Gaussian Schell-model Beams Research Articles

Comparison of polarization property of partially coherent beam between propagating along an uplink path and a downlink path in atmospheric turbulence

In this article, we take partially coherent electromagnetic Gaussian-Schell model (EGSM) beam as a research object. Based on the unified theory of coherence and polarization and the generalized Stokes parameters of random electromagnetic beams, the expressions of degree of polarization (DoP) and orientation angle of EGSM beam that propagates in the slant atmospheric turbulence, are derived. And the expressions are used to investigate the difference in polarization property of EGSM beam between propagating along an uplink path and a downlink path in the atmospheric turbulence. The results show that under the same conditions, the DoP distribution of EGSM beam propagating along a downlink path is more concentrated than that along an uplink path. When EGSM beam propagates along a downlink path, the maximum DoP corresponding to the propagation distance is larger than along an uplink. Therefore, when EGSM beam propagates along a downlink path, the detector can receive beam information at the longer distances.

高斯-谢尔模型光束在海洋湍流中偏振传输特性

高斯-谢尔模型光束在海洋湍流中偏振传输特性

光阑对偏振高斯-谢尔模型光束偏振特性的影响

光阑对偏振高斯-谢尔模型光束偏振特性的影响

Propagation of electromagnetic stochastic beams in anisotropic turbulence.

The effects of anisotropic, non-Kolmogorov turbulence on propagating stochastic electromagnetic beam-like fields are discussed for the first time. The atmosphere of interest can be found above the boundary layer, at high (more than 2 km above the ground) altitudes where the energy distribution among the turbulent eddies might not satisfy the classic assumption represented by the famous 11/3 Kolmogorov's power law, and the anisotropy in the direction orthogonal to the Earth surface is possibly present. Our analysis focuses on the classic electromagnetic Gaussian Schell-model beams but can either be readily reduced to scalar and/or coherent beams or generalized to other beam classes. In particular, we explore the effects of the anisotropic parameter on the spectral density, the spectral degree of coherence and on the spectral degree of polarization of the beam.

Propagation of electromagnetic spectral Gaussian Schell-model beams in atmosphere

The evolution of electromagnetic spectral Gaussian Schell-model (EM SGSM) beams, for which the beam rms width and the rms coherence length are assumed to depend on wavelength, in atmosphere is investigated. It was shown that the parameters newly embedded in the source can lead to changes relating to the spectral density, the degree of coherence, and in particular, the degree of polarization on propagation, moreover, some distinctive features were also discussed, and this may offer us a method for modulating the degree of polarization.

Propagation factors of cosine-Gaussian-correlated Schell-model beams in non-Kolmogorov turbulence.

Based on the extended Huygens-Fresnel principle and second-order moments of the Wigner distribution function (WDF), we have studied the relative root-mean-square (rms) angular width and the propagation factor of cosine-Gaussian-correlated Schell-model (CGSM) beams propagating in non-Kolmogorov turbulence. It has been found that the CGSM beam has advantage over the Gaussian Schell-model (GSM) beam for reducing the turbulence-induced degradation, and this advantage will be more obvious for the beams with larger parameter n and spatial coherence δ or under the condition of stronger fluctuation of turbulence. The CGSM beam with larger parameter n or smaller spatial coherence δ will be less affected by the turbulence. In addition, the effects of the slope-parameter α, inner and outer scale and the refractive-index structure constant of the non-Kolmogorov's power spectrum on the propagation factor are also analyzed in detailed.

Influence of non-Kolmogorov atmospheric turbulence on the spectral changes of rectangular array beams

Abstract Based on the non-Kolmogorov spectrum, using the extended Huygens–Fresnel principle, the analytical expressions for the spectrum of the coherent and incoherent superpositions of rectangular array Gaussian Schell-model (RAGSM) beams propagating through non-Kolmogorov atmospheric turbulence are derived, and are used to study the influence of non-Kolmogorov atmospheric turbulence on spectral changes of coherent and incoherent superpositions RAGSM beams. It is shown that, with the increment of the general exponent α and the inner scale of turbulence l 0 , as well as the decrement of the general structure constant C ˜ n 2 , the magnitude of the spectral shift will increase, the magnitude of spectral transition will decrease and the critical position of spectral transition will decrease. The outer scale of turbulence L 0 has little effect on the spectral shift and spectral transition.

Scattering of a general partially coherent beam from a diffuse target in atmospheric turbulence

The second-order and fourth-order statistical moments of the speckle field from a diffuse target in atmospheric turbulence are studied which have great influence on the performance of lidar systems. By expanding a general rotationally symmetric beam as a sum of Gaussian—Schell model (GSM) beams, the mean intensity of the general beam propagating over a distance in an atmospheric turbulence is formulated. Expressions for the degree of coherence (DOC) and the normalized intensity variance of the scattered field of a general beam from a rough surface in turbulence are derived based on the extended Huygens—Fresnel principle. The general expressions reduce to the well-known forms for a GSM beam. Another example for the general beam used in this paper is the collimated flat-topped beam. The results of both kinds of beams show that the intensity profile on the target plane is a key factor affecting the statistical characteristics of the speckle field. A larger beam spot on the target plane induces a smaller coherence length and a smaller normalized intensity variance of the received field. As turbulence gets stronger, the coherence length becomes smaller, and the normalized intensity variance firstly increases and declines to unity finally.

