Gaussian Schell-model Research Articles

Statistical Characteristics of a Twisted Anisotropic Gaussian Schell-Model Beam in Turbulent Ocean

The analytical expression of the cross-spectral density function of a twisted anisotropic Gaussian Schell-model (TAGSM) beam transmitting in turbulent ocean is derived by applying a tensor method. The statistical properties, including spectral density, the strength of twist and beam width of the propagating beam are studied carefully through numerical examples. It is demonstrated that the turbulence of ocean has no effect on the rotation direction of the beam spot during propagation. However, the beam shape will degrade into a Gaussian profile under the action of oceanic turbulence with sufficiently long propagation distance, and a beam with a larger initial twist factor is more resistant to turbulence-induced degeneration. As oceanic turbulence becomes stronger, the beam spot spreads more quickly while the twist factor drops more rapidly upon propagation. The physical mechanisms of these phenomena are addressed in detail. The obtained results will be helpful in optical communication systems underwater.

Effect of beam mode of partially Gaussian Schell-model beam on a heterodyne detection system in turbulence.

A mathematical model considering the transmission of a partially coherent Gaussian Schell-model (GSM) beam in slant turbulence atmosphere of heterodyne detection was established. A closed-form expression of the weighting factor for the partially GSM beam at the receiving end was derived. The effect of the beam mode on the performance of the proposed detection system was theoretically investigated. The results show that the proportion of the fundamental mode and heterodyne efficiency can be optimized by controlling the waist radius of the signal and local oscillator beams. The inner scale of turbulence significantly affects the heterodyne efficiency and normalized M2. With a larger mode order, the proportion of the fundamental mode and heterodyne efficiency are lowered.

Research on characteristics of Bessel–Gaussian Schell-model beam in weak turbulence

The Bessel–Gaussian Schell-model (BGSM) beam has been proved to have an annular distant facula. In this paper, we found the radius of the halo is determined by the Bessel parameter and propagation length, rather than turbulence, which means the BGSM beams with different Bessel parameter could distinguish each other physically. we generated a BGSM beam and analyzed its scintillation index in weak atmosphere both in theory and experiment and studied its self-healing property. Compare to the GSM beam, the Bessel factor in coherence domain improves the BGSM beam in terms of scintillation index (SI). According to the mean-square error (MSE), the BGSM beam suffers the same amount of shape distortion as that of the GSM beam under blocking, both of which present excellent resistance to occlusion compared to coherent Gaussian beam. To alleviate the source-introduced optical intensity distribution, statistical average in both time domain and spatial domain was studied and presents adequate efficiency. The result indicated the BGSM beam has potential application for space-division multiplexing in free-space optical communication.

Polarimetric dimension and nonregularity of tightly focused light beams

Polarimetric dimension and nonregularity are newly introduced concepts that characterize three-dimensional (3D) polarization states of light. We analyze the spectral polarimetric dimension and the degree of nonregularity associated with two kinds of tightly focused beams: a radially fully polarized Gaussian Schell-model (GSM) beam and a partially polarized beam composed of an incoherent superposition of two orthogonally polarized (coherent) plane-wave modes. We show that for both beams the focal field can exhibit genuine 3D and nonregular character, with even perfect nonregularity encountered for the tightly focused two-mode beam. These features originate from the partial spatial coherence and partial polarization of the incident beams, and in the limit of full coherence and polarization the three-dimensionality and nonregularity of the focal field vanish. We also find that the GSM beam can generate a nanoscale region around the focus where the field is essentially 3D unpolarized. The results demonstrate the rich polarimetric structure of focal fields and may find uses in optical particle manipulation and sensing.

Properties of off-axis hollow Gaussian-Schell model vortex beam propagating in turbulent atmosphere**Project supported by the Natural Science Foundation of Jilin Province, China (Grant No. 20180101031JC) and the Jilin Provincial Science Foundation for Basic Research, China (Grant No. 2019C040-7).

