentally implement a method for the generation of a wide class of partially spatially coherent vortex beams whose cross-spectral density has a separable functional form in polar coordinates. We study phase singularities of the spectral degree of coherence of the new beams.

The Emerging Field of Correlation Optics

Correlation optics provides tools-both conceptual and experimental-for measuring various parameters of an optical field in partial coherence and polarization. This area of study could enable unique applications for industrial quality control, solid-state physics, medical diagnostics and ecological monitoring.

Optical correlation algorithm for reconstructing phase skeleton of complex optical fields for solving the phase problem.

We propose an optical correlation algorithm illustrating a new general method for reconstructing the phase skeleton of complex optical fields from the measured two-dimensional intensity distribution. The core of the algorithm consists in locating the saddle points of the intensity distribution and connecting such points into nets by the lines of intensity gradient that are closely associated with the equi-phase lines of the field. This algorithm provides a new partial solution to the inverse problem in optics commonly referred to as the phase problem.

Singular-optical coloring of regularly scattered white light

When the surface roughness is comparable with the wavelength of the probing radiation, the scattered field contains both the regular (forward-scattered) component of coherent nature and the diffusely scattered part. Coloring of the regular component of white light scattered by a colorless dielectric slab with a rough surface is considered as a peculiar effect of singular optics with zero (infinitely extended) interference fringes. To explain the observed alternation of colors with respect to the increasing depth of the surface roughness, we apply a model of transition layers associated with the surface roughness. By applying the chromascopic technique, it is shown that the modifications of the normalized spectrum of the forward-scattered white light can be interpreted as the effect of a quarter-wavelength (anti-reflecting) layer for some spectral component of a polychromatic probing beam.

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.

Polarization singularities in partially coherent combined beams

Vector singularities are predicted and discovered experimentally in partially polarized combined fields formed by incoherent superposition of orthogonally polarized beams. Such singularities are U contours with zero degree of polarization and isolated P points with unit degree of polarization centered at vortices of the orthogonally polarized component of the combined beam. Crossing a U contour switches the polarization state to the orthogonal one. The above-mentioned singularities are adequately described in terms of the complex degree of polarization in the Stokes-space representation. It is shown that the field elements corresponding to the extrema of the complex degree of polarization form the vector skeleton of a partially coherent nonuniformly polarized field.

Influence of evanescent wave on birefringent microplates

Mechanical action caused by the optical forces connected with the canonical momentum density associated with the local wavevector or Belinfantes spin angular momentum is experimentally verified. The helicity-dependent and the helicity-independent forces determined by spin momenta of different nature open attractive prospects for the use of optical structures for manipulating minute quantities of matter of importance in nanophysics, nanooptics and nanotechnologies, precision chemistry and pharmacology and in numerous other areas. Investigations in this area reveal new, extraordinary manifestations of optical forces, including the helicity-independent force caused by the transverse helicity-independent spin or vertical spin of a diagonally polarized wave, which was not observed and exploited up to recently. The main finding of our study consists in a direct experimental demonstration of the physical existence and mechanical action of this recently discovered extraordinary transverse component of the spin here arising in an evanescent light wave due to the total internal reflection of a linearly polarized probing beam with azimuthal angle 45° at the interface between the birefringent plate and air, which is oriented perpendicularly to the wavevector of an evanescent wave and localized over the boundary of the transparent media with polarization-dependent refraction indices.

New polarization singularities of partially coherent light beams

It is shown that for an incoherent superposition of the orthogonally polarized laser beams the polarization singularities of a new type arise at the transversal cross-section of a paraxial combined beam instead of common singularities, such as amplitude zeroes (optical vortices) inherent in scalar fields, and polarization singularities such as C points and L lines inherent in completely coherent vector fields. There are U contours along which the degree of polarization equals zero and the state of polarization is undetermined (singular), 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. Optical vortices of the orthogonally polarized component lie under P points. P points differ essentially from C points of singular optics of coherent fields by the absence of topological charge and certain morphology of heighborhood (S, M, L). Crossing U line is accompanied by step-like change of the state of polarization onto orthogonal one (sign principle). U and P singularities are represented at a whole Stokes space, namely at and inside of the Poincare sphere. Correlation among completely coherent and completely incoherent vector singularities is considered for the first time. First 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.

Polarization degree singularities

New type of vector singularities inherent in partially coherent combined beams is explored. There are the polarization degree singularities, such as U (unpolarized) and P (completely polarized) elements of a field. The fundamental properties of such singularities are derived for the general case of elliptical polarization basis using the notion of the complex degree of polarization represented at the Stokes space that is limited by the Poincare sphere. Experimental procedure for detecting the polarization degree singularities and reconstruction of a vector skeleton of partially coherent combined beams is presented.

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.