Propagation of astigmatic stochastic electromagnetic beams in oceanic turbulence

In this paper, we investigate the characteristics of astigmatic stochastic electromagnetic beams through oceanic turbulence. Taking the electromagnetic Gaussian Schell-model (GSM) beam as an example, the analytic expressions for the spectral density and the spectral degree of polarization of the beam propagating the oceanic turbulence are derived. It is indicated that the spectral density along the z-axis of the GSM beam in the oceanic turbulence is severely influenced by the source correlation properties, as well as by the sea-related parameters. We show that the characteristics of the spectral density along the x-axis, y-axis and z-axis of astigmatic electromagnetic GSM beams passing through the oceanic turbulence are qualitatively different. Furthermore, we find that as the astigmatic coefficient becomes larger, the maximum value of the spectral density along the z-axis increases rapidly and the width of the spectral density becomes shorter rapidly. Finally, the results have shown that different strengths of astigmatism have different effects on the spectral degree of polarization.     

随机电磁高阶Bessel-Gaussian光束在海洋湍流中的传输特性

利用广义惠更斯-菲涅耳衍射积分公式得到了随机电磁高阶Bessel-Gaussian光束在海洋湍流中传输的交叉谱密度矩阵的一般表达式,通过数值计算主要研究了随机电磁高阶Bessel-Gaussian光束在海洋湍流中传输时其在远场输出面的统计特性的变化,包括归一化光谱强度、光谱偏振度、两点的光谱相干度等.数值模拟结果显示海洋湍流能够对随机电磁高阶Bessel-Gaussian光束的归一化光谱强度分布产生影响,随着传输距离的增加,零阶Bessel-Gaussian光束中心出现凹陷,高阶Bessel-Gaussian光束中心会变平坦继而又凹陷下去,不管零阶还是高阶,当传输距离增加到足够远,光强分布都会演变成最终的类高斯分布.x轴上各点的偏振度改变与相干长度δ_(xx),δ_(yy)以及海洋湍流参数有关.x轴上任意一点和原点这两点的光谱相干度也随x的增加而呈振荡变化,并且海洋的均方温度耗散率χT对光谱相干度有影响.     

The statistical properties of anisotropic electromagnetic beams passing through the biological tissues

We report the analytic formula of an electromagnetic Gaussian–Schell-model (EGSM) beam propagating through the turbulent biological tissues. With the help of this formula, the changes in characteristics of the beam such as the spectral density, the spectral degree of coherence, the spectral degree of polarization, and the spectral degree of cross-polarization of the EGSM beam passing through the biological tissues are illustrated and compared by numerical examples. The changes in anisotropic and isotropic EGSM beams are indicated. Necessary comparisons and analyses of the beams generated by the anisotropic source and the isotropic source through the turbulent biological tissues are given. Moreover, the influence of the light source and turbulence of tissues on the changes of the spectral degree of cross-polarization of the EGSM beam passing through the biological tissues are compared in the near-field and the far-field.     

部分相干环状偏心光束通过海洋湍流的传输特性

推导出了部分相干环状偏心光束在海洋湍流中传输的平均光强和光束质心位置的解析表达式, 并给出了最大光强位置满足的传输方程. 研究发现: 经足够长距离传输后, 在自由空间中最大光强位置比光束质心更靠近传输z轴, 并且其位置随着光束相干参数的增大而靠近传输z 轴, 随着光束偏心参数和遮拦比的增大而远离传输z轴. 但是, 在海洋湍流中最大光强位置趋于质心位置, 并且海洋湍流的增强会加速最大光强位置趋于质心位置的进程. 在海洋湍流中光束的相干性对光束传输特性的影响明显减小. 另一方面, 光束质心位置与光束的相干性、光束传输距离以及海洋湍流均无关系, 并且光束质心位置随着光束偏心参数和遮拦比的增大而远离传输z 轴. 所得结果对工作于水下湍流环境中的部分相干环状偏心光束的应用具有重要意义.     

Changes in polarization properties of partially polarized,partially coherent vectorial cosh-Gaussian beams propagating in oceanic turbulence

Changes in polarization properties of partially polarized, partially coherent vectorial cosh-Gaussian (ChG) beams propagating in oceanic turbulence are studied with the unified theory of coherence and polarization. Numerical examples of changes in optical intensity and polarization properties such as the degree of polarization, orientation angle, and degree of ellipticity of the beam propagating in the turbulent ocean are given. We find that both parameters of the source and oceanic turbulence have an effect upon the polarization properties of the beam. The degree of polarization fluctuates when the ChG beam propagates in the oceanic turbulence, and it has an obvious reconstruction phenomenon in the far-field zone.     

