Changes in the coherence of quasi-monochromatic electromagnetic Gaussian Schell-model beams propagating through turbulent atmosphere

Based on the extended Huygens-Fresnel principle, the mutual coherence function of quasi-monochromatic electromagnetic Gaussian Schell-model (EGSM) beams propagating through turbulent atmosphere is derived analytically. By employing the lateral and the longitudinal coherence length of EGSM beams to characterize the spatial and the temporal coherence of the beams, the behavior of changes in the spatial and the temporal coherence of those beams is studied. The results show that with a fixed set of beam parameters and under particular atmospheric turbulence model, the lateral coherence of an EGSM beam reaches its maximum value as the beam propagates a certain distance in the turbulent atmosphere, then it begins degrading and keeps decreasing along with the further distance. However, the longitudinal coherence length of an EGSM beam keeps unchanging in this propagation. Lastly, a qualitative explanation is given to these results.     

Statistical properties of correlated radial stochastic electromagnetic array beams on propagation

A kind of array beam named the correlated radial stochastic electromagnetic array beam that is generated by an electromagnetic Gaussian Schell-model source is introduced by use of tensor method. The analytical expression for the cross-spectral density matrix of this array beam propagating through the turbulent atmosphere and in free space is obtained after performing vector integration. Some typical numerical calculations are illustrated for the changes in the spectral density, spectral degree of polarization, and spectral degree of coherence of the beam on propagation. We find that the atmospheric turbulence can destroy the correlated effect among the beamlets.     

Turbulence-induced changes in degree of polarization, degree of coherence and spectrum of partially coherent electromagnetic beams

Based on a recently formulated unified theory of coherence and polarization, a method is described to study turbulence-induced changes in the polarization, the coherence and the spectrum of partially coherent electromagnetic beams on propagation. The electromagnetic Gaussian Schell-model beam is taken as a typical example of partially coherent electromagnetic beams, and the closed-form expressions for the degree of polarization, the degree of coherence and the spectrum of electromagnetic Gaussian Schell-model beams propagating through atmospheric turbulence are derived in the quadratic approximation of Rytov's phase structure function. Some interesting results are obtained, which are illustrated by numerical examples and are explained in physics.     

大气湍流对部分相干电磁平顶光束传输的影响

基于相干性和偏振性统一理论,采用Rytov相位结构函数平方近似推导出了部分相干电磁平顶光束在湍流大气中传输的偏振度、相干度和光谱强度公式,并研究了湍流对其传输特性的影响.研究表明,偏振度和相干度与源光谱的带宽无关.大气湍流使得不同阶数的部分相干电磁平顶光束的偏振度经长程传输后均趋于其初始值.大气湍流使得部分相干电磁平顶光束与电磁高斯-谢尔模型光束相干度的差别减小,并导致相干度的振荡和相位奇异现象消失.大气湍流使得相干性较好的部分相干电磁平顶光束的光谱跃变现象消失.     

大气湍流对部分相干电磁平顶光束传输的影响

基于相干性和偏振性统一理论,采用Rytov相位结构函数平方近似推导出了部分相干电磁平顶光束在湍流大气中传输的偏振度、相干度和光谱强度公式,并研究了湍流对其传输特性的影响.研究表明,偏振度和相干度与源光谱的带宽无关.大气湍流使得不同阶数的部分相干电磁平顶光束的偏振度经长程传输后均趋于其初始值.大气湍流使得部分相干电磁平顶光束与电磁高斯一谢尔模型光束相干度的差别减小,并导致相干度的振荡和相位奇异现象消失.大气湍流使得相干性较好的部分相干电磁平顸光束的光谱跃变现象消失.     

Polarization properties of two Gaussian Schell-model beams in the turbulent atmosphere

General expressions are derived for the spectral degree of polarization of a beam generated by the superposition of two Gaussian Schell-model (GSM) beams propagating in a turbulent atmosphere by adopting the beam coherence-polarization matrix and Young's interference theory. We analyzed the distance of two beams, atmospheric turbulence intensity, and the location of the imaging plane affect the degree of polarization by numerical calculation. In particular, when the correlation coefficients of x and y components of the electric field are the same (i.e. δ_xx = δ_yy), the degree of polarization will obtain the same value.     

