Coherent Gaussian Schell-model Beams Research Articles

Nonparaxial Focusing of Partially Coherent Gaussian Schell-Model and Bessel-Correlated Beams in Free Space

The nonparaxial focusing of partially coherent beams in free space has been studied using the coherent-state and coherent-mode decomposition methods. Analytical expressions for the width and angular divergence of partially coherent Gaussian Schell-model (GSM) beams have been obtained using the coherent-state method. It has been shown that the focusing plane is shifted in the opposite axial direction compared to the geometric focusing plane. The influence of the nonparaxiality and spatial coherence of Bessel-correlated vortex beams on the intensity distribution and displacement of the focus plane has been analyzed. It has been shown that the shift of the focus plane increases with a decrease in the coherence radius of the source. A smaller diffraction spread has been shown for partially coherent Bessel-correlated beams compared to GSM beams.

Beam Properties of a Partially Coherent Beam Propagating Horizontally in Atmospheric Turbulence

This study explored the impact of atmospheric turbulence on partially coherent light propagation. Atmospheric turbulence causes random modulation of the intensity and phase of light, resulting in a speckle pattern in the far field. This study focused on partially coherent Gaussian Schell model beams and derived an analytical expression of the cross-spectral density function for their transmission through atmospheric turbulence, based on the generalized Huygens–Fresnel principle and the Tatarski spectrum model. Numerical simulations were used to investigate the effects of the source parameters and turbulence strength on the intensity distribution, beam width, and coherence length of partially coherent light in horizontal atmospheric transmission. The results demonstrate that diffraction-induced broadening primarily affects the intensity distribution of light in free-space transmission. Short transmission distances in atmospheric turbulence have comparable characteristics to those in a vacuum; however, as the turbulence intensity and transmission distance increase, the beam broadening effect amplifies, and the coherence length is reduced. The findings are relevant to the design of acquisition, pointing, and tracking systems for wireless laser communication systems and offer insights into the optimization of optical systems for atmospheric conditions.

Three-dimensional polarization state and spin structure of a tightly focused radially polarized Gaussian Schell-model beam

In this work, we revisit the tight focusing of a radially polarized partially coherent Gaussian Schell-model beam and examine the effect of spatial coherence of the incident beam on the focal-plane three-dimensional (3D) polarization characters, including the 3D degree of polarization, polarimetric dimensionality, and polarimetric structure. The polarimetric structure and the associated structure for the spin density vector of the tightly focused field are obtained via the 3D characteristic decomposition of the $3\ifmmode\times\else\texttimes\fi{}3$ polarization matrix. We demonstrate that the generated focused field shows the genuine 3D polarization state and a sophisticated spin structure due to the reduced spatial coherence in the incident beam. We find the contributions to whole 3D polarization state of the focused field from the pure state, middle-term state, and 3D unpolarized state in the characteristic decomposition, as well as the contributions to the total spin density vector from the spins of pure state and middle-term state can be controlled by the transverse spatial coherence width of the incident Gaussian Schell-model beam. In addition, the genuine 3D polarization and the spin structure are analyzed in the connection of the recently introduced concept of polarimetric nonregularity.

An Effective Method for Enhancing Heterodyne Efficiency by Comparing the Effect of Degree of Polarization on an Uplink Path and a Downlink Path

By analyzing the effect of the degree of polarization (DoP) of the partially coherent Gaussian Schell-model (GSM) beam on a heterodyne system of an uplink path and a downlink path, we developed an innovative and noteworthy theory according to which σsy (signal beam waist radius in the y direction component) and δSyy (coherence length of the signal beam in the yy direction component) had a more significant impact on heterodyne efficiency and DoP than the turbulence term on uplink and downlink paths. Namely, the DoP and heterodyne efficiency of an uplink path are higher than that of a downlink path when σsy > 0.02 m or δSyy ≥ 0.03 m. This innovative rule provides an efficient way for increasing the heterodyne efficiency of a signal beam propagating along an uplink or a downlink path channel in satellite-ground communication links in free-space optical heterodyne detection communication.

An advanced method for evaluating Lommel integral and its application in marine environment

In this work, our main aim is to examine theoretically the so-called “Lommel integral”. By introducing a new hypergeometric function of three variables, some new mathematical derivations are performed and a closed form of this integral is established for the first time. As an application of our main result we also examine an analysis of the fiber coupling efficiency for a partially coherent electromagnetic Gaussian Schell-model beam propagating through a turbulent marine medium by using two new power spectrum densities.

Complex coherent square Gaussian Schell-model beams

A class of random sources with complex multi-Gaussian coherence states producing a square flat topped far field with transverse self-shifting properties is introduced. The beams generated by such sources are called complex coherent square Gaussian Schell-model beams (GSM). The analytic propagating formulas of the cross-spectral density function of such beams propagating in isotropic random medium are derived. With the help of the analytic formulas, the evolutions of statistical characteristics for such beams in linear medium are illustrated numerically and interpreted physically. The effect of turbulence parameters on the beam propagation properties is stressed.

