Transformation and spatial shaping of partially coherent cosh-Gaussian beams through an astigmatic lens

Based on the propagation law of partially coherent beams, the closed-form propagation expression for partially coherent cosh-Gaussian (ChG) beams through an astigmatic lens is derived. The transformation and spatial shaping of partially coherent ChG beams through the astigmatic lens are studied and illustrated by numerical examples. It is shown that a suitable choice of the spatial coherence parameter and/or astigmatic coefficient, different beam profiles, such as Gaussian-like, flat-topped and bottle beam profiles, and beam profile with a central dip, at the geometric focal plane and at a certain plane are realizable.     

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.     

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.     

Decentered twisted Gaussian Schell-model beams and their propagation through a misaligned first-order optical system

The propagation properties of decentered twisted Gaussian Schell-model (DTGSM) beams passing through a misaligned first-order optical system are studied. The explicit expressions for the cross-spectral density function and Wigner distribution function of the output beam are derived, which retain their form unchanged. It is shown that the DTGSM beams preserve their closed property. The second-order moments matrix and the Wigner distribution function evolve with the usual laws, whereas the first-order moments matrix varies, as if a ray passes through such system. The propagation of DTGSM beams through an aligned first-order optical system is treated as the limiting case that corresponds to the vanishing misalignment parameters.     

Polynomial Gaussian beams and topological charge conservation

We investigate polynomial Gaussian beams with rotationally symmetric Gaussian envelops and complex bivariate polynomial prefactors of finite order. A formalism for the propagation of such beams is developed, which expresses how the coefficients of the polynomial transform during propagation. This formalism is used to proof that global topological charge is conserved for this class of polynomial Gaussian beams.     

Phase-flipped Hermite-Gaussian beams and their propagation beyond the paraxial approximation

An extension of phase-flipped Gaussian (PFG) beams to the multi-mode nonparaxial case is made. The recurrence propagation expressions for phase-flipped Hermite-Gaussian (PFHG) beams beyond the paraxial approximation are derived and used to study nonparaxial propagation properties of PFHG beams in free space and through a knife edge and an aperture, and to compare nonparaxial results with paraxial ones. The propagation of paraxial PFHG beams and PFG beams and nonparaxial PFG beams is treated as special cases of nonparaxial PFHG beams. Numerical examples are given to illustrate the theoretical results.     

Circular beams

A very general beam solution of the paraxial wave equation in circular cylindrical coordinates is presented. We call such a field a circular beam (CiB). The complex amplitude of the CiB is described by either the Whittaker functions or the confluent hypergeometric functions and is characterized by three parameters that are complex in the most general situation. The propagation through complex ABCD optical systems and the conditions for square integrability are studied in detail. Special cases of the CiB are the standard, elegant, and generalized Laguerre-Gauss beams; Bessel-Gauss beams; hypergeometric beams; hypergeometric-Gaussian beams; fractional-order elegant Laguerre-Gauss beams; quadratic Bessel-Gauss beams; and optical vortex beams.     

Propagation of Gaussian array beams in uniaxial crystals orthogonal to the optical axis

The propagation of phase-locked and non-phase-locked Gaussian array beams in uniaxial crystals orthogonal to the optical axis is investigated. Analytical formulas are derived and the propagation properties of phase-locked and non-phase-locked Gaussian array beams are illustrated by numerical examples. Our results show that for non-phase-locked combination, the Gaussian array beams involve into an elliptical Gaussian-like distribution when the propagation distance is far enough, while for phase-locked combination, the Gaussian array beams involve into a central peak distribution and some small peaks are around the center peak when the propagation distance is far enough.     

The effects of induced heat loads on the propagation of Ince-Gaussian beams

Thermal effects are very much influential in high power beam generators. Their impacts on special types of beams such as Helmholtz-Gauss beams have attracted special attentions. This work reports thermal effects on the generation and propagation of Ince-Gaussian beams. The results show considerable beam spot size variations for near fields under various induced heat loads. As Ince-Gaussian beams are directly related to cavity symmetry breaking, the results can greatly help system designers for circumventing these types of symmetry breaks usually encountered in high power lasers.     

