Nonparaxial accelerating waves as a superposition of nondiffracting Bessel-lattice optical fields.

In the first part of this work, we introduce a monochromatic solution to the scalar wave equation in free space, defined by a superposition of monochromatic nondiffracting half Bessel-lattice optical fields, which is determined by two scalar functions; one is defined on frequency space, and the other is a complete integral to the eikonal equation in free space. We obtain expressions for the geometrical wavefronts, the caustic region, and the Poynting vector. We highlight that this solution is stable under small perturbations because it is characterized by a caustic of the hyperbolic umbilical type. In the second part, we introduce the corresponding solution to the Maxwell equations in free space.

Experimental determining the coherent-mode structure of vector electromagnetic field through its decomposition in reference basis.

A technique for experimental determining the coherent-mode structure of electromagnetic field is proposed. This technique is based on the coherence measurements of the field in some reference basis and represents a nontrivial vector generalization of the dual-mode field correlation method recently reported by F. Ferreira and M. Belsley [Opt. Lett.38(21), 4350 (2013)]. The justifiability and efficiency of the proposed technique is illustrated by an example of determining the coherent-mode structure of some specially generated and experimentally characterized secondary electromagnetic source.

Self-focusing transmittances.

In this Letter, we describe the optical field associated with transmittances characterized by a slit-shaped curve. The influence of the curvature is that the diffraction field generates focusing regions. The focusing geometry corresponds to the geometry of the transmittance curve, except for scaling, rotations or translations. A relevant point is that the changes in the morphology of the diffraction field are bounded by the focusing regions. Our experimental and computational results are in good agreement with the theoretical predictions.

The van Cittert-Zernike theorem for electromagnetic fields.

The van Cittert-Zernike theorem, well known for the scalar optical fields, is generalized for the case of vector electromagnetic fields. The deduced theorem shows that the degree of coherence of the electromagnetic field produced by the completely incoherent vector source increases on propagation whereas the degree of polarization remains unchanged. The possible application of the deduced theorem is illustrated by an example of optical simulation of partially coherent and partially polarized secondary source with the controlled statistical properties.

Modulation of coherence and polarization using liquid crystal spatial light modulators.

We propose a method for modulation of coherence and polarization of electromagnetic fields, employing two crossed zero-twisted nematic liquid crystal spatial light modulators. In contrast to a similar technique analyzed by Shirai and Wolf [J. Opt. Soc. Am A, 21, 1907, (2004)] our method provides a wide range simultaneous modulation of coherence and polarization. The dependence of the obtained results on different definitions of electromagnetic coherence is considered.

Impact of velocity distribution assumption on simplified laser speckle imaging equation.

Since blood flow is tightly coupled to the health status of biological tissue, several instruments have been developed to monitor blood flow and perfusion dynamics. One such instrument is laser speckle imaging. The goal of this study was to evaluate the use of two velocity distribution assumptions (Lorentzian- and Gaussian-based) to calculate speckle flow index (SFI) values. When the normalized autocorrelation function for the Lorentzian and Gaussian velocity distributions satisfy the same definition of correlation time, then the same velocity range is predicted for low speckle contrast (0 < C < 0.6) and predict different flow velocity range for high contrast. Our derived equations form the basis for simplified calculations of SFI values.

Generation of partially coherent diffraction-free fields with tunable geometry.

The synthesis of diffraction-free fields with different profiles is described. The synthesis is done by illuminating a screen containing a circular slit with a cosine beam. The treatment is equivalent to the modulation of the slit transfer characteristics and makes possible a tunable interference interaction of Bessel beams with noncommon axes. These results are generalized, and it is shown that coherent diffraction-free fields with arbitrary profiles can be expressed as the superposition of shifted zero-order Bessel beams and temporary parametric representations of the shifted functions. Diffraction-free fields with partially coherent features can be obtained. Experimental results are shown for each case.