Self-reconstruction of twisted Laguerre-Gaussian Schell-model beams partially blocked by an opaque obstacle

Identifying the twist factor of twisted partially coherent optical beams

Twisted partially coherent light, characterized by its unique twist factor, offers novel control over the statistical properties of random light. However, the recognition of the twist factor remains a challenge due to the low coherence and the stochastic nature of the optical beam. This paper introduces a method for the recognition of twisted partially coherent beams by utilizing a circular aperture at the source plane. This aperture produces a characteristic hollow intensity structure due to the twist phase. A deep learning model is then trained to identify the twist factor of these beams based on this signature. The model, while simple in structure, effectively eliminates the need for complex optimization layers, streamlining the recognition process. This approach offers a promising solution for enhancing the detection of twisted light and paves the way for future research in this field.

Twisted splitting and propagation factor of superimposed twisted Hermite-Gaussian Schell-model beams in turbulent atmosphere

We believe this to be a new superposition twisted Hermite-Gaussian Schell-model (STHGSM) beam hat is proposed. Analytic formulas for the intensity distribution and propagation factor of the STHGSM beam in non-Kolmogorov turbulence are derived by utilizing the generalized Huygens-Fresnel principle (HFP) and the Wigner function. The evolution characteristics of STHGSM beams propagating are numerically calculated and analyzed. Our findings indicate that the light intensity of the STHGSM beam gradually undergoes splitting and rotation around the axis during propagation through non-Kolmogorov turbulence, eventually evolving into a diagonal lobe shape at a certain distance of transmission. The anti-turbulence capability of the beam strengthens with higher beam order or twist factor values.

Coherence-OAM matrix properties of a twisted Gaussian Schell model beam

Based on the cross-spectral density (CSD) function, the coherence-orbital angular momentum (COAM) matrix of twisted Gaussian Schell-model (TGSM) beam is proposed, and the COAM matrix is used to describe the correlation between OAM modes in TGSM optical field. The COAM matrix characteristics of TGSM beam are analyzed by numerical simulation. The results show that the COAM matrix characteristics of TGSM beam depend on the initial parameters of the beam. In addition, a method of generating TGSM beam by superposition of COAM matrix element modes is described, and the influence of different initial parameters on the superposition characteristics is studied. The results reveal the internal relationship between the coherent structure of the optical field, the twist phase and the OAM modes. Our work helps to explore new expressions of partially coherent beams and promote the practical application of optimizing partially coherent beams.

Second-order statistics of a Hermite-Gaussian correlated Schell-model beam carrying twisted phase propagation in turbulent atmosphere

We investigate the second-order statistics of a twisted Hermite-Gaussian correlated Schell-model (THGCSM) beam propagation in turbulent atmosphere, including the spectral density, degree of coherence (DOC), root mean square (r.m.s.) beam wander and orbital angular momentum (OAM) flux density. Our results reveal that the atmospheric turbulence and the twist phase play a role in preventing the beam splitting during beam propagation. However, the two factors have opposite effects on the evolution of the DOC. The twist phase preserves the DOC profile invariant on propagation, whereas the turbulence degenerates the DOC. In addition, the influences of the beam parameters and the turbulence on the beam wander are also studied through numerical examples, which show that the beam wander can be reduced by modulating the initial parameters of the beam. Further, the behavior of the z-component OAM flux density in free space and in atmosphere is thoroughly examined. We show that the direction of the OAM flux density without the twist phase will be suddenly inversed at each point across the beam section in the turbulence. This inversion only depends on the initial beam width and the turbulence strength, and in turn, it offers an effective protocol to determine the turbulence strength by measuring the propagation distance where the direction of OAM flux density is inversed.

Polarization and coherence properties in self-healing propagation of a partially coherent radially polarized twisted beam

With the help of generalized Huygens-Fresnel integral, an analytical expression for the self-healing of a partially coherent radially polarized twisted (PCRPT) beam is derived. The coherence and polarization properties of the PCRPT beam in self-healing propagation are studied in detail. It shows that the existence of the twist phase is a double-edged sword for the self-healing properties of the beam. With the increase of the twist factor, the self-healing ability of beam intensity distribution decreases. However, the anti-disturbance performance of beam polarization improves at the same time. Besides, the polarization and coherence distribution of the beam are proved that own a slight self-healing ability when the obstacle is small. Our results will be helpful to the fields of optical tweezers, microscopy, optical communication, and so on.

Radially polarized twisted partially coherent vortex beams

We introduce a new type of partially coherent vector beam, named the radially polarized twisted partially coherent vortex (RPTPCV) beam. Such a beam carries the twist phase and the vortex phase simultaneously, and the initial state of polarization (SOP) is radially polarized. On the basis of the pseudo-modal expansion and fast Fourier transform algorithm, the second-order statistics such as the spectral density, the degree of polarization (DOP) and the SOP, propagation through a paraxial ABCD optical system are investigated in detail through numerical examples. The results reveal that the propagation properties of the RPTPCV beam closely depends on the handedness of the twist phase and the vortex phase. When the handedness of the two phases is same, the beam profile is easier to remain a dark hollow shape and the beam spot rotates faster during propagation, compared to the partially coherent vortex beam or the RPTPCV beam with the opposite handedness of the two phases. In addition, the same handedness of two phases resists the coherence induced de-polarization of the beam upon propagation, and the SOP is also closely related to the handedness, topological charge of the vortex phase and the twist factor of the twist phase, providing an efficient way to modulate the beam's DOP and SOP in the output plane. Moreover, we establish an experiment setup to generate the RPTPCV beam. The average spectral density and the polarization properties are examined in the experiment. The experimental results agree reasonable well with the theoretical predictions. Our results will be useful for particle manipulating, free-space optical communications, and polarization lidar systems.

A New Type of Shape-Invariant Beams with Structured Coherence: Laguerre-Christoffel-Darboux Beams

A new class of sources presenting structured coherence properties is introduced and analyzed. They are obtained as the incoherent superposition of coherent Laguerre-Gaussian modes with suitable coefficients. This ensures that the shape of the intensity profile and the spatial coherence features of the propagated beams are invariant during paraxial approximation. A simple analytical expression is obtained for the cross-spectral density of the sources of this class, regardless of the number of superposed modes. Properties of these sources are analyzed and described by several examples.

Progress on Studies of Beams Carrying Twist

Optical twist has always been a hot spot in optics since it was discovered in 1993. Twisted beams can be generated by introducing the twist phase into partially coherent beams, or by introducing the twisting phase into anisotropic beams, whose spectral density and degree of coherence will spontaneously rotate during propagation. Unlike conventional beams, twisted beams have unique properties and can be used in many applications, such as optical communications, laser material processing, and particle manipulation. In this paper, we present a review of recent developments on phase studies of beams carrying twist.