The analytical expression of off-axis hollow Gaussian–Schell model vortex beam (HGSMVB) generated by anisotropic Gaussian–Schell model source is first introduced. The evolution properties of off-axis HGSMVB propagating in turbulent atmosphere are analyzed. The results show that the off-axis HGSMVB with smaller coherence length or propagating in stronger turbulent atmosphere will evolve from dark hollow beam into Gaussian-like beam with a larger beam spot faster. The beams with different values of integer order N or the position for hollow and vortex factor R will have almost the same Gaussian-like spot distribution at the longer propagation distance.

Evolution properties of the radially polarized Laguerre-Gaussian-correlated Schell-model beams propagating in uniaxial crystals.

In this paper, we discuss, both analytically and numerically, the paraxial propagation of the radially polarized Laguerre-Gaussian-correlated Schell-model (LGCSM) beams orthogonal to the optical axis in uniaxial crystals. The analytical expression for the cross-spectral density function and the second-order moments of the radially polarized LGCSM beams are derived, and the evolution properties of the normalized intensity distribution, the spectral degree of the coherence (SDOC), and the spectral degree of the polarization (SDOP) in uniaxial crystals are elucidated by numerical examples. It is found that the intensity distribution of the radially polarized LGCSM beams evolves from a doughnut shape into a solid shape and finally converts into an elliptical symmetric hollow-ring profile in uniaxial crystals due to the combined effect of special correlation functions and the anisotropy effect of the uniaxial crystals. The evolution of the SDOC and SDOP for the radially polarized LGCSM beams is quite different from that of the radially polarized Gaussian-Schell-model beams. In addition, the propagation properties of the radially polarized LGCSM beams are closely related to the spatial coherence length, the mode order, and the ratio of extraordinary and ordinary reflective indices. The results show that the uniaxial crystals could modulate the evolution properties of the radially polarized LGCSM beams.

Intensity Evolution of Cosine-Gaussian-Correlated Schell-Model Pulse Scattered by a Medium

According to first-order Born approximation, the scattering of a partially coherent pulse with cosine-Gaussian correlation by a medium was studied. On the basis of analytic expression, the changes in intensity evolution of the scattered pulse are discussed. The influences of pulse and medium characteristics on the intensity of the scattered pulse were investigated. The intensities of a Gaussian Schell-model (GSM) pulse and a cosine-Gaussian-correlated Schell-model (CGSM) pulse, both scattered by the same medium, are compared, and their similarities and differences are examined in detail. The effective angular width of the scattered pulse could be modulated by the parameters of the pulse and medium. The obtained results could find potential applications in pulsed beam scattering.

The evolution of spectral intensity and orbital angular momentum of twisted Hermite Gaussian Schell model beams in turbulence.

We introduce a new class of twisted partially coherent beams with a non-uniform correlation structure. These beams, called twisted Hermite Gaussian Schell model (THGSM) beams, have a correlation structure related to Hermite functions and a twist factor in their degree of coherence. The spectral density and total average orbital angular momentum per photon of these beams strongly depend on the distortions applied to their degree of coherence. On propagation through free space, they exhibit both self-splitting and rotation of their spectral density profile, combining the interesting effects of twisted beams and non-uniformly correlated beams. We demonstrate that we can adjust both the beam order and the twist factor of THGSM beams to improve their resistance to turbulence.

Characterization of the electromagnetic Gaussian Schell-model beam using first-order interference.

We propose a method for the characterization of electromagnetic Gaussian Schell-model (EMGSM) beams. This method utilizes the first-order interference consisting of polarization-state projections along with the two-point (generalized) Stokes parameters. The second-order field correlations employed in this method enable us to determine both the magnitude and the argument of the complex degree of electromagnetic coherence. We experimentally demonstrate this method by characterizing an EMGSM beam, which is synthesized using a laser beam passing through a rotating ground glass diffuser. This beam-characterization method is expected to be potentially useful for probing the partially coherent and partially polarized beams, and have tremendous applications in broad areas of optical communication and beam propagation.

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.

