部分相干余弦-高斯光束

引入部分相干余弦-高斯光束,推导出部分相干余弦-高斯光束通过近轴ABCD光学系统的传输公式和M2因子,研究了部分相干余弦-高斯光束通过像散透镜的传输特性.结果表明,部分相干余弦-高斯光束的M2因子与部分相干余弦-高斯光束的空间相干参量和离心参量有关,但与透镜的像散系数无关.适当选取空间相干参量,离心参量或像散系数,在几何焦面处可得到类高斯、平顶和空心等不同的光强剖面,实现部分相干余弦-高斯光束的空间整形.     

Off-axis Gaussian Schell-model beam and partially coherent laser array beam in a turbulent atmosphere

The propagation of an off-axis Gaussian Schell-model (GSM) beam in a turbulent atmosphere is investigated based on the extended Huygens-Fresnel integral formula. Analytical formulae for the cross-spectral density and corresponding partially coherent complex curvature tensor of an off-axis GSM beam propagating in a turbulent atmosphere are derived. Based on these formulae, the propagation properties of such kind of beam in a turbulent atmosphere are investigated in detail. Furthermore, the methods are extended to investigate the propagation properties of a partially coherent laser array beam in a turbulent atmosphere. The properties of an off-axis GSM beam and a partially coherent laser array beam in a turbulent atmosphere are closely related with the beam parameters and the structure constant of the turbulent atmosphere.     

Statistical properties of a cylindrical vector partially coherent beam in turbulent atmosphere

Cylindrical vector (CV) partially coherent beam was introduced (Dong et al. Opt Express 19:5979–5992, 2011) and generated (Wang et al. Appl Phys Lett 100:051108, 2012) recently. In this paper, we derive the realizability conditions for a CV partially coherent beam, and we derive the analytical formula for the cross-spectral density matrix of a CV partially coherent beam propagating in turbulent atmosphere based on the extended Huygens-Fresnel formula. The statistical properties, such as the average intensity, the complex degree of coherence and the degree of polarization of a CV partially coherent beam in turbulent atmosphere are studied in detail and compared with those in free space. It is found that the statistical properties of a CV partially coherent beam in turbulent atmosphere are much different from those in free space, and are affected by the initial beam parameters.     

M 2-factors of a non-circular partially coherent flat-topped beam

Based on the extended Huygens-Fresnel integral and the second-order moments of the Wigner distribution function, analytical formulae for the propagation factors (known as M ²-factors) of a non-circular (i.e., rectangular or elliptical) partially coherent flat-topped beam in turbulent atmosphere are derived. The properties of the M ²-factors of a non-circular partially coherent flat-topped beam in turbulent atmosphere and in free space are studied numerically and comparatively. It is found that the evolution properties of the M ²-factors are mainly determined by the parameters of the beam and the turbulent atmosphere. The relative M ²-factors of a non-circular partially coherent flat-topped beam can be smaller than a circular partially coherent flat-topped beam and a Gaussian Schell-model beam, particularly at long propagation ranges in turbulent atmosphere. Our results will be useful in long-distance free-space optical communications.     

Analytical formula for a decentered elliptical Gaussian beam propagating in a turbulent atmosphere

Analytical formulas for the average intensity and decentered parameter of a decentered elliptical Gaussian beam (DEGB) propagating in a turbulent atmosphere are derived in a tensor form. The propagation properties of a DEGB in a turbulent atmosphere are investigated in detail, and found to be different from that in free space. Furthermore, as an application example, we investigate the propagation of a decentered elliptical flat-topped beam (DEFB) by expressing its electric field as a finite sum of DEGBs in a turbulent atmosphere. The properties of a DEGB or a DEFB in a turbulent atmosphere are closely related with the beam’s parameters and the structure constant of the turbulent atmosphere.     

Scintillation index of astigmatic annular beams in a turbulent atmosphere

The scintillation properties of astigmatic annular beams in a weak turbulent atmosphere are investigated. Expression for the on-axis scintillation index of an astigmatic annular beam is derived. It is found that the scintillation index of an astigmatic annular beam can be smaller than that of a Gaussian beam, an elliptical Gaussian beam and a stigmatic annular beam in a weak turbulent atmosphere under certain conditions. The scintillation properties of astigmatic annular beams are closely controlled by its beam parameters.     

The propagation of radially polarized partially coherent beam through an optical system in turbulent atmosphere

The propagation of a radially polarized partially coherent beam through an optical system in turbulent atmosphere is investigated. Analytical propagation formulae for the radially polarized partially coherent beam through an optical system in turbulent atmosphere are derived, and some analyses are illustrated by numerical examples related to propagation properties of the radially polarized partially coherent beam through a double-lens system in turbulent atmosphere. It is shown that the optical system, structure constant of turbulent atmosphere and the initial coherent length have significant influence on intensity, degree of polarization and degree of coherence for radially polarized partially coherent beam.     

