Radiation force of a self-focused vortex beam on Rayleigh particles.

The radiation force of a partially coherent self-focusing vortex beam on Rayleigh particles is studied in this paper. According to the generalized Huygens-Fresnel principle and Rayleigh scattering theory, the effects of two main parameters of the beam, namely relative coherence length and non-trivial phase factor, on the self-focusing characteristics and radiation force are respectively researched. We have also conducted a brief analysis of the stability of particle capture using this self-focusing vortex beam.

Asymmetric cosine-Gaussian Schell-model sources.

We introduce a new class of Schell-model source whose spatial correlation function carries a finite series of nontrivial phases and is modulated by cosine function. The propagating formula for the cross-spectral density (CSD) function of the beams generated by this new source in free space is derived and used to investigate the characteristics of the light fields for different modulation parameters. The results show that the appearance of the modulating function and the nontrivial phase sequence cause the radiated fields with extraordinary characteristics during propagation, such as self-splitting and self-interfering in an asymmetric manner.

Atmospheric turbulence effects on hollow Gaussian Schell-model array beams.

Two types of hollow array beams with circular and rectangular distributions on propagating in atmospheric turbulence are investigated and analyzed comparatively with that in free space. Analytical formulas for the cross-spectral density function of two kinds of hollow array beam propagation in linear isotropic random media are derived and used to examine the behavior of the spectral densities. It is found that such beams possess stable hollow arrays with any dimension and lobes in free space, while such distributions only maintain small distances in atmospheric turbulence and ultimately tend to a Gaussian shape due to the turbulence destroying the hollow array profiles.

Spatial correlated vortex arrays.

Spatial correlated vortex arrays may form in the same beam when a random source contains multiple helical phase structures. We introduced two types of partially coherent sources with Cartesian and polar symmetric helical phase structure and reveal the characteristics of their radiated fields, respectively. It is demonstrated that far fields generated by these families of sources carry interesting features through the joint regulation of coherence and topological charge, being lattice-like vortex patterns with adjustable dimension and shape.

Effect of chirped factors on the abrupt autofocusing ability of a chirped circular Airyprime beam.

Recently, a new type of abruptly autofocusing beam called circular Airyprime beam (CAPB) has been reported. Its abrupt autofocusing ability has been proven to be approximately seven times that of a circular Airy beam under the same conditions. Further improving the abrupt autofocusing ability of the CAPB without changing the beam parameters is a concern in optical research.

Random sources with rectangular coherence.

A convenient method for modeling partially coherent sources with rectangular coherence is introduced by structuring the degree of coherence as two separable arbitrary functions with arbitrary dependence of variables. The included examples have demonstrated new opportunities of modeling random sources for beam shaping applications by coherence modulation. The first example discusses a class of rectangular sinc-correlated models generating radiating fields with self-focusing features.

Special correlation model sources producing a self-focusing field.

We evaluate the modes for non-Schell-model sources whose degrees of spectral coherence depend on the difference of the special function values of the position coordinated of two points. It is shown that such sources modulated by various function possess different spatial coherence properties, and cause them to produce the self-focusing fields with different characteristics. The results suggest a convenient method for modeling novel classes of partially coherent self-focusing optical fields.

Self-focusing vortex beams.

A class of wide-stationary optical sources with a specially designed degree of coherence profile is introduced for radiating spectral densities with a vortex whose core's location and size can be controlled at a specified range. This is achieved by modeling of the source coherence state as a combination of a helicoidal separable phase and a Cartesian phase factor, depending on the separation between the $ n $th power of the radius-vectors of two points.

Generalized Schell-model sources.

We evaluate the modes for generalized Schell-model planar source whose complex degree of coherence (CDC) is a function of the n-th power difference of two position coordinates instead of their direct distance between two source points. We discuss through two examples how new classes of CDCs can be devised and how they affect the radiation fields. It is demonstrated that the light beams generated by these families of sources carry interesting propagation characteristics, such as the lateral self-shifting and the self-focusing effect with controllable focal length determined by the non-trivial phase, power n and other source parameters.

Cross-spectral densities with helical-Cartesian phases.

We introduce a class of planar, stationary sources whose cross-spectral densities carry a combination of helical and Cartesian phases. The helical phase is linear, separable in polar coordinates, resulting in a vortex-like average intensity with a dark area centered on the optical axis; the Cartesian counterpart is separable in the x- and y-coordinates and is responsible for asymmetric average intensity redistribution along the x- and y-axes. While endless possibilities exist for modeling of the Cartesian phase factor, in this paper we employ a superposition of linear phases with arbitrarily assigned weighing factors.

Propagation characteristics of a partially coherent self-shifting beam in random media.

In a recent publication [Opt. Lett.43, 4727 (2018)OPLEDP0146-959210.

Asymmetric coherence gratings.

