Propagation of partially coherent Bessel-Gaussian beams in turbulent atmosphere

The characteristics of partially coherent Bessel-Gaussian beams propagating in turbulent atmosphere are investigated. Based on the extended Huygens–Fresnel principle, the influence of topological charges and coherence of the source on the intensity and the degree of coherence in the received plane are considered. The influence of atmospheric turbulence on beam profile and coherence in the received plane is also analyzed. It is found that a Bessel-Gaussian shaped intensity distribution will eventually transform into a Gaussian distribution after propagating in turbulent atmosphere. Meanwhile, topological charges, coherence of the source and atmospheric turbulence will also influence the propagation characterizations of the beams.     

Propagation properties of partially coherent Laguerre-Gaussian beams in turbulent atmosphere

To study the propagation properties of partially coherent Laguerre-Gaussian (PLG) beams through turbulent atmosphere, the analytical formulas are derived for the angular width and the beam-propagation factor (M²-factor) of PLG beams by using the extended Huygens-Fresnel principle and the second-order moments of the Wigner distribution function (WDF). The corresponding numerical results are also calculated. When propagation distance increases, the angular width is found to spread faster for PLG beams with higher beam order, smaller correlation length and bigger structure constant The angular width of PLG beams decreases with increase in waist width (w₀).The M²-factor of PLG beams with higher beam order and smaller correlation length is less affected by turbulence with increase in propagation distance. The propagation properties of the M²-factor for PLG beams with the smaller structure constant are better than that with bigger structure constant . The M²-factor of PLG beams decreases with increase in the wavelength λ, and it is also less affected by turbulence for beams with higher order and smaller correlation length. Furthermore, for the PLG beams with the same beam order, the angular width and the M²-factor keep invariable in free space.     

Propagation factor of a truncated partially coherent flat-topped beam in turbulent atmosphere

Analytical expression for the propagation factor of a truncated partially coherent flat-topped (FT) beam in turbulent atmosphere is derived based on the extended Huygens-Fresnel integral and the second-order moments of the Wigner distribution function. Numerical results show that the radius of the aperture (i.e., truncation parameter) has strong influence on the evolution properties of the propagation factor of a truncated partially coherent FT beam, and the advantage of a truncated partially coherent FT beam over a truncated Gaussian Schell-model (GSM) beam or a truncated coherent FT beam for overcoming the turbulence-induced degradation disappears gradually with the decrease of the radius of the aperture.     

Quantum polarization fluctuations of partially coherent dark hollow beams in non-Kolmogorov turbulence atmosphere

Non-classical polarization properties of dark hollow beams propagating through non-Kolmogorov turbulence are studied. The analytic equation for the polarization degree of the quantization partially coherent dark hollow beams is obtained.It is found that the polarization fluctuations of the quantization partially coherent dark hollow beams are dependent on the turbulence factors and beam parameters with the detection photon numbers. Furthermore, an investigation of the changes in the on-axis propagation point and off-axis propagation point shows that the polarization degree of the quantization partially coherent dark hollow beams presents oscillation for a short propagation distance and gradually returns to zero for a sufficiently long distance.     

部分相干空心光束在湍流介质中的传输特性

根据广义的惠更斯-菲涅耳原理，得到了相干度为零阶贝塞耳函数的部分相干空心光束在湍流介质中传输特性的理论公式.据此研究了这种光束在湍流介质中的传输变化规律.研究结果表明，湍流介质的强弱，光源的相干性以及光源光斑大小均会影响光束的传输特性.     

Propagation and coherence properties of higher order partially coherent dark hollow beams in turbulence

We formulate and evaluate in terms of graphical outputs, source and receiver plane expressions, the complex degree of coherence, beam size variation and power in bucket performance for higher order partially coherent dark hollow beams propagating in turbulent atmosphere. Our formulation is able to cover square, rectangular, circular, elliptical geometries for dark hollow and flat-topped beams in one single expression. From the graphical outputs of the receiver plane, it is observed that higher order partially coherent dark hollow beams will initially develop an outer ring around a central lobe, but will eventually evolve towards a Gaussian shape as the propagation distance is extended. It is further observed that stronger turbulence levels and greater partial coherence have similar effects on beam profile. During propagation, modulus of complex degree of coherence of partially coherent dark hollow beams appears to rise above that of the source plane values, reaching as high as near unity. Beam size analysis shows that, among the types examined, (nearly) flat-topped beam experiences the least beam expansion. Power in bucket analysis indicates that lowest order square fully coherent dark beam offers the best power capturing.     

