Twisted partially coherent array sources and their transmission in anisotropic turbulence

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.

Controllable self-rotating array beam with an arc-shaped accelerating trajectory

In this study, a modified interfering vortex phase mask (MIVPM) is proposed to generate a new type of self-rotating beam. The MIVPM is based on a conventional and stretched vortex phase for generating a self-rotating beam that rotates continuously with increasing propagation distances. A combined phase mask can produce multi-rotating array beams with controllable sub-region number. The combination method of this phase was analyzed in detail. This study proves that this self-rotating array beam has an effectively enhanced central lobe and reduced side lobe owing to adding a vortex phase mask compared with a conventional self-rotating beam. Furthermore, the propagation dynamics of this beam can be modulated by varying the topological charge and constant a. With an increase in the topological charge, the area crossed by the peak beam intensity along the propagation axis increases. Meanwhile, the novel self-rotating beam is used for optical manipulation under phase gradient force. The proposed self-rotating array beam has potential applications in optical manipulation and spatial localization.

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.

Rotating anisotropic rectangular hollow Gaussian array

A new class of partially coherent sources that can produce stable rotating anisotropic rectangular hollow Gaussian array profiles in the far field is presented. The cross-spectral density function and the spectral density of this kind of source on the propagation are derived, and its propagation characteristics, which are quite different from twisted Gaussian Schell-model beams, are discussed. The results show that each hollow lobe in the array tends to rotate around the axis during propagation. In addition, the dimension of the array, the distance between the lobes of the array, and the number of rows and columns of the rectangular array can be flexibly manipulated by adjusting the source parameters. Our work may provide a method to generate rotating anisotropic array beams with hollow lobes, which could have certain reference values in optical manipulation.

Orbital angular momentum spectra of twisted Laguerre-Gaussian Schell-model beams propagating in weak-to-strong Kolmogorov atmospheric turbulence

The presence of atmospheric turbulence in a beam propagation path results in the spread of orbital angular momentum (OAM) modes of laser beams, limiting the performance of free-space optical communications with the utility of vortex beams. The knowledge of the effects of turbulence on the OAM spectrum (also named as spiral spectrum) is thus of utmost importance. However, most of the existing studies considering this effect are limited to the weak turbulence that is modeled as a random complex "screen" in the receiver plane. In this paper, the behavior of the OAM spectra of twisted Laguerre-Gaussian Schell-model (TLGSM) beams propagation through anisotropic Kolmogorov atmospheric turbulence is examined based on the extended Huygens-Fresnel integral which is considered to be applicable in weak-to-strong turbulence. The discrepancies of the OAM spectra between weak and strong turbulence are studied comparatively. The influences of the twist phase and the anisotropy of turbulence on the OAM spectra during propagation are investigated through numerical examples. Our results reveal that the twist phase plays a crucial role in determining the OAM spectra in turbulence, resisting the degeneration of the detection mode weight by appropriately choosing the twist factor, while the effects of the anisotropic factors of turbulence on the OAM spectra seem to be not obvious. Our findings can be applied to the analysis of OAM spectra of laser beams both in weak and strong turbulence.

Changes in orbital angular momentum distribution of a twisted partially coherent array beam in anisotropic turbulence

Based on the generalized Huygens Fresnel integral, we derive the analytical formula of the cross-spectral density of a twisted partially coherent array beam propagating in non-Kolmogorov anisotropic turbulence, and investigate the changes in orbital angular momentum (OAM). The results show that the anisotropy of the turbulence causes different effects in horizontal and vertical directions. The spectral density distribution of twisted partially coherent array beam in turbulence presents self-splitting and rotation, which combines the interesting effects of the twist phase and coherent structure. Although OAM is conserved, the spatial distribution of OAM flux density can be changed by changing the propagation distance, power and anisotropy of turbulence, and the modulation of the twist phase affects not only the magnitude of OAM but also its distribution. Our work is helpful for exploring new forms of OAM sources, and promote the application of free-space optical communications and optical field modulation.