We introduce a class of partially coherent, Schell-type sources whose degree of coherence is represented by a finite series of complex-valued functions. The significance of implementing such a series is due to the fact that one can manipulate the weighting coefficients of its terms having a computationally trivial linear phase of the degree of coherence for obtaining the radiated beams of the same complexity as could only be previously achieved with analytically intractable nonlinear phases. Our examples illustrate new opportunities for modeling asymmetric coherence gratings and lattices.

Hyperbolic sine-correlated beams.

An explicit expression is given for the cross-spectral density that characterizes a new family of partially coherence sources with hyperbolic sine correlated function. Beam conditions for such sources are established. The propagation properties of such partially coherent beams are studied by numerical simulations.

Electromagnetic multi-Gaussian Schell-model vortex light sources and their radiation field properties.

A procedure for modeling the general electromagnetic Schell-model vortex light source is proposed. Based on this method, we introduce a new class of stochastic electromagnetic vortex light sources with multi-Gaussian Schell-model coherence function. The far-field statistical properties of the beams generated by such sources are studied in detail by numerical examples.

Twisted EM beams with structured correlations.

The possibility of restructuring the spectral density of a random light beam up to three times along the propagation path in free space is demonstrated. This can be achieved by prescribing special correlations and different twist factors (by magnitude and/or direction) in the two mutually orthogonal electric field components in the source plane. We also show that the degree of polarization of such a light beam can rotate or not on propagation.

Sources for random arrays with structured complex degree of coherence.

Simultaneous control of the far-field spectral density distribution, together with the modulus and the phase of the complex degree of coherence of a beam radiated by a stationary source, is hard to achieve in view of the intrinsic constraints on the source cross-spectral density. We tackle this problem by employing the Laguerre-Gaussian modes instead of the commonly used Gaussian mode for the source field realizations, in combination with structuring the degree of source coherence radiating to spectral density arrays. We show that the produced spectral density arrays with Cartesian and polar symmetries have special features in both the modulus and the phase of the complex degree of coherence.

Random sources for rotating spectral densities.

The propagating modes of a wide-sense stationary Schell-like source with arbitrary coherence state and a twist factor are determined. This suggests a convenient practical method for modeling novel classes of twisted partially coherent beam-like fields. The first example discusses the previously introduced twisted anisotropic Gaussian Schell-model source and verifies the feasibility of this method.

Electromagnetic Schell-model sources generating far fields with stable and flexible concentric rings profiles.

A class of electromagnetic sources with multi-cosine Gaussian Schell-model correlation function is introduced. The realizability conditions for such sources and the beam conditions for the beams generated by them are established. Analytical formulas for the cross-spectral density matrix of such beams propagating in free space are derived and used to examine their statistical properties by numerical simulations.

Gaussian Schell-model arrays.

We introduce a novel class of planar, quasi-homogeneous Schell-model source for producing far fields with optical lattice average intensity patterns and derive the corresponding beam conditions. The array dimension, lobes intensity profile, and periodicity of the optical lattice can be flexibly tuned by changing the correlation parameters of the source field. It is also found that, with an appropriate choice of the source parameters, the radiant intensity may possess flat-topped intensity patterns.

Random electromagnetic model beams with correlations described by two families of functions.

The electromagnetic Schell-model beams whose cross-spectral matrices have elements belonging to different families of functions are considered for the first time. The spatial distributions of polarization properties of such beams are shown to be made completely or partially different from that of the average intensity.

Source coherence-based far-field intensity filtering.

An inherent relationship between an invariant far-field beam intensity pattern and the convolution of any two legitimate degrees of coherence in the source plane is established. Two classes of random sources are introduced by modeling the source degree of coherence with the help of the convolution operation of the Gaussian Schell-model correlation function and the multi-sinc Schell-model correlation function in the polar and Cartesian symmetries. The established relationships are used to explore the far-field intensity features produced by the new sources.

Convolution of degrees of coherence.

The conditions under which convolution of two degrees of coherence represents a novel legitimate degree of coherence are established for wide-sense statistically stationary Schell-model beam-like optical fields. Several examples are given to illustrate how convolution can be used for generation of a far field being a modulated version of another one. Practically, the convolutions of the degrees of coherence can be achieved by programming the liquid crystal spatial light modulators.

Alternating series of cross-spectral densities.

We establish a sufficient condition under which the alternation series of cross-spectral densities (CSD) constitutes a valid CSD. Using such a condition, we introduce a novel class of multi-sinc Schell-model sources with circular and Cartesian symmetries. It is demonstrated that far fields produced by the new sources carry interesting characteristics, being adjustable multi-rings and lattice patterns.

Powers of the degree of coherence.

We establish conditions under which a legitimate degree of coherence of a statistically stationary beam-like field raised to a power results in a novel legitimate degree of coherence. The general results and examples relate to scalar beams having uniform and non-uniform correlations.

Products of Schell-model cross-spectral densities.

The condition under which a product of two cross-spectral densities (CSD) constitutes a valid correlation function is established. The results are obtained for the CSDs of two one-dimensional, scalar Schell-model sources, but can be readily generalized to other situations. It is shown via a number of numerical examples how new source classes of Schell-model type and the beam-like fields they radiate can be designed.