Statistical properties of partially coherent vector beams propagating through anisotropic atmospheric turbulence

Statistical properties of partially coherent vector beams propagating through anisotropic non-Kolmogorov atmospheric turbulence have attracted a large quantity of interest in recent years. Here, we show that the partially coherent vector Gaussian Schell-model (PCVGSM) beams for different initial correlation lengths will appear splitting phenomenon in turbulence, and the distribution of degree of coherence gradually evolves into circularly symmetric distribution with increasing propagation distance. We find that the distribution of degree of polarization of PCVGSM beam displays four petals pattern. It can also be found that the PCVGSM beam still keeps linearly polarized through turbulence without initial phase difference. In spite of this, it will gradually evolve into an elliptically polarized beam in turbulence by controlling the initial correlation lengths and the correlation coefficient. Our results are of great significance to detect and image for atmospheric lidar.

Application of self-healing property of partially coherent beams to ghost imaging

The theoretical model for studying the self-healing of the spatial coherence of a light beam is constructed. Based on this model, the evolution of the degree of coherence for a partially coherent Gaussian Schell-model beam is studied in detail. This study shows the existence of the self-healing effect of the partial coherence for this beam. The self-healing process is determined by the disturbing strength of the turbid medium, the beam width, and the initial coherence. An example of the application of the self-healing property is provided in the case of ghost imaging, if the initial beam is blurred by certain turbid media.

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.

Turbulence-induced changes in the state of polarization of partially polarized, partially coherent pulsed electromagnetic beams propagating through anisotropic turbulence

The changes in the state of polarization of partially polarized, partially coherent pulsed electromagnetic beams propagating along a horizontal path through anisotropic turbulence are investigated. Unpolarized and partially polarized, partially coherent pulsed electromagnetic Gaussian Schell-model beams are compared in terms of the turbulence-induced changes in the spectral degree of polarization. Our analysis is focused on models pertaining to electromagnetic Gaussian Schell-model pulsed beams but can either be readily reduced to scalar or be readily generalized to other beam classes. Within the framework of the anisotropic generalized exponential spectrum, considering simultaneously the finite inner and outer scales of turbulence and the asymmetric property of turbulence eddies in the orthogonal x y -plane throughout the propagation path, we derive analytical expressions for the cross-spectral density matrix, spectral degree of polarization, orientation angle, and degree of ellipticity. Finally, we study the effects of the anisotropic turbulence parameter on the spectral degree of polarization, orientation angle, and degree of ellipticity of the beams. Our results can be useful for applications involving partially polarized, partially coherent pulsed beams propagating through atmospheric turbulence.

Analytical study of the self-reconstruction of a partially coherent Gaussian Schell-model beam

An analytical expression for partially coherent Gaussian Schell-model (GSM) beams partially blocked by an opaque obstacle is derived. Based on the formula, the self-reconstruction is studied in detail. It is found that the reconstruction process, characterized by the reconfiguration distance that is defined in this paper, is long when the beam size is large or the obstacle size is large or the coherence length is large. Moreover, we find that there is one condition for the existence of the self-reconstruction effect of a partially coherent GSM beam. Our findings are useful in optical tweezers and optical trapping.

Effect of partial coherence on diffraction intensity of a Gaussian Schell-model beam using two-level atomic grating

The role of spatial coherence on diffraction intensity is investigated for a partially coherent incident Gaussian Schell-model beam which is diffracted from a two-level atomic grating. It is shown that the performance of the atomic grating is greatly influenced by the spectral coherence width of the partially coherent fields. It is observed that relatively large intensity of the diffracted light can be obtained via spatial coherence, beam width, interaction length, and mode index of partially coherent incident light. The scheme provides possibilities for the potential applications of atomic grating in lensless imaging using the partially coherent light field.

The performance of heterodyne detection system for partially coherent beams in turbulent atmosphere

The performance of heterodyne system is discussed for partially coherent beams in turbulent atmosphere by introducing turbulence spectrum of refractive-index fluctuations. Several analytic formulae for the heterodyne detection system using the partially coherent Gaussian Schell-model beam are presented. Based on Tatarskii spectrum model, some numerical results are given for the variation in the heterodyne efficiency with the misalignment angle, detector diameter, turbulence conditions, and parameters of the overlapping beams. According to the numerical results, we find that the turbulent atmosphere degrades the heterodyne efficiency significantly, and the variation in heterodyne efficiency is even slower against the misalignment angle in turbulence. For the deterministic received signal and the detector, the performance of the heterodyne detection can be adjusted by controlling the local oscillator signal parameters.