Self-rotating beam in the free space propagation

We introduce a class of self-rotating beams whose intensity profile tends to self-rotate and self-bend in the free space propagation. The feature of the self-rotating beams is acceleration in the three-dimensional (3D) space. The acceleration dynamics of the self-rotating beams is controllable. Furthermore, multiple self-rotating beams can be generated by a combined diffractive optical element (DOE) simultaneously. Such a beam can be viewed as evolution of a vortex beam by changing the exponential constant of phase. We have generated this beam successfully in the experiment and observed the expected phenomenon, which is basically consistent with the result of the numerical simulation. Our results may provide new insight into the self-rotating beam and extend potential applications in optical imaging.

Generating non-uniformly correlated twisted sources

The inverse method of proving the twistability of cross-spectral density (CSD) inevitably falls into spontaneous difficulties. Based on a nonnegative self-consistent design guideline for generating genuine CSDs introduced by Gori and Santarsiero, we demonstrate a feasible way for twisting partially coherent sources by sticking a Schell-model function to CSDs, which also determines the upper bound of the twisting strength. Analysis shows that the degree of coherence of a new class of twisted pseudo-Gaussian Schell-model beam is neither shift invariant nor shift-circular symmetric. In the presence of a vortex phase, the two different types of chiral phases affect each other and together control the propagation behavior. We further carry out an experiment to generate this non-uniformly correlated twisted beam using weighted superposition of mutually uncorrelated pseudo modes. The result is beneficial for devising nontrivial twisted beams and offers new opportunities.

Propagation properties of phase-locked radially-polarized vector fields array in turbulent atmosphere

Owing to the increasing demand for information transmission, the information capacity of free-space optical communications must be increased without being significantly affected by turbulence. Herein, based on a radially-polarized vector field array, analytical formulae for three parameters are derived: average intensity, degree of polarization, and local states of polarization (SoPs). Propagation properties varying with propagation distance, strength of turbulence, beam waist, and beamlet number are investigated. In particular, the results show that the sign of local SoPs on different receiver planes is consistent with that of the source field, and that the SoPs remain constant at specific locations as the propagation distance increases; hence, the effect of turbulence on local SoPs is slight. Meanwhile, three different SoPs, i.e., linear, right-handed, and left-handed rotation polarizations, appear at corresponding locations, thereby enabling the channel capacity to be increased. This study may not only provide a theoretical basis for vector beam array propagation in a turbulent environment, but also propose a feasible solution for increasing the channel capacity and reliability to overcome challenges in a free-space link. Additionally, this study may benefit potential applications in laser lidar and remote sensing.

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.

Customizing twisted Schell-model beams

Since the celebrated twist phase was proposed by Simon and Mukunda, despite the tremendous progress made in theory over the past decades, developing a simple and flexible experimental method to customize this novel phase has long been a tricky challenge. In this Letter, we demonstrate a general experimental method for generating twisted Schell-model beams by implementing the continuous coherent beam integral function in a discrete form. Experimental results based on rigorous Laguerre-Gauss modes superposition are also demonstrated, indicating that our method is more convenient and of higher quality. The twist factor is also measured using the rotation characteristics during propagation, and the results agree well with the theoretical prediction. The method could serve as a general way for customizing bona fide twisted cross-spectral densities while facilitating certain applications.

Propagation of twisted EM Gaussian Schell-model array beams in anisotropic turbulence

The behavior of the twisted electomagnetic (EM) Gaussian Schell-model array beams in anisotropic random turbulence is investigated. An example illustrates that a twisted EM source can produce lattice-like patterns in degree of polarization with rotation or not, which depends on the setting of the initial twist phase. One also finds that the anisotropy of the medium leads to an anisotropic beam spreading, and we can effectively limit such turbulence-induced effects by optimizing the initial twist and source correlation widths. Moreover, after transmitting through the turbulence for sufficiently long distances, the intensity and coherence are mainly affected by turbulence statistics; however, for the case of polarization, the initial twist plays a dominant role in determining its distribution profile.