部分相干涡旋光束在湍流大气中的传输特性

根据广义的惠更斯-菲涅耳原理,推导了部分相干涡旋光束在湍流介质中传输时光强分布情况的理论公式,详细研究了部分相干涡旋光束在湍流介质中的传输变化规律。研究结果表明,湍流介质的强弱,光源的相干性以及光束所带拓扑电荷数大小均会影响光束传输特性。     

Propagation of a decentered astigmatic partially coherent beam in a turbulent atmosphere

Propagation properties of a decentered general astigmatic partially coherent beam (i.e., decentered twisted anisotropic Gaussian Schell-model beam) in a turbulent atmosphere are investigated. Analytical formulas for the cross-spectral density and decentered parameter of a decentered astigmatic partially coherent beam propagating in a turbulent atmosphere are derived. Irradiance properties of a decentered astigmatic partially coherent beam in a turbulent atmosphere are studied graphically, and are found to be quite different from its properties in free space.     

部分相干电磁光束在湍流介质中传输的偏振变化

 从推广的惠更斯-菲涅尔原理出发,推导出了部分相干电磁光束的偏振态在湍流介质中传输的表达式。并以电磁高斯-谢尔模型(EGSM)光束为例,研究了湍流对电磁高斯-谢尔模型光束偏振态的影响。研究结果表明,对于轴上点,湍流介质的折射率结构常数越大,偏振度趋于最大值的速度越快,达到的最大值越小;光斑越大,偏振度达到最大值的位置离光源越远,在光斑增大的过程中,偏振度所达到的极大值会先增大后减小,最后保持与光源相同的偏振度不变。对于轴外点,一个固定的z,光的偏振度随着离轴距离的增大而逐渐下降,并最终等于零。折射率结构常数越大,偏振度随离轴距离的增大而下降得越缓慢;光斑越大,偏振度随离轴距离的增大下降得越快。     

Propagation of partially coherent partially phase-locked laser array in turbulent atmosphere

The mechanism for beam quality degradation in recently developed phase locking of high power solid state lasers, which is caused mainly by partially coherent property of element beam and partially phase locking of the laser array, is analyzed in detail. Analytical expression for propagation of partially coherent partially phase-locked laser array in turbulent atmosphere is obtained based on extended Huygens-Fresnel principle. The effect of coherence width, phase error and intensity of turbulence on the beam quality in the target-plane is studied in detail. The tolerance on phase error for laser array with different coherence property is analyzed. It is concluded that the laser array with better coherence is more sensitive to turbulence, and phase control can improve beam quality in the receiving plane only in the case when the element beam has good beam quality and propagates in weak turbulence.     

Partially coherent aberrated beam propagating in a turbulent atmosphere

Based on the extended Huygens-Fresnel principle, the propagation formulate for partially coherent aberrated beam in a turbulent atmosphere has been derived. Then the propagation of such beams in the turbulent atmosphere has been studied in great detail. It is found that beams with spherical aberration spread more rapidly than those without spherical aberration. It is also found that the beam spreads more rapidly for a stronger turbulence or a source with lower coherence. In addition, some explanation to those results is also given.     

Propagation of a phase-locked circular dark hollow beams array in a turbulent atmosphere

The propagation of phase-locked circular dark hollow beams array in a turbulent atmosphere is studied. An analytical expression for the average intensity distribution at the receiving plane is obtained based on the extended Huygens-Fresnel principle. The effects of turbulence, dark parameter and beam order of the beams array on the intensity pattern are studied and analyzed. It is found that the intensity pattern of the phase-locked circular dark hollow beams array will evolve from a multiple-spot-pattern into a Gaussian beam spot under the isotropic influence of the turbulence. The intensity pattern of beam array with a larger dark parameter and beam order evolves into the Gaussian-shape faster with increasing propagation distance.     

