Sources for random arrays with structured complex degree of coherence

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.

Radial phased-locked Laguerre-Gaussian correlated schell-model beam array

A new beam array called radial phased-locked Laguerre-Gaussian correlated Schell-model (LGCSM) beam array is presented, the beamlet of this beam array is partially coherent beam with Laguerre Gaussian-Schell model correlation. The propagation expression of a radial phased-locked LGCSM beam array in free space is derived. It is aimed to give the effect of beam parameters on evolutions of beam array composed by LGCSM beam. The radial phased-locked LGCSM beam array has unique properties on propagation, the intensity of such beam array will evolve from a beam array composed of Gauss beams into a beam array formed of LGCSM beams. Furthermore, the intensity evolutions of such beam array are modulated by coherence length and beam order of beamlets. The obtained results are important in areas such as light field shaping, and free space optical communication.

Azimuthally periodic and radially quasi-periodic Bessel-correlated fields

We introduce a class of partially coherent sources, which are capable of producing beams with radially quasi-periodic and azimuthally fully periodic intensity profiles. The physical properties of the source, as well as the propagation of the intensity distribution and the complex degree of spatial coherence of the ensuing beams are investigated and interpreted. It is shown that the shape and symmetry of the intensity and the degree of spatial coherence are generally adjustable and modulated by the parameters related to the beam source. Moreover, the periodic changes of intensity arise from the discontinuity of the phase. The results provide a method for synthesizing fields with peculiar periodic intensity distributions in polar coordinates.

Twisted anisotropic electromagnetic beams with Laguerre Gaussian-Schell model correlation

A class of twisted anisotropic electromagnetic beams with Laguerre Gaussian-Schell model correlation is introduced as an extension of the scalar beams into electromagnetic domain. The analytical formula for the cross-spectral density matrix of such a beam on propagation has been derived. Then the degree of coherence, the degree of polarization and the state of polarization are discussed in detail. Our results reveal that it is feasible and efficient to engineer the characteristics of beams via setting the anisotropy of the beam source, the topological charge, and specially the twisted factor. This provides us a method for synthesizing fields presenting peculiar coherence and polarization patterns.

Hollow rectangular multi-Gaussian Schell-model source

We introduced a new class of a partially coherent source that can generate a field with a hollow rectangular profile, named the hollow rectangular multi-Gaussian Schell-mode source. The dependence of distribution of far-zone spectral density on the properties of the proposed source was analyzed. The results show that one can control the distribution properties of the far-zone intensity profile, including the thickness of the hollow edge, the shape of the hollow, the size of the hollow, and the orientation of the hollow, by adjusting the corresponding structural parameters of the source.

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. Such construction is analytically and experimentally useful in general and, in particular, as we show, for generation of asymmetric vortex lattices.

Random sources generating hollow array beams

A novel class of partially coherent light sources that can yield stable optical lattice termed hollow array in the far field is introduced. The array dimension, the distance of hollow lobes intensity profile, the size and shape of the inner and outer lobe contours and other features can be flexibly controlled by altering the source parameters. Further, every lobe can be shaped with polar and Cartesian symmetry and even combined to form nested structures. The applications of the work are envisioned in material surface processing and particle trapping.

Electromagnetic Schell-model beams with arbitrary complex correlation states

A recently suggested technique for modeling of the complex coherence states of scalar stationary light beams [Opt. Lett.43, 4727 (2018)OPLEDP0146-959210.1364/OL.43.004727] is extended to the electromagnetic (EM) domain. It is shown that spatially varying phase profiles of the 2×2 source correlation matrix allow for fine, independent, two-dimensional spatial control of the three components of the polarization matrix in the far field. An EM coherence sorter based on the linear phases of the coherence matrix components is introduced which enables spatial separation of the three independent components of the far-field polarization matrix without affecting their initial distributions.

Generalized partially coherent beams with nonseparable phases

A new, to the best of our knowledge, family of partially coherent beams incorporating a set of nonseparable phases is introduced. Due to the nonnegative definiteness of the cross-spectral density function, these phases cannot survive in the limit of full coherence, which distinguishes them from conventional phase terms. An example of a nonuniform model beam with a quartic nonseparable phase is presented. It is shown that the presence of such a phase in effect stretches the beam in a specific direction upon propagation. In particular, the interplay between the magnitude and phase of the source coherence state endows the beam with a wing-like structure. The fundamental concept developed here brings into evidence the countless nonseparable phases differing from twist, and can be exploited to generate customized partially coherent beams for applications in optics.

Numerical Approach for Studying the Evolution of the Degrees of Coherence of Partially Coherent Beams Propagation through an ABCD Optical System

In this paper, we propose a numerical approach to simulate the degree of coherence (DOC) of a partially coherent beam (PCB) with a Schell-model correlator in any transverse plane during propagation. The approach is applicable for PCBs whose initial intensity distribution and DOC distribution are non-Gaussian functions, even for beams for which it is impossible to obtain an analytical expression for the cross-spectral density (CSD) function. Based on our approach, numerical examples for the distribution of the DOC of two types of PCBs are presented. One type is the partially coherent Hermite–Gaussian beam. The simulation results of the DOC agree well with those calculated from the analytical formula. The other type of PCB is the one for which it is impossible to obtain an analytical expression of CSD. The evolution of the DOC with the propagation distance and in the far field is studied in detail. Our numerical approach may find potential applications in optical encryption and information transfer.

Controllable rotating Gaussian Schell-model beams

Optical twists are the rotation of light structures along the beam axis, which can be caused by the quadratic twist phase of a partially coherent field. Here, we introduce a new class of partially coherent beams whose spectral density and degree of coherence tend to rotate during propagation. Unlike the previously reported twisted Gaussian Schell-model beams, this family of rotating beams is constructed without the framework of rotationally invariant cross-spectral density functions. Thus, these beams have different underlying physics and exhibit distinctive twist effects. It is shown that such beams can undergo a twist of more than 90 deg, providing larger degrees of freedom for flexibly tailoring the beam twist. Our results may pave the way toward synthesizing rotating beams for applications in optics and, in particular, inspire further studies in the field of twist phase proposed 25 years ago.

Discrimination of incoherent vortex states of light

Coherence vortex (CV) states provide a new way for optical manipulation and communication. As a promising option for increasing the data-transmission capacity, CV multiplexing warrants investigation. However, few studies have focused on discriminating and sorting CV states with different topological charges. In this work, we examine the cross-spectral density (CSD) of a CV state embedded in an incoherent light field and so-called incoherent vortex (ICV). Given a multiplexed ICV, we propose a method to recognize the constituting single ICVs therein. Our analytical results, which are derived according to the coherence theory and the paraxial propagation law and are given in analytical forms, show that the CSD can reveal the topological charge spectrum of a multiplexed incoherent Laguerre-Gaussian mode. This proposal can be used for free-space communication and remote sensing where light fields with low coherence are preferable to completely coherent beams.