Experimental synthesis of partially coherent sources

A flexible pseudo-mode sampling superposition method for synthesizing partially coherent sources has been introduced that can be thought of as an approximate discrete representation of Gori's nonnegative definiteness criterion for designing spatial correlation functions. Importantly, without performing formidable mode analysis, this method enables us to develop a convenient and efficient experimental technology to customize partially coherent sources without sacrificing theoretical accuracy. As an example, we experimentally generate a new, to the best of our knowledge, class of nontrivial pseudo-Schell model sources recently proposed by de Sande et al. Our approach opens up a useful avenue for manipulating nontrivial partially coherent beams and promotes applications for optical tweezers and photolithography.

Ring-shaped twisted Gaussian Schell-model array beams

A new partially coherent source which can generate a beam field with a ring-shaped twisted array profile is presented, and the distribution characteristics of spectral density and degree of coherence of the field are discussed. It is shown that both the spectral density and degree of coherence will rotate along the propagating direction, but in opposite rotating directions. Furthermore, we find that the distribution properties of the ring-shaped array of the spectral density, including the number of the rings, the number of the lobes of each ring, and the distance of all adjacent lobes, can be properly controlled by adjusting structural parameters of the source.

Propagation of Gaussian Schell-model beams through a jet engine exhaust

Theoretical predictions of light beam interactions with jet engine exhaust are of importance for optimization of various optical systems, including LIDARs, imagers and communication links operating in the vicinity of aircrafts and marine vessels. Here we extend the analysis previously carried out for coherent laser beams propagating in jet engine exhaust, to the broad class of Gaussian Schell-Model (GSM) beams, being capable of treating any degree of coherence in addition to size and radius of curvature. The analytical formulas for the spectral density (SD) and the spectral degree of coherence (DOC) of the GSM beam are obtained and analyzed on passage through a typical jet engine exhaust region. It is shown that for sources with high coherence, the transverse profiles of the SD and the DOC of the GSM beams gradually transition from initially circular to elliptical shape upon propagation at very short ranges. However, such transition is suppressed for sources with lower coherence and disappears in the incoherent source limit, implying that the GSM source with low source coherence is an excellent tool for mitigation of the jet engine exhaust-induced anisotropy of turbulence. The physical interpretation and the illustration are included.

Twisted elliptical multi-Gaussian Schell-model beams and their propagation properties

We introduce a new kind of partially coherent source whose cross-spectral density (CSD) function is described as the incoherent superposition of elliptical twisted Gaussian Schell-model sources with different beam widths and transverse coherence widths, named twisted elliptical multi-Gaussian Schell-model (TEMGSM) beams. Analytical expression for the CSD function propagating through a paraxial ABCD optical system is derived with the help of the generalized Collins formula. Our results show that the TEMGSM beam is capable of generating a flat-topped elliptical beam profile in the far field, and the beam spot during propagation exhibits clockwise/anti-clockwise rotation with respect to its propagation axis. In addition, the analytical expressions for the orbital angular momentum (OAM) and the propagation factor are also derived by means of the Wigner distribution function. The influences of the twisted factor and the beam index on the OAM and the propagation factor are studied and discussed in detail.

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.

Higher-order twisted/astigmatic Gaussian Schell-model cross-spectral densities and their separability features

Adding a twist phase term to the cross-spectral density (CSD) function of a partially coherent source can be done if and only if the resulting function remains nonnegative definite. Constraints on the twist term that guarantee the validity of the resulting CSD have been derived only for Twisted Gaussian Schell-model (TGSM) sources. Here, an infinite family of higher-order TGSM sources is introduced, whose CSDs are expressed as products of the CSD of a standard TGSM source times Hermite polynomials of arbitrary orders and suitable arguments. All the members present the same twist term and for all of them the twist-coherence constraint keeps obeying the form valid for a standard TGSM source. They can be used as building blocks for constructing an endless number of valid twisted CSDs, with an assigned value of the twist parameter and intensity and/or coherence features that can be very different from those of a standard TGSM source. Through partial transposition, higher-order TGSM CSDs are converted into higher-order Astigmatic Gaussian Schell-model (AGSM) CSDs. The problem of the separability of higher-order TGSM and AGSM CSDs is addressed, and conditions ensuring their separability are derived.

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.