Security Enhancement in Free-Space Optics Using Acousto-Optic Deflectors

In this paper, we propose a novel physical layer design for beam transmission that enhances the data security in a terrestrial free-space optical (FSO) communication system. The optical transmitter sends successive packets through different beam paths between the transmitter apertures and the receiver apertures using acousto-optic deflectors (AODs) with synthetic holographic gratings. Increasing the radius and intensity of the beam at the optical link raises the probability of eavesdropping; however, these parameters are sensitive to atmospheric turbulence. More precisely, as atmospheric turbulence increases, the radius of the beam increases while the intensity of the beam decreases. Thus, if the intensity of the beam is adjusted based on the strong turbulence in order to receive sufficient intensity at the receiver, then the intensity of the beam increases when atmospheric turbulence decreases, which causes the link security to be reduced. We formulate the beam settings at the transmitter where the AOD’s parameters are varied, which cause the Gaussian beam changes to the secondary Gaussian Schell-model (GSM) beam with different parameters. For such a situation, it is demonstrated, analytically supported by simulation results, that the radius of the beam at different beam paths can be controlled by changing the AOD’s parameters in different atmospheric turbulence. In addition, the radius of the adjusted beam in the secured FSO transceiver is compared with that of the ideal Gaussian and the ideal GSM beams in various turbulence conditions.

Evolution behavior of Gaussian Schell-model vortex beams propagating through oceanic turbulence.

The analytical expressions for the cross-spectral density and average intensity of Gaussian Schell-model (GSM) vortex beams propagating through oceanic turbulence are obtained by using the extended Huygens-Fresnel principle and the spatial power spectrum of the refractive index of ocean water. The evolution behavior of GSM vortex beams through oceanic turbulence is studied in detail by numerical simulation. It is shown that the evolution behavior of coherent vortices and average intensity depends on the oceanic turbulence including the rate of dissipation of turbulent kinetic energy per unit mass of fluid, rate of dissipation of mean-square temperature, relative strength of temperature salinity fluctuations, and beam parameters including the spatial correlation length and topological charge of the beams, as well as the propagation distance.

Experimental study of turbulence-induced beam wander and deformation of a partially coherent beam.

We carry out an experimental study of the effect of spatial coherence on the beam wander and the deformation of a Gaussian Schell-model (GSM) beam propagating through thermally induced turbulence. It is demonstrated that a GSM beam with lower coherence indeed experiences smaller beam wander and deformation than that with higher coherence. Our experimental results are explained by the beam wander theory of partially coherent beam reasonably, and will be useful in free-space optical communications.

Scintillation of partially coherent Gaussian—Schell model beam propagation in slant atmospheric turbulence considering inner- and outer-scale effects

Based on the modified Rytov theory and the international telecommunication union-radio (ITU-R) slant atmospheric structure constant model, the uniform scintillation index of partially coherent Gaussian—Schell model (GSM) beam propagation in the slant path is derived from weak- to strong-turbulence regions considering inner- and outer-scale effects. The effects of wavelength of beams and inner- and outer-scale of turbulence on scintillation are analyzed numerically. Comparison between the scintillation of GSM beams under the von Karman spectrum and that of beams under the modified Hill spectrum is made. The results obtained show that the scintillation index obtained under the von Karman spectrum is smaller than that under the modified Hill spectrum. This study can find theory bases for the experiments of the partially coherent GSM beam propagation through atmospheric turbulence.

Propagation of a twist Gaussian–Schell model beam in non-Kolmogorov turbulence

Based on the extended Huygens–Fresnel integral, an analytical formula for the cross-spectral density (CSD) function of a twist Gaussian–Schell model (TGSM) beam propagating through non-Kolmogorov turbulence is derived. The statistical properties, such as the beam width, the radius of curvature, the transverse coherence length and the twist factor of the TGSM beam in non-Kolmogorov turbulence, are studied numerically. It is found that the TGSM beam is less affected than a GSM beam without twist phase both in non-Kolmogorov turbulence and in Kolmogorov turbulence. Our results will be useful in free-space communication.

Orbital angular moment of a partially coherent beam propagating through an astigmatic ABCD optical system with loss or gain

We derive the general expression for the orbital angular momentum (OAM) flux of an astigmatic partially coherent beam carrying twist phase [i.e., twisted anisotropic Gaussian-Schell model (TAGSM) beam] propagating through an astigmatic ABCD optical system with loss or gain. The evolution properties of the OAM flux of a TAGSM beam in a Gaussian cavity or propagating through a cylindrical thin lens are illustrated numerically with the help of the derived formula. It is found that we can modulate the OAM of a partially coherent beam by varying the parameters of the cavity or the orientation angle of the cylindrical thin lens, which will be useful in some applications, such as free-space optical communications and particle trapping.