扰动大气中部分相干光束的光谱特性

对扰动大气中传输的部分相干光束的光谱演化特性进行了研究。利用推广的惠更斯一菲涅耳原理．得到了扰动大气中部分相干光束的交叉光谱密度,据此分析了在大气扰动影响下部分相干光束的频移效应以及空间相干度的变化规律。结果表明：由于大气扰动的影响,在光束传输过程中,轴上光谱先是出现蓝移,蓝移量先增大后减小,传输足够远距离之后将出现红移,并且光束的相干性越差,就需要传播越远的距离才会发生红移;而光束的空间相干度随传输距离增大到一定程度之后开始减小,最终将趋于零。通过与自由空间中部分相干光的传输特性比较,发现当光束的传输距离比较小时．大气扰动效应对光谱特性的影响很小,只有在传输距离足够远时,大气扰动对光谱特性的影响才会明显地表现出来。     

部分相干双曲正弦高斯光束的M~2因子与湍流距离

基于广义惠更斯-菲涅耳原理和维格纳分布函数方法,推导出了部分相干双曲正弦高斯(ShG)光束在湍流大气中M2因子的解析表达式。在此基础上研究了部分相干ShG光束的湍流距离,即湍流引起的光束扩展可忽略的范围。采用Von Karman谱分别对M2因子和湍流距离进行了数值计算,并分析了内外尺度的影响。研究表明:M2因子随束腰宽度和离心参数的增加存在极小值;湍流距离随束腰宽度的增加存在极大值,随离心参数的增加而增加,大气湍流对离心参数较大的光束影响较小。另外,M2因子和湍流距离与折射率结构参数、内尺度、外尺度、波长和相干参数等密切相关。     

Partially coherent elegant Hermite–Gaussian beam in turbulent atmosphere

Based on the extended Huygens–Fresnel integral, analytical formulas for the cross-spectral density, mean-squared beam width and angular spread of a partially coherent elegant Hermite–Gaussian (HG) beam in turbulent atmosphere are derived. The evolution properties of the average intensity, spreading and directionality of a partially coherent elegant HG beam in turbulent atmosphere are studied numerically. It is found that the partially coherent elegant HG beam with smaller initial coherence width, larger beam order and longer wavelength is less affected by the atmospheric turbulence. Compared to the partially coherent standard HG beam, the partially coherent elegant HG beam is less affected by turbulence under the same condition. Furthermore, it is found that there exist equivalent partially coherent standard and elegant HG beams, equivalent fully coherent standard and elegant HG beams, and an equivalent Gaussian–Schell-model beam may have the same directionality as a fully coherent Gaussian beam whether in free space or in turbulent atmosphere. Our results can be utilized in short and long atmospheric optical communication systems.     

Partially coherent vortex beams propagation in a turbulent atmosphere

Based on the Rytov approximation and the cross-spectral density approximation for the mutual coherence function of the partially coherent field, the propagation properties of the partially coherent beams with optical vortices in turbulent atmosphere are discussed. The average intensity and the mutual coherence function of the partially coherent vortex beams propagation in weak turbulent atmosphere are obtained.It is shown that the vortex structure of the average cross-spectral density of partially coherent beams has the same helicoidally shape as that of the phase of the fully coherent Laguerre-Gauss beams in free space and the relative intensity of the beam is degraded by optical vortex.     

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.     

Propagation of partially coherent controllable dark hollow beams with various symmetries in turbulent atmosphere

Normalized intensity distribution, the complex degree of coherence and power in the bucket for partially coherent controllable dark hollow beams (DHBs) with various symmetries propagating in atmospheric turbulence are derived using tensor method and investigated in detail. Analytical results show that, after sufficient propagation distance, partially coherent DHBs with various symmetries eventually become circular Gaussian beam (without dark hollow) in turbulent atmosphere, which is different from its propagation properties in free space. The partially coherent DHBs return to a circular Gaussian beam rapidly for stronger turbulence, higher coherence, lower beam order, smaller p or smaller beam waist width. Another interesting observation is that the profile of the complex degree of coherence attains a similar profile to that of the average intensity of the related beam propagating in a turbulent atmosphere. Besides the laser power focusablity of DHBs are better than that of Gaussian beam propagating in turbulent atmosphere.     

Twist phase-induced reduction in scintillation of a partially coherent beam in turbulent atmosphere

The scintillation index of a Gaussian Schell-model beam with twist phase (i.e., twisted GSM beam) in weak turbulent atmosphere is formulated with the help of a tensor method. Variations of the scintillation index of a twisted GSM beam on propagation in turbulent atmosphere are studied in detail. It is interesting to find that the scintillation index of a twisted GSM beam can be smaller than that without twist phase in weak turbulent atmosphere. Thus, modulation of the twist phase of a partially coherent beam provides a new way to reduce turbulence-induced scintillation.     

