Evolution of C-point singularities and polarization coverage of Poincaré-Bessel beam in self-healing process.

As a vector version of scalar Bessel beams, Poincaré-Bessel beams (PBBs) have attracted a great deal of attention due to their non-diffracting and self-healing properties as well as the presence of polarization singularities. Previous studies of PBBs have focused on cases that consist of a superposition of Bessel beams in orthogonal circular polarization states; here, we present a theoretical and experimental study of PBBs for which the polarization states are taken to be linear, which we call a linear PBB. Using a mode transformation of a full Poincaré beam constructed from linear polarization states, we observe the linear PBB as providing an in-principle infinite number of covers of the Poincaré sphere in the transverse plane and with an infinite number of C-points with positive and negative topological indices. We also study the dynamics of C-point singularities in a linear PBB in the process of self-healing after being obstructed by an obstacle, providing insight into "Hilbert Hotel" style evolution of singularities in light beams. The present study can be useful for imaging in the presence of depolarizing surroundings, studying turbulent atmospheric channels, and exploring the rich mathematical concepts of transfinite numbers.

Orbital angular momentum spectrum of model partially coherent beams in turbulence.

The use of partial coherence has been extensively studied as a potential solution to mitigate the destructive effects of atmospheric turbulence in optical applications involving the free space propagation of light. However, in OAM-based optical systems, reducing coherence leads to the broadening of the orbital angular momentum (OAM) spectrum, consequently increasing the cross-talk between adjacent modes. In this paper, we have investigated three fundamental classes of partially coherent OAM beams under the influence of turbulence. The aim is to identify a distinct type of partially coherent beam (PCB) in which the reduction in coherence results in higher resistance of the OAM spectrum against atmospheric disturbances. It is demonstrated that, for a specific propagation distance, we can prepare a PCB in which the benefits of reducing coherence outweigh its drawbacks.

Circularly coherent vortex beams optimized for propagation through turbulence.

Self-focusing partially coherent beams with circular coherence have shown high potential for robust propagation through atmospheric turbulence. In this paper, we introduce a criterion to approximate the degrading effects of turbulence and we show how the coherence of the source can be optimized to generate a beam with the highest stability in turbulence. To test our prediction, we analytically compare the turbulence propagation of the OAM spectrum of circularly coherent Gaussian vortex sources with three different coherence parameters. It is shown that by satisfying the introduced optimizing conditions, we can minimize the adverse effects of turbulence on the OAM spectrum.

Evolution of the polarization singularities in partially coherent beams on propagation through turbulence.

In recent years, topological singularities of wavefields have been considered as structures that can improve a variety of optical technologies, including remote sensing and free-space optical communications. However, atmospheric turbulence can distort the features of singularities over long propagation distances, limiting their use in many cases. One solution being considered is the reduction of spatial coherence of light, as partially coherent beams have shown increased resistance to turbulence under a broad range of situations. In this paper, we look at the evolution of polarization singularities that arise in a particular projection of a partially coherent vector beam, and how the position and number of singularities are affected by atmospheric turbulence. We find that there are projections where the singularities persist on propagation, suggesting their possible use in applications.

Visions of invisibility in optics: retrospective.

Invisibility was long thought to be exclusively the domain of science fiction and fantasy authors, but in recent years it has been the subject of extensive theoretical and experimental research. In this retrospective we look back on the evolution of invisibility in science, from the earliest hints of invisible objects in the late 19th century up to the modern concepts of cloaking, and some of the connections between them.

Lissajous singularities in Young's interference experiment.

We explore the interference of two bichromatic vector beams in Young's interference experiment. Our analysis focuses on determining the conditions under which the superposition of such beams, emerging from the pinholes, can give rise to Lissajous-type polarization singularities on the observation screen. Two independent sufficiency conditions are derived. This analysis aids in comprehending the inherent characteristics of Lissajous singularities. To the best of our knowledge, this is the first demonstration of the singular behavior of polarization in a two-frequency field in Young's interference experiment.