Spectral properties of apertured stochastic electromagnetic twist anisotropic Gaussian Schell-model beam propagating in turbulent atmosphere

Based on the extended Huygens-Fresnel principle, analytical formulas are derived for the cross-spectral density matrix of an apertured stochastic electromagnetic twist anisotropic Gaussian Schell-model (ETAGSM) beam propagating in a turbulent atmosphere by use of a tensor method. Spectral properties of apertured ETAGSM beam are closely related with the strength of atmospheric turbulence, the aperture widths and the beam's parameters, etc. Our main attention was focused on the influence of the aperture widths, atmospheric turbulence, twist parameters and partial coherence on the spectral properties (including spectral degree of polarization, the spectral degree of coherence and the spectral density) of apertured ETAGSM beam propagating in turbulent atmosphere. Numerical calculation results and analysis are given.     

Polarization Changes of Partially Coherent Electromagnetic Vortex Beams Propagating in Turbulent Atmosphere

We investigate the polarization change of partially coherent electromagnetic vortex beams propagating in turbulent atmosphere. It is shown that the polarization of the beams will experience changes, and the changes of the polarization are dependent on the spatial coherence, topological charges of the beams, and the degree of polarization of the source plane and the atmospheric turbulence. The results obtained may have applications in space optical communication.     

Propagation of a stochastic electromagnetic Gaussian Schell-model beam through an optical system in turbulent atmosphere

A generalized diffraction integral formula for stochastic electromagnetic beams propagating through an optical system in turbulent atmosphere is derived with the help of tensor method. Some analyses are illustrated by a numerical example relating to changes in the average intensity and the degree of polarization of an electromagnetic Gaussian Schell-model beam propagating through a double-lenses system. It is shown that the optical system has strong influence on the propagation properties of the beam. The method used in this paper can be widely applied to the propagation of astigmatic beams through an optical system in turbulent atmosphere.     

Propagation Characteristics of a Partially Coherent Gaussian Schell-model Array Vortex Beam in the Joint Turbulence Effect of a Jet Engine and Atmosphere

This work investigates the joint effects of jet engine exhaust-induced turbulence and atmospheric turbulence on the propagation of a partially coherent Gaussian Schell-model Array (GSMA) vortex beam. Using the two-process propagation method, analytical formulae are derived for the cross-spectral density, spectral density, degree of coherence, and beam width of the considered beam. The results show that the considered beam takes different shapes; when the spatial coherence is large, the spectral density of the GSMA vortex beam takes an elliptical shape, whereas when the spatial coherence is smaller, the spectral density remains a Gaussian shape. The evolution profile of the degree of coherence weakens gradually when the propagation distance, topological charge, and turbulence strength increase. Moreover, the profile of the degree of coherence takes the Gaussian profile when the propagation distance is longer or turbulence atmospheric is stronger. Furthermore, the results reveal that the corresponding beam spreads faster with a larger propagation distance, lower spatial coherence, and high-strength turbulence. This study also concludes from the results that the beam is affected more when its propagation is near the jet engine exhaust, which means that this latter has a significant impact.     

Effects of coherence and polarization on the beam spreading and direction through atmospheric turbulence

Based on extended Huygens-Fresnel principle, analytical expressions of beam width and far-field angular spreading for electromagnetic Gaussian Schell-model (EGSM) beams propagating in atmospheric turbulence are obtained. The effects of coherence and polarization on beam spreading and directionality in atmospheric turbulence are investigated in detail. A condition is obtained under which beams with different degrees of spatial coherence and polarization will generate the same far-field angular spreading in atmospheric turbulence. Our results have potential application in long-distance free space optical communications.     

Numerical Simulation for Coherent and Partially Coherent Beam Propagation through Atmospheric Turbulence

Propagation properties of coherent and partially coherent beams in atmospheric turbulence are investigated respectively by using numerical simulation It is found that a partially coherent beam has a spreading larger than a coherent beam. However, from the point view of relative beam spreading and intensity scintillation, a partially coherent beam is less affected than the corresponding coherent beam, which may be the most important virtue of partially coherent beams that could be utilized to improve the performance of laser engineering. The beam wandering is almost independent of the degree of the source coherence. More aperture averaging occurs when beam becomes more coherent.     

Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere

In this paper, we study the effects of turbulent atmosphere on the degree of polarization of a partially coherent electromagnetic beam, which propagates through it. The beam is described by a 2⊗2 cross-spectral density matrix and is assumed to be generated by a planar, secondary, electromagnetic Gaussian Schell-model source. The analysis is based on a recently formulated unified theory of coherence and polarization and on the extended Huygens-Fresnel principle. We study the behaviour of the degree of polarization in the intermediate zone, i.e. in the region of space where coherence properties of the beam and the atmospheric turbulence are competing. We illustrate the analysis by numerical examples.     