Stokes beams formed by superposition of a completely unpolarized and a completely polarized Gaussian Schell-model beam

Analytic expressions and computed examples are given to elucidate the coherence and polarization properties of Stokes beams, i.e. beams formed by superposition of a completely unpolarized and a completely polarized electromagnetic Gaussian Schell-model beam. We found that superposition of such two beams cannot form a Stokes beam with a constant state of polarization on propagation. An additional constraint on the source plane parameters of the two Gaussian Schell-model beams is proposed. The resultant Stokes beam with a constant state of polarization on propagation is found to be a Gaussian Schell-model beam with the same variances as the two constituent Gaussian Schell-model beams. However, the modulus of the Gaussian intensity distributions across the source planes of these beams may be different.     

Nonparaxial Lorentz and Lorentz-Gauss beams

The Lorentz and Lorentz-Gauss beams are extended to the nonparaxial regime. Analytical propagation expressions of nonparaxial Lorentz and Lorentz-Gauss beams in free space are derived, and the propagation of paraxial Lorentz and Lorentz-Gauss beams is treated as a special case of our general results. The propagation properties of Lorentz and Lorentz-Gauss beams are illustrated and compared with numerical examples.     

部分相干刃型位错光束的谱Stokes奇点

利用交叉谱密度函数的传输公式,推导出部分相干刃型位错光束在自由空间中传输的解析表达式.结合谱Stokes参数,详细讨论了其Stokes场的奇点变化规律.结果表明,部分相干刃型位错光束在自由空间传输过程中存在谱s12,s23和s31奇点.改变刃型位错的离轴量、斜率、空间相关长度等光束参数以及随着传输距离的变化,会有谱Stokes奇点的移动、产生和湮没,也会有V点的产生和C点旋性的反转.     

高功率激光在非均匀大气中传输的自聚焦效应研究进展

地基激光空间碎片清除和利用激光辐射把转换的太阳能从空间轨道输运到地面等应用中,不可避免地遇到高功率激光在非均匀大气中的传输问题。由于激光功率已远远超过大气非线性自聚焦临界功率,大气自聚焦效应是影响光束质量的一个重要物理因素。概述了近年来国内外高功率激光在非均匀大气中上行或下行传输的自聚焦效应研究进展,主要介绍了高功率激光在非均匀大气中的传输模型、理论基础、数值和解析研究方法,着重介绍了自聚焦效应对激光传输特性和光束质量的影响,并总结了优化靶面光束质量的方案。此外,还介绍了大气群速度色散效应和大气湍流效应等物理因素对激光光束质量的影响。最后,还提出了该领域值得进一步深入研究的一些问题。     

Automatic Fourier transform and self-Fourier beams due to parabolic potential

We investigate the propagation of light beams including Hermite–Gauss, Bessel–Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. In addition to oscillation, the finite-energy Airy beams exhibit periodic inversion during propagation. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. Based on the propagation in parabolic potential, we introduce a class of optically-interesting beams that are self-Fourier beams—that is, the beams whose Fourier transforms are the beams themselves.     

Changes in the statistical properties of stochastic anisotropic electromagnetic beams propagating through the oceanic turbulence

On the basis of the extended Huygens?CFresnel principle, an analytical propagation expression for the elements of the cross-spectral density matrix of a stochastic anisotropic electromagnetic beam through oceanic turbulence is derived. From this formula the spectral density, spectral degree of coherence, spectral degree of polarization, orientation angle and the degree of ellipticity of such a beam on propagation are determined. Some numerical calculations are illustrated relating to the anisotropic electromagnetic Gaussian Schell-model beams propagating through oceanic turbulence. The results indicate that the spectral degree of coherence of stochastic anisotropic electromagnetic beams tends to zero with increasing propagation distance through oceanic turbulence, which is in agreement with results previously reported for turbulent atmosphere. It is also found that the changes in the statistical properties of the anisotropic source on propagation are qualitatively different from those of the isotropic source.     