Modulation in the statistical properties of stochastic electromagnetic beams through an electromagnetic induced transparency atomic vapor

We report analytical expressions for the elements of the 2 × 2 cross-spectral density matrix of a stochastic electromagnetic beam passing through an electromagnetic induced transparency (EIT) atomic vapor. By use of the derived formulas the changes in the spectral density, the spectral degree of coherence, and the spectral degree of polarization of such a beam on propagation can be studied in detail. Numerical examples show that the statistical properties of the stochastic electromagnetic beam can be modulated by the Rabi frequency of the control light when the beam propagates through the EIT atomic vapor.     

Generalized Stokes parameters of random electromagnetic vortex beams propagating through atmospheric turbulence

By using the extended Huygens–Fresnel principle, the analytical expressions for the generalized Stokes parameters of random electromagnetic Gaussian Schell-model (GSM) vortex beams propagating through atmospheric turbulence are derived, and used to study the changes in spectral Stokes parameters of random electromagnetic GSM vortex beams in atmospheric turbulence and to compare the results of random electromagnetic GSM vortex-free beams. The influence of atmospheric turbulence on the spectral Stokes parameters is analyzed. The validity of our results is interpreted physically.     

Change in degree of coherence of partially coherent electromagnetic beams propagating through atmospheric turbulence

We study the change in the degree of coherence of partially coherent electromagnetic beam (so called electromagnetic Gaussian Schell-model beam). It is shown analytically that with a fixed set of source parameters and under a particular atmospheric turbulence model, an electromagnetic Gaussian Schell-model beam propagating through atmospheric turbulence reaches its maximum value of coherence after the beam propagates a particular distance, and the effective width of the spectral degree of coherence also has its maximum value. This phenomenon is independent of the used turbulence model. The results are illustrated by numerical curves.     

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.     

Propagation of spectral Stokes singularities of stochastic electromagnetic beams through atmospheric turbulence

The propagation of spectral Stokes singularities (vortices) of stochastic electromagnetic vortex beams through atmospheric turbulence is studied, where the electromagnetic Gaussian Schell-model (GSM) vortex beam is taken as an illustrative example. It is shown that the spectral Stokes vortices S ₁₂ (C-points), S ₂₃ and S ₃₁ introduced to describe the polarization singularities of stochastic electromagnetic beams appear in turbulence. The motion, creation, annihilation and polarization changes of S ₁₂, S ₂₃ and S ₃₁ vortices, as well as the handedness inversion of S ₁₂ vortices may appear as the propagation distance or one beam parameter varies. In the process the topological relationship holds true. In comparison with the free-space propagation, the variation of the refractive index structure constant C_n²C_{n}^{2} in atmospheric turbulence results in similar effects as above. The dependence of S ₁₂, S ₂₃ and S ₃₁ vortices on the propagation distance and beam and turbulence parameters are illustrated by numerical examples.     

Changes in the spectrum of twist anisotropic Gaussian Schell-model beams propagating through turbulent atmosphere

Based on the extended Huygens-Fresnel principle, the spectrum of twist anisotropic Gaussian Schell-model (TAGSM) beams propagating through turbulent atmosphere is derived analytically by using the partially coherent complex curvature tensor. The relative spectral shift of TAGSM beams propagating through turbulent atmosphere is closely related with the strength of atmospheric turbulence, the beam’s parameter and the radial coordinate. The on-axis spectral shift of TAGSM beams propagating through turbulent atmosphere changes from blue shift to red shift with the increasing of the propagation distance z, and at a certain propagation distance z, there exists a rapid transition of the spectrum at the critical position r_c.     

Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere

During the last few years, changes in the state of polarization of a class of random electromagnetic beams (so-called electromagnetic Gaussian Schell-model beams), propagating in free space have been investigated. In the present paper, we extend the analysis to propagation of such beams in homogeneous, isotropic, non-absorbing atmospheric turbulence. We find that the effects of turbulence on the state of polarization are most significant when the atmospheric fluctuations are weak or moderate, whereas in a strong regime of atmospheric fluctuations the state of polarization of the beam returns to its original state. Our results might find possible useful applications for sensing, imaging and communication through the atmosphere.     

Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere

During the last few years, changes in the state of polarization of a class of random electromagnetic beams (so-called electromagnetic Gaussian Schell-model beams), propagating in free space have been investigated. In the present paper, we extend the analysis to propagation of such beams in homogeneous, isotropic, non-absorbing atmospheric turbulence. We find that the effects of turbulence on the state of polarization are most significant when the atmospheric fluctuations are weak or moderate, whereas in a strong regime of atmospheric fluctuations the state of polarization of the beam returns to its original state. Our results might find possible useful applications for sensing, imaging and communication through the atmosphere.     

Spatiotemporal coherence properties of broadband Gaussian Schell-model beams propagating through atmospheric turbulence

The spatiotemporal coherence properties of broadband Gaussian Schell-model (GSM) beams with different spectral bandwidths propagating through atmospheric turbulence are numerically calculated and analyzed. The results show that although the spatial coherence properties of an intermediate-broadband GSM beam almost do not depend on the spectral bandwidth, those of its ultra-broadband counterpart do. The temporal coherence of an ultra-broadband GSM beam not only has radial dependence in the observation plane, but also varies with the increasing propagation distance; however, the same behavior does not hold for an intermediate-broadband GSM beam of which the temporal coherence remains nearly invariable as the radial distance of the observation point or propagation distance changes.     

Spatial correlation properties of apertured partially coherent beams propagating through atmospheric turbulence

The spatial correlation properties of apertured partially coherent beams propagating through atmospheric turbulence are studied in detail. By using the quadratic approximation of the Rytov’s phase structure function and the finite complex Gaussian expansion of the aperture function, the closed-form expression for the spectral degree of coherence of apertured partially coherent beams in turbulence is derived. It is shown that the larger the aperture width h is, and the smaller the spatial correlation length σ₀ of the source is, the less the spatial correlation is affected by turbulence. Specially, the influence of turbulence on the spatial correlation for unapertured partially coherent beams is less than that for apertured ones. The spectral degree of coherence is shown to possess phase singularities for apertured partially coherent beams, but the phase singularities behavior disappears when the turbulence is strong enough, which is very different from the behavior of unapertured partially coherent beams. In addition, a comparison between the width of the spectral degree of coherence and that of the spectral intensity of apertured partially coherent beams in turbulence is also given, and some interesting results are obtained. The results are interpreted physically. PACS  42.68.Bz; 42.79.Ag; 42.25.Fx     

Spectral and polarization properties of stochastic electromagnetic beams propagating in gain or absorbing media

Based on the generalized Huygens-Fresnel diffraction principle and on the unified theory of coherence and polarization of light, the analytical expressions for the cross-spectral density matrix of a class of stochastic electromagnetic beams in linear, deterministic media with gain or absorption, in which the wave number is generally complex, has been derived. In particular, through numerical examples based on our analytical formulas the behavior of the spectral density, and of the degree of polarization of the Electromagnetic Gaussian Schell-model is analyzed. It is demonstrated how these statistical properties of the beam propagating in such media depend on the properties of the source and on the wave number of the medium. Numerical examples relate to two model sources: with uncorrelated and partially correlated mutually orthogonal transverse components of the electric field. The results will impact potential applications involving natural absorbing media, such as oceanic waters, and man-made media such as active lasers, for instance.     

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.     

Properties of multi-Gaussian Schell-model beams carrying an edge dislocation propagating in oceanic turbulence

Based on the theory of coherence, the model of multi-Gaussian Schell-model(MGSM) beams carrying an edge dislocation generated by the MGSM source is introduced. The analytical cross-spectral density of MGSM beams carrying an edge dislocation propagating in oceanic turbulence is derived, and used to study the evolution properties of the MGSM beams carrying an edge dislocation. The results indicate that the MGSM beam carrying an edge dislocation propagating in oceanic turbulence will evolve from the profile with two intensity peaks into a flat-topped beam caused by the MGSM source, and the beam will evolve into the Gaussian-like beam due to the influences of oceanic turbulence in the far field.As the propagation distance increases, the MGSM beam carrying an edge dislocation propagating in oceanic turbulence with the larger rate of dissipation of mean-squared temperature(χT) and ratio of temperature to salinity contribution to the refractive index spectrum(?) or the smaller rate of dissipation of kinetic energy per unit mass of fluid(ε) evolves into the flat-topped beam or a Gaussian beam faster.     

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 properties of stochastic electromagnetic beams

The behavior of the degree of polarization of a Gaussian Schell-model beam propagating in free space is investigated. Contour diagrams for the degree of polarization, and for the spectral density (‘intensity’) of the polarized and the unpolarized portions of the beam are presented.