Propagation properties of a partially polarized electromagnetic twist anisotropic Gaussian Schell-model beam in turbulent atmosphere

Based on the extended Huygens-Fresnel integral formula, analytical formulae for the elements of cross-spectral density matrix of partially polarized electromagnetic twist anisotropic Gaussian Schell-model (TAGSM) beam propagating in turbulent atmosphere can been derived by a tensor method. Our main attention was focus on the effect of the atmospheric turbulence, twist parameters and partial coherence on the spectral degree of polarization, the spectral degree of coherence and the spectral density. Numerical calculation results and analysis are given.     

The far-field spatial coherence of Gaussian Schell-model beam in turbulence in terms of position vectors

Spatial coherence properties of beam produced by Gaussian Schell-model source when the beam is propagating through atmosphere have been analyzed in terms of position vectors. New expressions for cross-spectral density of optical field and spectral degree of coherence as well as radiant intensity have been developed. Numerical results illustrated in this paper indicate the coherence degradation suffered from atmospheric turbulence and their directional dependence.     

Propagation of random electromagnetic beams through axially nonsymmetrical optical systems

When random electromagnetic beams passing through axially nonsymmetrical ABCD optical systems, the analytical formula for the transformation of the elements of 2 × 2 cross-spectral density matrix is obtained with the help of vector integration. We derive analytical expressions of the spectral degree of polarization, the spectral degree of coherence, and the spectral density in any output plane z > 0. Some numerical calculations are illustrated relating to the electromagnetic Gaussian Schell-model beams propagating through such optical systems.     

Extension of the van Cittert-Zernike theorem for completely polarized incoherent electromagnetic beam propagating through non-Kolmogorov turbulence

Based on the 2 × 2 cross-spectral density matrix, the van Cittert-Zernike extended theorem is developed for the completely polarized incoherent beams propagation through the paraxial non-Kolmogorov turbulence. On the consequence of the extended theorem and the definition of general spectral degree of cross-polarization of a beam, we found that the spectral degree of cross-polarization of the resultant field is independent of the refractive index structure constant of atmospheric turbulence. We investigated the influences of the propagation distance and the distance of two detection points on the degree of coherence and the spectral degree of cross-polarization.     

Effect of oceanic turbulence on polarization of stochastic beams

On the basis of the extended Huygens-Fresnel principle and the unified theory of coherence and polarization of light we determine the changes in various polarization properties of stochastic beams propagating through the turbulent clear-water ocean. The ocean-induced fluctuations in the refractive index are described via the recently developed power spectrum which takes into account both temperature and salinity variations. Numerical examples of changes in the spectral density, the degree of polarization and in the polarization ellipse are given for electromagnetic Gaussian Schell-model beams. We demonstrate, in particular, how polarization of the propagating beam is affected by statistical properties of the source and by several parameters of oceanic turbulence. We find that propagation of light beams in the oceanic turbulence resembles that in the atmospheric turbulence qualitatively, however evolution and asymptotic saturation of polarization in the oceanic turbulence occurs at much shorter distances.     

Parametric study of uniformly polarized stochastic electromagnetic beam and its imaging

A parametric study is performed in investigating the stochastic electromagnetic beam generated by a uniformly polarized electromagnetic Gaussian Schell-model source and passing through ABCD optical systems. Through theoretical analysis, the requirement is derived that the uniformly polarized electromagnetic field can be obtained at the output plane of the imaging optical system. Furthermore, the general imaging formula of the stochastic electromagnetic beam is derived. Numerical examples are also presented to illustrate the application.     

Changes in the polarization, the coherence and the spectrum of partially coherent electromagnetic Hermite–Gaussian beams in turbulence

The unified theory of coherence and polarization is applied to an investigation of the changes in the polarization, the coherence and the spectrum of partially coherent electromagnetic Hermite–Gaussian (EHG) beams propagating through atmospheric turbulence. Based on the extended Huygens–Fresnel principle, the 2×2 electric cross-spectral density matrix of partially coherent EHG beams in turbulence is expressed analytically by using a quadratic approximation of Rytov's phase structure function. The analytical expressions for the degree of polarization, the degree of coherence and the spectrum of partially coherent EHG beams in turbulence are derived, and the corresponding analytical results of electromagnetic Gaussian Schell-model (EGSM) beams can be obtained when the order number of the Hermite polynomial is zero. Some interesting results are obtained, which are illustrated by using numerical examples.