Partially coherent electromagnetic beams propagating through double-wedge depolarizers

The irradiance and polarization characteristics of quasi-monochromatic partially coherent electromagnetic beams are analyzed when they propagate after passing through a deterministic linear optical element, i.e., an optical element that can be represented by a Jones matrix. A class of such optical elements, which includes double-wedge depolarizers and polarization gratings, is defined and studied in detail. Analytical expressions are obtained for the case of double-wedge depolarizers and examples are given for an incident Gaussian Schell-model beam. For such an input beam, the effects on the irradiance and degree of polarization of the field propagating beyond the optical element are investigated in detail. A rich variety of behaviors is obtained by varying the beam size, coherence width and polarization state of the input field. The results not only provide a mathematical extension of well-known results to the domain of partial coherence, but they also exemplify mixing between coherence and polarization, which is, of course, not possible if, for example, fully spatially coherent fields are analyzed.

Second-order moments of an electromagnetic Gaussian Schell-model beam in a uniaxial crystal

We derive the analytical expressions for the second-order moments of an electromagnetic Gaussian Schell-model (EGSM) beam propagating in a uniaxial crystal. With the help of the derived formulas, we study the evolution properties of the propagation factor, the effective radius of curvature and the Rayleigh range of an EGSM beam in a uniaxial crystal. It is found that the evolution properties of an EGSM beam in a uniaxial crystal are much different from its evolution properties in free space and are closely determined by the initial beam parameters and the parameters of the uniaxial crystal. The uniaxial crystal provides one way for modulating the properties of an EGSM beam.

Correlations between intensity fluctuations in stochastic electromagnetic Gaussian Schell-model beams

Recent researches about the vector theory of the Hanbury Brown–Twiss effect at optical frequencies have shown that a new statistical quantity, called the degree of cross-polarization, is needed to predict the correlations between intensity fluctuations in stochastic electromagnetic beams. This note is devoted to an investigation of the variations of the degree of cross-polarization and then to a comparison of the distributions of degree of coherence and the correlations between intensity fluctuations across the cross-section of stochastic electromagnetic Gaussian Schell-model (GSM) beams. Analysis leads to a generalization of scalar theory of the degree of global coherence that describes the GSM sources that generate the electromagnetic GSM beams of either spatially very coherent or spatially very incoherent in the global sense.

Effects of source spatial partial coherence on temporal fade statistics of irradiance flux in free-space optical links through atmospheric turbulence

The temporal covariance function of irradiance-flux fluctua-tions for Gaussian Schell-model (GSM) beams propagating in atmospheric turbulence is theoretically formulated by making use of the method of effective beam parameters. Based on this formulation, new expressions for the root-mean-square (RMS) bandwidth of the irradiance-flux temporal spectrum due to GSM beams passing through atmospheric turbulence are derived. With the help of these expressions, the temporal fade statistics of the irradiance flux in free-space optical (FSO) communication systems, using spatially partially coherent sources, impaired by atmospheric turbulence are further calculated. Results show that with a given receiver aperture size, the use of a spatially partially coherent source can reduce both the fractional fade time and average fade duration of the received light signal; however, when atmospheric turbulence grows strong, the reduction in the fractional fade time becomes insignificant for both large and small receiver apertures and in the average fade duration turns inconsiderable for small receiver apertures. It is also illustrated that if the receiver aperture size is fixed, changing the transverse correlation length of the source from a larger value to a smaller one can reduce the average fade frequency of the received light signal only when a threshold parameter in decibels greater than the critical threshold level is specified.

Increase of spatial coherence by subwavelength metallic gratings

We study the coherence changes in partially coherent beams transmitted through binary metallic gratings. The interaction of Gaussian Schell-model beams with grating structures supporting surface plasmons is rigorously modeled using the Fourier modal method and the coherent mode representation of partially coherent fields. Our numerical results show that, by choosing suitable parameters for the grating, the degree of coherence of the beam can be significantly increased. The studied approach offers new possibilities to alter the coherence properties of fields using nanophotonic components.

Coherence properties of focused X-ray beams at high-brilliance synchrotron sources.

An analytical approach describing properties of focused partially coherent X-ray beams is presented. The method is based on the results of statistical optics and gives both the beam size and transverse coherence length at any distance behind an optical element. In particular, here Gaussian Schell-model beams and thin optical elements are considered. Limiting cases of incoherent and fully coherent illumination of the focusing element are discussed. The effect of the beam-defining aperture, typically used in combination with focusing elements at synchrotron sources to improve transverse coherence, is also analyzed in detail. As an example, the coherence properties in the focal region of compound refractive lenses at the PETRA III synchrotron source are analyzed.