Optical trapping of the low index of refraction particles by focused vortex beams and two face-to-face focused beams

Using the extended Huygens–Fresnel principle and Rayleigh scattering theory, optical trapping of the low index of refraction particles using a focused Gaussian Schell-model (GSM) non-vortex beam, a focused GSM vortex beam, and two face-to-face focused GSM vortex beams have been studied. The results demonstrate that the focused GSM non-vortex beam cannot capture the low index of refraction particles, however, the focused GSM vortex beam can be a two-dimensional trap of particles in the z-axis, and the transverse gradient force Fgrad,x and the trapping equilibrium region increase as the topological charge m increases. As the focal length f or the refractive index of particles np decreases, the radiation forces increase and the trapping ability also enhances. To trap the low index particles in three-dimensional space, we adopt that the two face-to-face focused GSM vortex beams can be used to construct an optical potential well. The transverse gradient force of two face-to-face focused GSM vortex beams is twice that of a single GSM vortex beam. The limit of the radius for the low index of refraction particles that were stably captured has also been determined. The obtained results provide valuable information for trapping and manipulating the low index of refraction particles using GSM vortex beams, which may be applied in micromanipulation, biotechnology, nanotechnology and so on.

Evolution properties of the orbital angular momentum spectrum of twisted Gaussian Schell-model beams in turbulent atmosphere.

We derive the analytical formula of the energy weight of each orbital angular momentum (OAM) mode of twisted Gaussian Schell-model (TGSM) beams propagating in weak turbulent atmosphere. The evolution of its OAM spectrum is studied by numerical calculation. Our results show that the OAM spectrum of a TGSM beam changes with the beam propagating in turbulent atmosphere, which is completely different from that of the TGSM beam propagating in free space. Furthermore, influences of the source parameters and the turbulence parameters on the OAM spectrum of a TGSM beam in turbulent atmosphere are analyzed. It is found that the source parameters and turbulence parameters, such as twist factor, coherence length, beam waist size, and structure constant, have a significant influence on the OAM spectrum, but the value of the wavelength and inner scale have little influence. Increasing the beam waist size or decreasing the coherence length would lead to the OAM spectrum broadened in the source plane, but would be robust for the OAM modes of the TGSM beam in the turbulent atmosphere. It is clear that the bigger the value of the twist factor, the more asymmetric the OAM mode of the TGSM beam is, and the better mode distribution can be maintained when it propagates in turbulent atmosphere. Our results have potential applications in reducing the error rate of free-space optical communication and detecting the atmospheric parameters.

Generating electromagnetic nonuniformly correlated beams.

We develop a method to generate electromagnetic nonuniformly correlated (ENUC) sources from vector Gaussian Schell-model (GSM) beams. Having spatially varying correlation properties, ENUC sources are more difficult to synthesize than their Schell-model counterparts (which can be generated by filtering circular complex Gaussian random numbers) and, in past work, have only been realized using Cholesky decomposition-a computationally intensive procedure. Here we transform electromagnetic GSM field instances directly into ENUC instances, thereby avoiding computing Cholesky factors resulting in significant savings in time and computing resources. We validate our method by generating (via simulation) an ENUC beam with desired parameters. We find the simulated results to be in excellent agreement with the theoretical predictions. This new method for generating ENUC sources can be directly implemented on existing spatial-light-modulator-based vector beam generators and will be useful in applications where nonuniformly correlated beams have shown promise, e.g., free-space/underwater optical communications.

Elliptical Laguerre Gaussian Schell-model beams with a twist in random media.

A class of partially coherent elliptical sources with twisted Laguerre Gaussian Schell-model (TLGSM) correlation function is proposed, which are capable of producing beams whose intensity profiles may vary substantially. This kind of beam can be viewed as the generalization of the LGSM beams. Properties of the spectral density during propagation in free space and atmospheric turbulence are investigated with varying quantities related to the beam source and the medium. It is shown that the elliptical TLGSM beams evolve in a manner that is much more complex compared to the LGSM beams. In addition, the behaviour of the rotation angle is further analysed by quantitative examples.

