Christina V. Felde

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.

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.

Some new experiments with scattering induced spectral changes

New experimental data are represented supporting the model of intermediary rough surface of colorless dielectric slab as transition peculiar layer between two media with different refraction indices. Here we consider reflection of white-light beam from such surfaces of ground glass for which rms deviations from a mean surface line is comparable with a wavelength of some spectral component of probing beam. It is shown, in part, that regularly (coherently) Scattered light can undergo several blue and red shifts as the angle of incidence of the probing beam changes. Peculiarities of this phenomenon are discussed using chromascopic processing of regularly reflected light.

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.

Influence of the higher-order nonlinearities in embodying the second-order holographic associative memories

Recording nonlinearity is conventionally considered as the source of noise in holographic imaging. Important exclusion from this general statement is nonlinear holographic associative memory, where the quadratic recording nonlinearity causes true brightness rendering and the possibility for associative coupling and reconstructing optical signals of arbitrary complexity which are stored at the same carrier without interference. In this paper we discuss the role of nonlinearities of an amplitude response of a hologram of the orders higher than the quadratic one in implementing the second-ordered holographic associative memory. We show that higher-order nonlinearities are also involved in implementing this type of memory. This conclusion may be of importance for interpretation of biological/human memory also. The highlight of our study is the conclusion that reconstruction of the complex conjugate heteroassociative response is provided directly, viz. by the set of specified by us pseudogratings, rather than by the mechanism of sequential diffractions.

Polarization structure of combined vortex beams

Nongeneric polarization structures of the vortex beams resulting from coherent coaxial mixing of orthogonally polarized one-charged Laguerre-Gaussian modes with different mode numbers are analyzed. General solution is derived for a superposition of elliptically orthogonally polarized partial vortex beams, and the limiting partial cases when the mixed modes are polarized linearly or circularly are explored both theoretically and experimentally. It is established that in such combined beams unusual spatially stable polarization structures arise, such as closed C -- contours and L -- contours with a constant azimuth of linear polarization.