Spectral changes of aberrated stochastic electromagnetic flat-topped beams propagating in turbulent atmosphere

In this paper, taking the electromagnetic partially coherent flat-topped (PCFT) beam as an example, we investigate the spectral changes of stochastic electromagnetic beams with astigmatic aberration propagating through a turbulent atmosphere. The analytic expressions for the spectrum of the beams propagating through the turbulent atmosphere are derived. It is shown that the spectral changes of the electromagnetic PCFT beams in the turbulent atmosphere are closely related with the astigmatism aberration, the strength of atmospheric turbulence, the inner scale of turbulence, the correlation of source and the order of flatness of electromagnetic PCFT beams. It is important to note that the spectral changes of the aberrant electromagnetic PCFT beams are insensitive to the atmospheric turbulence. Some possible explanations have also been given for the interesting physical phenomena.     

部分相干双曲余弦-高斯光束的传输特性和空间整形

 通过加入高斯项的空间相干度，引入部分相干双曲余弦-高斯（ChG）光束，推导出部分相干ChG光束通过近轴ABCD光学系统传输的解析表达式，并用以研究其传输特性和空间整形。结果表明，部分相干ChG光束的光强分布不能保持传输不变性，其光强分布不仅与传输距离和离心参数有关，而且还与空间相干参数有关。在传输距离固定时，适当改变部分相干ChG 光束的离心参数和空间相干参数，可实现光束的空间整形。光束质量因子随空间相干性的增大和离心参数的减小而减小。高斯-谢尔模型光束和完全相干ChG光束可作为部分相干ChG光束的特例处理。     

TAGSM光束在大气湍流中传输

基于广义惠更斯－菲涅耳原理,利用部分相干光复曲率张量研究了有扭曲的各向异性高斯－谢尔模型光束在湍流大气中的传输规律.根据有扭曲的各向导性高斯-谢尔模型光束在大气湍流中传播距离z处的部分相干复曲率张量给出了光束参量的表达式和详细的数值计算结果.结果表明：大气湍流减缓了光束扭曲参量随传播距离的衰减趋势,增大了主方向上的波前曲率的峰值,而且大气湍流退化了光束的相干性,使得光束扩展严重;光源扭曲参量大小和相干性也都会影响TAGSM光束在大气湍流中传输时各个光束参量的变化规律.     

Intensity distribution for the broadband aberrated partially coherent flat-topped beam propagating through turbulent atmosphere

In this paper, taking the partially coherent flat-topped (PCFT) beam as an example, we investigate the intensity distribution of broadband beams with astigmatic aberration propagating through a turbulent atmosphere. The analytic expressions for the intensity of the beams propagating through the turbulent atmosphere are derived. It is shown that the intensity distribution of the broadband aberrated PCFT beams in the turbulent atmosphere are closely related with the astigmatism aberration, the strength of atmospheric turbulence, the order of flatness, the correlation of source and the bandwidth of PCFT beams. It is important to note that the position of the focal plane of the broadband aberrated (or not) PCFT beams can be modulated by changing the aberration, the order of flatness, the correlation and the bandwidth of PCFT beams.     

Generalized tensor ABCD law for an elliptical Gaussian beam passing through an astigmatic optical system in turbulent atmosphere

The propagation of an elliptical Gaussian beam (EGB) through an astigmatic ABCD optical system in a turbulent atmosphere is investigated. An analytical formula for the average intensity of an EGB and a generalized tensor ABCD law for the generalized complex curvature tensor are derived. As an application example, we derived an analytical formula for the average intensity of an elliptical flat-topped beam propagating through an astigmatic ABCD optical system in a turbulent atmosphere. As a numerical example, the focusing properties of an EGB focused by a thin lens in a turbulent atmosphere are studied. It is found that the focused beam at the focal plane becomes a circular Gaussian beam when the atmospheric turbulence is strong enough, and the beam width of the circular Gaussian beam is determined by atmospheric turbulence strength, focal length of the thin lens, and wavelength of the initial beam but is independent of the initial beam widths (i.e., initial intensity distribution).     

部分相干双曲余弦高斯光束通过湍流大气的光束扩展

基于广义惠更斯-菲涅尔原理，并采用将部分相干双曲余弦高斯光束用厄米-高斯光束的非相干叠加表示的方法，研究了部分相干双曲余弦高斯光束通过湍流大气的光束扩展问题，推导出了部分相干双曲余弦高斯光束通过湍流大气均方根束宽的解析表达式.研究表明，部分相干双曲余弦高斯光束的扩展随着湍流大气的折射率结构常数C²_n和光束离心参数δ的增大而加剧.但是，随着δ的增大，部分相干双曲余弦高斯光束受到湍流的影响减小. 关键词： 部分相干双曲余弦高斯光束 湍流大气 光束扩展