Generation of a Gaussian Schell-model field as a mixture of its coherent modes

Gaussian Schell-model (GSM) fields are examples of spatially partially coherent fields which in recent years have found several unique applications. The existing techniques for generating GSM fields are based on introducing randomness in a spatially completely coherent field and are limited in terms of control and precision with which these fields can be generated. In contrast, we demonstrate an experimental technique that is based on the coherent mode representation of GSM fields. By generating individual coherent eigenmodes using a spatial light modulator and incoherently mixing them in a proportion fixed by their normalized eigenspectrum, we experimentally produce several different GSM fields. Since our technique involves only the incoherent mixing of coherent eigenmodes and does not involve introducing any additional randomness, it provides better control and precision with which GSM fields with a given set of parameters can be generated.

Condition for keeping polarization invariant on propagation in space-to-ground optical communication downlink

We consider a Gaussian Schell-model (GSM) laser beam applied in space-to-ground optical communication downlink. Based on the derived analytic expression of cross-spectral density matrix of GSM laser beam, the sufficient conditions of the polarization properties remaining invariant through the space-to-ground optical communication downlink are obtained. The conditions reveal when the source light is linear polarization beam or the three coherence lengths ( δxx, δxy and δyy) are equal to each other, the polarization properties unchanged upon propagation. With full consideration of the coherence lengths and the zenith angle, the conditions of keeping polarization properties invariance is verified by numerical calculation.

Ghost Imaging with a Partially Coherent Beam Carrying Twist Phase in a Turbulent Ocean: A Numerical Approach

Ghost imaging (GI) is an indirect imaging approach that can retrieve an object’s image even in a harsh environment through measuring the fourth-order correlation function (FOCF) between the signal and idle optical paths. In this paper, we study lensless GI with a partially coherent beam carrying twist phase, i.e., twisted Gaussian Schell-model (TGSM) beam, in the presence of oceanic turbulence. Explicit expression of the FOCF is derived based on the optical coherence theory and Rytov approximation, and the effects of the twist phase and the oceanic turbulence on the quality and visibility of image are investigated in detail through numerical examples. Our results show that the simulated oceanic turbulence strongly affects the GI. The quality of image decreases monotonously with an increase of the strength of turbulence whereas the visibility increases. When the illumination light carries a twist phase, the visibility of the image is improved while the quality of the image is reduced in contrast to those without a twist phase. By properly selecting the strength of the twist phase, the image can still be maintained at an acceptable level of quality with high visibility. Furthermore, it is found that the quality and visibility of the ghost image are less affected by the oceanic turbulence using a TGSM beam with larger twist factor. Our findings will be useful for the application of GI in an oceanic turbulent environment.

Generating bona fide twisted Gaussian Schell-model beams.

We experimentally realize bona fide twisted Gaussian Schell-model (TGSM) beams by converting an anisotropic GSM beam into a TGSM beam with a set of just three cylindrical lenses. In contrast to the previously reported experimental technique for generating TGSM beams, we are able to explicitly generate anisotropic GSM beams with simultaneously controlled beam widths and transverse coherence lengths along two mutually orthogonal directions, prior to converting them to genuine TGSM beams.

Detection of a Semi-Rough Target in Turbulent Atmosphere by an Electromagnetic Gaussian Schell-Model Beam

The interaction of an electromagnetic Gaussian Schell-model beam with a semi-rough target located in atmospheric turbulence was studied by means of a tensor method, and the corresponding inverse problem was analyzed. The equivalent model was set up on the basis of a bistatic laser radar system and a rough target located in a turbulent atmosphere. Through mathematical deduction, we obtained detailed information about the parameters of the semi-rough target by measuring the beam radius, coherence radius of the incident beam and the polarization properties of the returned beam.

Temporal coherence modulation of pulsed, scalar light with a Fabry-Pérot interferometer.

We analyze the effect of a high-finesse Fabry-Pérot interferometer on the temporal coherence properties of scalar optical plane-wave pulse trains. We focus on the cases of single-peak and double-peak transmissions of Gaussian Schell-model (GSM) and supercontinuum (SC) pulses. For the GSM light, we show how the characteristics of the average intensity and temporal degree of coherence of the transmitted pulses depend on the coherence parameters of the incident field. Regarding the SC light, the output is found to depend specifically on the location of the transmission peak(s) within the average spectrum. The results demonstrate that a Fabry-Pérot etalon can act as a simple passive element for tailoring the temporal (and spectral) coherence properties of optical pulse trains.