Switch of orbital angular momentum flux density of partially coherent vortex beams.

We investigate the orbital angular momentum (OAM) flux density of beams which are the incoherent superposition of partially coherent vortex (PCV) beams with different topological charges and beam widths. Simulation results show that such beams can exhibit counter-rotating radial regions of the OAM flux density, and that we can "switch" the order of these regions by adjusting the topological charges and beam widths in the source plane. Furthermore, these counter-rotating regions can switch on propagation in free space without any change to the beam parameters. We discuss how these unusual OAM dynamics may find use in OAM-based applications.

Angular momentum of vector-twisted-vortex Gaussian Schell-model beams.

In this paper, we generalize a recently introduced class of partially coherent vortex beams known as twisted-vortex Gaussian Schell-model beams. Through the addition of spatially varying polarization, we created a beam whose angular momentum comes from three different sources: the underlying vortex order of the beam, the twist given to the random ensemble of beams, and the circular polarization of the beam. The combination of these angular momentum types allows for unprecedented control over the total angular momentum of the field and its transverse distribution.

Super-resolution imaging system developed from vector superoscillatory field illumination.

Superoscillations are oscillations of a band limited waveform with a local frequency higher than the bandlimit. Spatial superoscillations show great potential for performing super-resolution imaging. However, these superoscillatory waveforms are inevitably surrounded by high intensity sidelobes which severely limit the usable super-resolved area of an image. In this study, we demonstrate how polarization engineering can be used in some circumstances to suppress superoscillation sidelobes, taking advantage of the transverse wave nature of light. We illustrate the principle by a model super-resolution imaging system that can image Rayleigh scatterers with separations smaller than the classic Rayleigh criterion.

Modified Huygens-Fresnel method for the propagation of partially coherent beams through turbulence.

Partially coherent beams (PCBs) have been extensively studied as a method to mitigate the deleterious effects of atmospheric turbulence for applications such as free-space optical communication. However, it can be difficult to study and assess the performance of PCBs in turbulence due to the complicated physics of the atmosphere and the wide variety of PCBs possible. Here, we introduce a modified approach to study the propagation of second-order field moments of PCBs analytically in turbulence, reformulating the problem in terms of free-space propagation of the beam. We illustrate the method by studying a Gaussian Schell-model beam in turbulence.

Generating multi-focus beams with a spatial non-uniform coherence structure.

We introduce a class of structured light beams, named multi-focus beams, which exhibit self-focusing at multiple propagation distances. We show that the proposed beams not only have the ability to produce multiple longitudinal focal spots, but also that the number, intensity, and position of the foci can be controlled by adjusting the initial beam parameters. Furthermore, we demonstrate that these beams still exhibit self-focusing in the shadow of an obstacle. We have experimentally generated such beams and the results are consistent with the theoretical predictions. Our studies may find application where fine control of the longitudinal spectral density is needed, such as longitudinal optical trapping and manipulation of multiple particles, and transparent material cutting.

On z-coherence of Schell-model sources carrying a prescribed astigmatic phase.

A simple expression for the correlations of beams radiated by Schell-model sources carrying a prescribed astigmatic phase (cross phase) in 3D space is derived. The z-coherence of such sources upon free-space propagation is investigated in detail. It is demonstrated that the z-coherence does not decrease to zero with an increasing separation of two axial points. Our results show that the initial cross phase, coherence, and correlation state of such sources affect the distribution of the z-coherence. Furthermore, the cross phase plays a role in maintaining z-coherence, which will be useful in applications where high z-coherence is required.

100 years of Emil Wolf: introduction.

