Twisted Gaussian Schell-model beams as series of partially coherent modified Bessel-Gauss beams.
TL;DR: It is shown that twisted Gaussian Schell-model beams can be represented through an incoherent superposition of partially coherent beams carrying optical vortices and whose cross-spectral densities are expressed in terms of modified Bessel functions.
Abstract: We show that twisted Gaussian Schell-model (TGSM) beams can be represented through an incoherent superposition of partially coherent beams carrying optical vortices and whose cross-spectral densities are expressed in terms of modified Bessel functions. Moreover, starting from this result, we show that the modal expansion of the cross-spectral density of a TGSM source can be directly obtained through simple mathematics.
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TL;DR: Partially coherent beams with a prescribed phase, state of polarization, and degree of coherence display many extraordinary propagation properties and are preferred in many applications, such as particle trapping, free-space optical communications, remote sensing, optical imaging, material thermal processing, image transformation, and optical encryption as discussed by the authors.
Abstract: Partially coherent beams with a prescribed phase, state of polarization, and degree of coherence display many extraordinary propagation properties and are preferred in many applications, such as particle trapping, free-space optical communications, remote sensing, optical imaging, material thermal processing, image transformation, and optical encryption. In this review, we begin with describing conventional Gaussian Schell-model beams and partially coherent beams with prescribed phases, states of polarization, and degrees of coherence. Then we introduce theoretical models for various partially coherent beams and the methods for generating them. Finally, a brief summary is presented.
104 citations
TL;DR: The propagating modes of a wide-sense stationary Schell-like source with arbitrary coherence state and a twist factor are determined and this suggests a convenient practical method for modeling novel classes of twisted partially coherent beam-like fields.
Abstract: 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. As a second example, we introduce a new type of twisted partially coherent beam in which a radiated flat-top average intensity pattern remains invariant in shape (but not size) while it twists around the axis upon propagation.
74 citations
TL;DR: The problem of when a twist can be impressed on a partially coherent beam is solved for Schell-model fields endowed with axial symmetry and a modal analysis can be performed, thus permitting evaluation of whether it will withstand the twisting process.
Abstract: The problem of when a twist can be impressed on a partially coherent beam is solved for Schell-model fields endowed with axial symmetry. A modal analysis can be performed for any such beam, thus permitting evaluation of whether it will withstand the twisting process. Beyond exemplifying some twistable beams, it is shown that, for certain correlation functions, the beam cannot be twisted, no matter how the numerical parameters are chosen.
45 citations
TL;DR: It is found that the vortex phase's and twist phase's contributions to the OAM are interrelated, which greatly increases the amount of OAM of the TLGSM beam.
Abstract: It is well known that a light beam with vortex phase or twist phase carries orbital angular momentum (OAM), while twist phase only exists in a partially coherent beam. In this paper, we introduce a new partially coherent beam, named twisted Laguerre-Gaussian Schell-model (TLGSM) beam. This TLGSM beam carries both vortex phase and twist phase. Further, the evolutional properties of the spectral density and spectral degree of coherence (SDOC)] of the TLGSM beam passing through a paraxial ABCD optical system are explored in detail. Our results reveal that the vortex and twist phases’ handedness significantly affects the evolution properties. When the twist phase’s handedness is the same as that of the vortex phase, the beam profile maintains a dark hollow shape during propagation and the side rings in SDOC are suppressed; however, when the handedness of two phases is opposite, then the beam shape evolves into a Gaussian shape and the side rings in SDOC are enhanced. Furthermore, we obtain the analytical expression for the OAM of the TLGSM beam. It is found that the vortex phase’s and twist phase’s contributions to the OAM are interrelated, which greatly increases the amount of OAM. In addition, the OAM variation of the TLGSM beam passing through an anisotropic optical system is also explored in detail. Our results will be useful for information transfer and optical manipulations.
39 citations
TL;DR: It is shown that both the irradiance profile of each element of the array and the degree of coherence rotate during propagation, but in opposite directions, which may provide new insight into the twist phase.
Abstract: We introduce, to the best of our knowledge, a new class of twisted partially coherent sources for producing rotating Gaussian array profiles The general analytical formula for the cross-spectral density function of a beam generated by such a novel source propagating in free space is derived, and its propagation characteristics are analyzed It is shown that both the irradiance profile of each element of the array and the degree of coherence rotate during propagation, but in opposite directions Further, the twist effects of the spectral density and the degree of coherence are quantified It is shown that the direction of rotation is changeable upon propagation Our results may provide new insight into the twist phase and may be applied in optical trapping
38 citations
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TL;DR: A sufficient condition for ensuring the satisfaction of the constraint of nonnegative definiteness on the choice of the mathematical form of spatial correlation functions for optical fields is discussed.
Abstract: The choice of the mathematical form of spatial correlation functions for optical fields is restricted by the constraint of nonnegative definiteness. We discuss a sufficient condition for ensuring the satisfaction of such a constraint.
364 citations
TL;DR: In this paper, a new class of partially coherent axially symmetric Gaussian Schell-model (GSM) beams incorporating a new twist phase quadratic in configuration variables is introduced.
Abstract: We introduce a new class of partially coherent axially symmetric Gaussian Schell-model (GSM) beams incorporating a new twist phase quadratic in configuration variables. This phase twists the beam about its axis during propagation and is shown to be bounded in strength because of the positive semidefiniteness of the cross-spectral density. Propagation characteristics and invariants for such beams are derived and interpreted, and two different geometric representations are developed. Direct effects of the twist phase on free propagation as well as on parabolic index fibers are demonstrated. Production of such twisted GSM beams, starting with Li-Wolf anisotropic GSM beams, is described.
292 citations
TL;DR: In this article, a new class of partially coherent beams with a separable phase, which carry optical vortices, is introduced, and the free-space propagation properties of such beams are studied analytically and their M2 quality factor is investigated numerically.
Abstract: A new class of partially coherent beams with a separable phase, which carry optical vortices, is introduced. It is shown that any member of the class can be represented as an incoherent superposition of fully coherent Laguerre-Gauss modes of arbitrary order, with the same azimuthal mode index. The free-space propagation properties of such partially coherent beams are studied analytically, and their M2 quality factor is investigated numerically.
199 citations
TL;DR: A review of recent developments on generation and propagation of partially coherent beams with nonconventional correlation functions is presented.
Abstract: Partially coherent beams with nonconventional correlation functions have displayed many extraordinary properties, such as self-focusing and self-splitting, which are totally different from those of partially coherent beams with conventional Gaussian correlated Schell-model functions and are useful in many applications, such as optical trapping, free-space optical communications, and material thermal processing. In this paper, we present a review of recent developments on generation and propagation of partially coherent beams with nonconventional correlation functions.
182 citations
TL;DR: The basic theoretical and computational tools used to investigate partially coherent beams' resistance to the deleterious effects of atmospheric turbulence are described and reviewed.
Abstract: Partially coherent beams hold much promise in free-space optical communications for their resistance to the deleterious effects of atmospheric turbulence. We describe the basic theoretical and computational tools used to investigate these effects, and review the research to date.
177 citations