Paraxial propagation of cosh-Airy vortex beams in chiral medium

Propagation dynamics of the cosh-Airy vortex(CAiV) beams in a chiral medium is investigated analytically with Huygens–Fresnel diffraction integral formula. The results show that the CAiV beams are split into the left circularly polarized vortex(LCPV) beams and the right circularly polarized vortex(RCPV) beams with different propagation trajectories in the chiral medium. We mainly investigate the effect of the cosh parameter on the propagation process of the CAiV beams.The propagation characteristics, including intensity distribution, propagation trajectory, peak intensity, main lobe's intensity, Poynting vector, and angular momentum are discussed in detail. We find that the cosh parameter affects the intensity distribution of the CAiV beams but not its propagation trajectory. As the cosh parameter increases, the distribution areas of the LCPV and RCPV beams become wider, and the side lobe's intensity and peak intensity become larger. Besides, the main lobe's intensity of the LCPV and RCPV beams increase with the increase of the cosh parameter at a farther propagation distance, which is confirmed by the variation trend of the Poynting vector. It is significant that we can vary the cosh parameter to control the intensity distribution, main lobe's intensity, and peak intensity of the CAiV beams without changing the propagation trajectory. Our results may provide some support for applications of the CAiV beams in optical micromanipulation.     

特殊关联结构光束的大气传输研究进展

近年来,光场调控逐渐成为光学领域的热点研究课题,光场相干性调控可以引发许多新颖物理效应。其中,通过相干性调控得到的特殊关联结构光束不仅展现出奇特的传输特性,而且可以有效地降低大气湍流引起的光强退化、光束漂移、光强闪烁和退偏振等负面效应。因此,特殊关联结构光束在自由空间光通信领域具有重要的应用前景。本文回顾了特殊关联结构光束的构建基础理论和大气传输研究方法及其发展历程,举例展示近些年典型特殊关联结构光束的大气传输研究成果。     

Propagation of laser array beams in a turbulent atmosphere

The propagation of phase-locked and non-phase-locked laser array beams of radial and rectangular symmetries in a turbulent atmosphere are investigated based on the extended Huygens–Fresnel integral. The beamlet used in our paper for constructing the laser array beams is of elliptical Gaussian mode. Analytical formulae for the average irradiance of phase-locked and non-phase-locked radial and rectangular laser array beams are derived through vector integration and tensor operation. The irradiance properties of these laser array beams in a turbulent atmosphere are studied numerically. It is found that both phase-locked and non-phase-locked radial and rectangular laser array beams eventually become circular Gaussian beams in a turbulent atmosphere, which is much different from their propagation properties in free space. The propagation properties are closely related to the parameters of laser array beams and the structure constant of the turbulent atmosphere. PACS 42.25.Bs; 41.85.Ew; 42.68.Ay     

强非局域介质中1+1维高斯型损耗空间双孤子的相互作用

研究了1+1维高斯型双光束在含小损耗的强非局域非线性介质中的传输特性。通过对该介质中光束传输遵循的非局域非线性薛定谔方程进行近似简化,得到了含小损耗强非局域非线性介质中1+1维高斯型双光束传输模型。在此基础上运用解析的方法研究了双光束传输的演化规律,得到了准双孤子解。经过进一步分析发现,在传输过程中两光束中心的轨迹为艾里函数;两光束会准周期性地碰撞、分离;随着传输距离的增大,两光束中心之间的最大距离会越来越大。另一方面,当损耗逐渐增大时,两光束的碰撞空间周期将变短,同时两光束中心之间的最大距离也越来越大。     

Cartesian beams

A new and very general beam solution of the paraxial wave equation in Cartesian coordinates is presented. We call such a field a Cartesian beam. The complex amplitude of the Cartesian beams is described by either the parabolic cylinder functions or the confluent hypergeometric functions, and the beams are characterized by three parameters that are complex in the most general situation. The propagation through complex ABCD optical systems and the conditions for square integration are studied in detail. Applying the general expression of the Cartesian beams, we also derive two new and meaningful beam structures that, to our knowledge, have not yet been reported in the literature. Special cases of the Cartesian beams are the standard, elegant, and generalized Hermite-Gauss beams, the cosine-Gauss beams, the Lorentz beams, and the fractional order beams.