The groundbreaking research and ideas introduced by Emil Wolf continue to inspire researchers and motivate ongoing research in the wave properties of light. This special issue commemorates the legacy of Emil Wolf with research in physical optics, with specific focus on those areas where Wolf was active, such as optical coherence theory, inverse problems, singular optics, imaging, and polarization, and the intersection of these fields of study. Here we discuss the life of Emil Wolf and his influence on optical science and the optics community.

Measurement of the coherence-orbital angular momentum matrix of a partially coherent beam.

The recently introduced coherence-orbital angular momentum (COAM) matrix of a partially coherent beam [Phys. Rev. A103, 023529 (2021)10.1103/PhysRevA.103.023529] is experimentally measured for the first time, to the best of our knowledge. The new methodology based on Young's interference experiment with a pair of ring-shaped slits with embedded spiral phases is thoroughly described. By introducing the phase shift of 0 and π / 2 between two ring slits, the real and imaginary parts of the elements of the COAM matrix are obtained by measuring the on-axis spectral density in the far field of the double-ring slit. We validate our protocol through measuring the COAM matrix of an elliptical Gaussian Schell-model (GSM) beam which reveals the existence of non-trivial correlations between modes with different topological indices. The experimental results agree reasonably well with the theoretical predictions.

Design of Lissajous beams.

Lissajous singularities were observed both theoretically and experimentally almost two decades ago, but their intrinsic properties and potential applications have remained relatively unexplored. In this Letter, we describe how to design a class of beams containing a single Lissajous singularity and discuss the parameters that control their structure and propagation characteristics. Such coherent Lissajous beams may find application in communication and subwavelength imaging.

Analysis and experimental demonstration of propagation features of radially polarized specific non-uniformly correlated beams.

With the development of the unified theory of coherence and polarization, the novel physical properties generated by different correlation structures of vector partially coherent beams (PCBs) have attracted much attention. Recently, a new class of structured beams have been proposed [Opt. Lett.45, 3824 (2020)10.1364/OL.397316], called vector specific non-uniformly correlated beams. These beams combine non-uniform polarization and non-uniform correlation, and they exhibit propagation features not seen in conventional vector PCBs. In this Letter, we continue the analysis of the previous work, taking radially polarized Hermite non-uniformly correlated (RPHNUC) beams as an example, and focus on the physical interpretation of the peculiar propagation features of such beams. We verify the predicted behavior of RPHNUC beams through experiment.

Orbital angular momentum transformations by non-local linear systems.

A matrix description of orbital angular momentum (OAM) transformations in scalar optical beams by non-local, linear systems is introduced and the amplitude transfer function (ATF) is generalized to include information about mode-to-mode OAM coupling. In particular, the analysis of radially independent systems suggests the existence of unexplored types of OAM transforming systems. The results are extended to random beams and random non-local systems and the optical transfer function (OTF) is generalized to the OAM space.

Tailoring the coherence-OAM matrices.

We establish a general framework for introducing novel, to the best of our knowledge, classes of beams possessing precisely tailored coherence-orbital angular momentum (COAM) matrices, with the help of Bochner's theorem. The theory is illustrated by several examples relating to COAM matrices having a finite and infinite number of elements.

Generalization of Malus' law and spatial coherence relations for linear polarizers and non-uniform polarizers.

We study the transmission of partially polarized, partially coherent beams through linear polarizers and polarization elements that are non-uniform. An expression for the transmitted intensity, which reproduces Malus' law for special cases, is derived, as are formulas for the transformation of spatial coherence properties.

Second-order statistical properties of conjugate mode "double-H" partially coherent beams in turbulence.

We present an analysis of the propagation properties of a recently introduced class of conjugate mode partially coherent beams (called "double-H" beams) in a turbulent atmosphere using the extended Huygens-Fresnel integral. We investigate how the phase constant φ0 between the modes plays a role in controlling the evolution of the intensity distribution and resisting the degradation effects of the atmosphere. Our results indicate that this new class of structured beams provides a new degree of freedom for controlling the shape of the beams and improves turbulence resistance, with potential application in free-space optical communications.