Ghost imaging and its visibility with partially coherent elliptical Gaussian Schell-model beams

The performances of the ghost image and the visibility with partially coherent elliptical Gaussian Schell-model beams have been studied. In that case we have derived the condition under which the goal ghost image is achievable. Furthermore, the visibility is assessed in terms of the parameters related to the source to find that the visibility reduces with the increase of the beam size, while it is a monotonic increasing function of the transverse coherence length. More specifically, it is found that the inequalities of the source sizes in x and y directions, as well as the transverse coherence lengths, play an important role in the ghost image and the visibility.

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.

The aperture averaging effect of scintillation of pseudo-partially Gaussian-Schell model beam propagation in turbulent atmosphere

By using numerical simulation, the propagation of pseudo-partially coherent Gaussian-Schell model beam in atmospheric turbulence is simulated. The properties of intensity fluctuation of different receiving aperture and aperture averaging factors are statistically analyzed. And the influence of relative changing frequency of the modulating phase which models the partial coherence of beam source on scintillation index is also discussed. The simulation results of pseudo-partially coherent beam are compared with those of the well-developed partially coherent beam and fully coherent Gaussian beam. It is found that the reduction of coherence degree may cause scintillation index to decrease. However, the aperture averaging effect is weakened at the same time. At the same receiving aperture diameter, the aperture averaging factor of pseudo-partially coherent beam is greater than that of the fully coherent beam. The increase of relative changing frequency of modulating phase may cause a reduction of scintillation index to some degree. And with the increase of relative changing frequency, the scintillation index of pseudo-partially coherent beam tends to be coincident with that of the partially coherent beam.

Study of Aperture-Averaged Scintillation for a Partially Coherent Gaussian Schell-Model Beam Propagation in Slant Atmospheric Turbulence

Based on the extended Huygens-Fresnel principle, scintillation of a partially coherent Gaussian Schell-model (GSM) beam propagation in weakly slant atmospheric turbulence is studied. The expression of aperture-averaging factor of the system receiver is derived. We analyzed the aperture-averaged scintillation index numerically. A comparison of the aperture-averaged scintillation of the beam propagation in slant path with that of the beam propagation in horizontal path is made. Results obtained show using partially coherent beams and considering aperture-averaging effect can decrease the scintillation and improve the optical communication system performance.

Long-distance propagation of pseudo-partially coherent Gaussian Schell-model beams in atmospheric turbulence

Propagation properties of spatially pseudo-partially coherent Gaussian Schell-model beams through the atmospheric turbulence over a long-distance uplink path are studied by numerical simulation. A linear coordination transformation is introduced to overcome the window effect and the loss-of-resolution problem. The beam spreading, beam wandering, and intensity scintillation as functions of turbulence strength, source correlation length, and change frequency of random phase that models the partial coherence of the source are analyzed. It is found that the beam spreading and the intensity scintillation of the partially coherent beam are less affected by the turbulence than those of the coherent one, but it suffers from a more severe diffractive effect, and the change frequency of random phase has no evident influence on it. The beam wandering is insensitive to the variation of source correlation length, and decreases firstly then goes to a fixed value as the change frequency increases.

Characteristics of a partially coherent Gaussian Schell-model beam propagating in slanted atmospheric turbulence

On the basis of the extended Huygens—Fresnel principle and the model of the refractive-index structure constant in the atmospheric turbulence proposed by the International Telecommunication Union-Radio Communication Sector, the characteristics of the partially coherent Gaussian Schell-model (GSM) beams propagating in slanted atmospheric turbulence are studied. Using the cross- spectral density function (CSDF), we derive the expressions for the effective beam radius, the spreading angle, and the average intensity. The variance of the angle-of-arrival fluctuation and the wander effect of the GSM beam in the turbulence are calculated numerically. The influences of the coherence degree, the propagation distance, the propagation height, and the waist radius on the propagation characteristics of the partially coherent beams are discussed and compared with those of the fully coherent Gaussian beams.

Nonparaxial propagation of spatially and spectrally partially coherent electromagnetic Cosh-Gaussian pulsed beams

Based on the generalized Rayleigh–Sommerfeld diffraction integral, the analytical expression for 3×3 cross-spectral density matrix of nonparaxial spatially and spectrally partially coherent electromagnetic Cosh-Gaussian (ChG) pulsed beams propagating in free space is derived, and used to formulate the spectral density and spectral degree of polarization of electromagnetic pulsed beams at the z-plane. It is found that the parameters f and fαα are the key parameters in determining the nonparaxiality of spatially and spectrally partially coherent electromagnetic ChG pulsed beams. And the decentered parameter, pulse duration and temporal coherence length can change the nonparaxial behavior of the electromagnetic ChG pulsed beams. The effect of decentered parameter, pulse duration and temporal coherence length on the spectral density and spectral degree of polarization of electromagnetic ChG pulsed beams is illustrated through numerical calculations. Propagation of nonparaxial spatially and spectrally partially coherent electromagnetic Gaussian Schell-model pulsed beams can be treated as a special case when the decentered parameter of electromagnetic ChG pulsed beams approaches to zero.