Propagation of non-uniformly polarized beams in a turbulent atmosphere

Based on the extended Huygens-Fresnel diffraction integral, the propagation of non-uniformly polarized (NUP) beam in a turbulent atmosphere has been investigated. The influence of the source parameters and the atmospheric turbulence on the intensity distribution and polarization distribution has been studied in great details. It is shown that the non-uniform polarization of the beam influences the intensity distribution and makes the polarization distribution oscillate in the output plane. It is also found that the atmospheric turbulence can reduce the influence of non-uniform polarization of the beam on the intensity distribution and polarization distribution in the output plane.     

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.     

部分相干光束经过湍流大气传输研究进展

相较于相干光束,部分相干光束经过湍流大气传输能够有效地抑制湍流引起的光束展宽、光斑漂移及光强闪烁等扰动效应,在自由空间光通信、激光雷达和激光遥感等方面有重要的应用前景.近年来,部分相干光束湍流大气传输研究受到越来越多学者的关注.本文回顾了部分相干光束在湍流大气中传输特性研究的发展历程、理论基础及常用的理论方法,介绍了处理光束经过湍流大气传输的相位屏数值模拟方法,以及如何把该方法运用到处理部分相干光束传输.     

The influence of turbulence on propagation properties of partially coherent sinh-Gaussian beams and their beam quality in the far field

Based on the extended Huygens–Fresnel principle, the closed-form propagation equation of partially coherent Sinh-Gaussian (ShG) beams through the turbulent atmosphere has been derived by using the quadratic approximation of the Rytov's phase structure function. The influence of turbulence on propagation properties of partially coherent ShG beams and their beam quality in the far field are studied both analytically and numerical. The fully coherent ShG beam has been treated as a special case of the partially coherent ShG beam when the degree of spatial coherence α=∞. It is shown that in comparison with the free-space propagation the turbulence accelerates the evolution of three stages that partially coherent ShG beams undergo. The smaller α is, the less partially coherent ShG beams are affected by the turbulence. In particular, we find that the β parameter decreases as the decentered parameter δ increases, but the dependence of the Strehl ratio on δ is not monotonous. There exists an optimal δ_opt, the influence of turbulence on the maximum intensity of the corresponding partially coherent ShG beam with δ_opt is the smallest. Therefore, a suitable choice of δ may reduce the influence of turbulence on the beam quality in the far field in practice.     

Propagation of phase-locked partially coherent flattened beam array in turbulent atmosphere

Analytical formulae for phase-locked partially coherent flattened beam array propagating in a turbulent atmosphere are derived based on the extended Huygens–Fresnel principle. Beam propagation factor (BPF) is introduced to evaluate the beam quality at the receiving plane. The influence of beam order, transverse coherence width length and the intensity of turbulence is discussed in detail.     

Propagation properties of stochastic electromagnetic double-vortex beams in turbulent atmosphere

Based on the extended Huygens-Fresnel principle, we study the propagation properties of stochastic electromagnetic double-vortex beams in turbulent atmosphere. The result shows that the spreading of the partially coherent double-vortex beams can be smaller than that of the fully coherent ones. The degree of polarization of this kind of beam will experience change, which is dependent on the degree of polarization of the source plane, the atmospheric turbulence, topological charge, and the spatial coherence. The results may have applications in space optical communication.     

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.     

Propagation factors of Hermite–Gaussian beams in turbulent atmosphere

Based on the extended Huygens–Fresnel integral and the second-order moments of the Wigner distribution function, an analytical formulae for the propagation factors (M²-factors) of coherent and partially coherent one-dimensional Hermite–Gaussian beams in a turbulent atmosphere are derived. Evolution properties of the M²-factor of the Hermite–Gaussian beam in a turbulent atmosphere are studied numerically in detail. Our results show that the M²-factor of the Hermite–Gaussian beam increases upon propagation in a turbulent atmosphere. The M²-factor of the Hermite–Gaussian beam with larger beam order (or lower coherence) increases slower that of the Hermite–Gaussian beam with smaller beam order (or higher coherence) in a turbulent atmosphere, which means that the Hermite–Gaussian beam with a larger beam order and lower coherence is less affected by a turbulent atmosphere. Our results will be useful in long-distance free-space optical communications.