平顶高斯光束经含失调圆孔光阑的失调光学系统的传输特性

为分析平顶高斯光束通过光学系统传输时圆孔光阑失调和光学元件失调对平顶高斯光束传输特性的影响,利用失调圆孔光阑的近似展开式和适用于失调光学系统的广义衍射公式,得出了平顶高斯光束经含失调圆孔光阑的失调光学系统传输的近似解析式,给出了输出光束场分布与光束参量、光阑孔径尺寸、光阑和光学元件失调量等的定量关系.针对特定光学系统定量分析了各失调量对输出光束场分布的影响,结果表明各元件失调都对输出光束强度分布产生较大影响.但在各失调量较小的情况下,透镜失调对输出光束传输特性的影响比光阑失调对输出光束传输特性的影响更明显.     

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).     

曲率波前传感器探测高斯光束时的信号误差

曲率波前传感器已被用于天文自适应光学和光学度量等领域。在这些领域使用时都假设入射波前光强均匀,但这种假设与曲率传感技术的基本原理不一致。利用傅里叶光学理论,给出了光强不均匀情况下曲率波前传感器的曲率信号解析式,并利用光强均匀和不均匀情况下的信号表达式对探测高斯光束时的信号误差进行了数值分析。结果表明：曲率波前传感器探测高斯光束时存在一定误差,相位分布为4阶Zernike多项式时,误差最大,且阶数越高,误差越小;分区平均曲率信号误差较小,一般在10％以下。     

Propagation aspects of Mathieu–Gaussian beams in turbulence

Based on our recent source plane formulation, the propagation characteristics of Mathieu–Gaussian beams in turbulent atmosphere are investigated. In this connection, the average receiver plane intensity expression is deduced using the Huygens–Fresnel integral. Our results offered in the form of graphical illustrations reveal that, for some settings of source and propagation parameters, the center of the source beam is evacuated after propagation, while the initially smaller side lobes begin to grow. In a parallel development, the angular distribution of the beam also changes. At small Gaussian source sizes and transverse components of the wave vector, the source beam profile remains almost invariant throughout the propagation. The larger refractive index structure constant values cause the final Gaussian beam profile to be attained at earlier propagation distances. Smaller refractive index structure constants, on the other hand, do not change the beam profile substantially from that of free space.     

Intensity correlations of general type beam in weakly turbulent atmosphere

In weakly turbulent atmosphere, intensity correlations at the receiver plane are formulated for a general type optical beam. Evaluating our formula at the appropriate source parameters versus the diagonal distance, intensity correlations for cos Gaussian, cosh Gaussian, annular and flat-topped Gaussian beams are obtained. As compared to Gaussian beam, intensity correlations are found smaller for cos Gaussian and larger for cosh Gaussian beams. Intensity correlations of cos Gaussian, cosh Gaussian and flat-topped Gaussian beams become larger at large source sizes. Thicker annular beams and flatter flat-topped Gaussian beams show larger intensity correlations. Without generalizing, intensity correlations tend to increase when the link length and the structure constant decrease and the wavelength increases. Our results show that the intensity correlations are not only built up using random medium effects, but also using the diffraction pattern formed at the receiver plane for the specific incidence investigated. As a check point, for all source types and medium parameters, our evaluations indicate that intensity correlations approach zero at sufficiently large diagonal distances.     

散斑位移法测量激光高斯光束的空间分布

 提出一种测量激光光束高斯空间分布特征的新方法——散斑位移法。该方法利用光传播的菲涅尔衍射公式和光场的统计规律,给出散斑场光强在散射体位移前后的高斯光束相关函数的表达式。测出相关函数在光路上某一位置的数值,并由此同时求出高斯光束的束腰位置和大小。     

Gaussian beam scattering by a chiral sphere

Based on the generalized Lorenz–Mie theory that provides the general framework, an analytic solution to Gaussian beam scattering by a chiral sphere is constructed, by expanding the incident Gaussian beam, scattered fields and internal fields in terms of spherical vector wave functions. The unknown expansion coefficients are determined by a system of equations derived from the boundary conditions. For a localized beam model, numerical results of the normalized differential scattering cross section are presented.     

横向激发线偏振高斯光束的非傍轴传输

文章提出一种横向激发的任意线偏振高斯光束,该光束场量的模与传统的任意线偏振高斯光束具有相同的模,在源场区,其满足自由空间无源场的场方程。同时利用瑞利—索末菲衍射积分对该高斯光束的非傍轴传输特性进行了解析研究,给出了空间光强分布、束腰和远场发散角的解析通式,发现该类光束的远场光强呈一平顶空心光束。     

Propagation of a four-petal Gaussian vortex beam through a paraxial ABCD optical system

Based on the Collins diffraction integral formula, an analytical expression of a general four-petal Gaussian vortex beam passing through a paraxial ABCD optical system is derived by means of the mathematical technique. As a numerical example, the normalized intensity distribution of a four-petal Gaussian vortex beam propagating in free space is graphically demonstrated. The influences of beam order and topological charge on the normalized intensity distribution are discussed in detail. This research is useful to the optical trapping, optical communications, and beam splitting techniques, etc.     

高斯光束通过含失调窄缝光阑的失调光学系统的传输特性

 利用硬边窄缝光阑的近似展开式和适用于失调光学系统的广义衍射公式,得出了高斯光束经含失调窄缝光阑的失调光学系统传输的近似解析式。模拟结果表明输出光束场分布与光束参量、光阑尺寸、ABCD矩阵元、光阑失调量和光学系统失调量有关。针对给定的光学系统和高斯光束定量分析了各失调量对输出光束场分布的影响,结果表明:光阑横向位移、光学系统横向位移和角位移均引起垂直于z轴截面内明显的光强非轴对称分布。当光阑半宽度为1 mm时,光阑的衍射作用使腰斑半径为0.5 mm的高斯光束产生-1.586π～1.465π范围的相对相移,且光阑横向位移、光学系统横向位移和角位移均引起焦平面前后相对相移的迅速变化。随光阑宽度变小,各失调量对输出光束特性的影响越明显。     

The simulation of ultrasonic beams with a Gaussian beam equivalent point source model

Point Sources and Gaussian beams are used frequently as fundamental building blocks for developing ultrasonic beam models. Both these models have different weaknesses that limit their effectiveness. Here, we will show that one can develop a Gaussian Beam Equivalent Point Source （GBEPS） model that removes those weaknesses and combines the accuracy and versatility of the point source models with much of the speed and well-behaved nature of Gaussian beam models. We will demonstrate the efficiency and versatility of this new GBEPS model in simulating the beams generated from ultrasonic phased arrays, using as few as one Gaussian beam per element of the array. A single element GBEPS model will be shown to be as accurate as a point source model even when substantial beam focusing or steering is present in the array or where the array beam is transmitted through an interface. At the same time the GBEPS model will be shown to be several orders of magnitude faster than the point source model.     

Propagation of higher order Bessel–Gaussian beams in turbulence

The propagation characteristics of higher order Bessel–Gaussian beams travelling in turbulent atmosphere are investigated. Using extended Huygens–Fresnel principle, I formulated receiver plane intensity and solved it down to a double integral stage. Source beam plots are made illustrating the variation of intensity against order and width parameter. From the examination of receiver intensity graphs, it is seen that Bessel–Gaussian beam are converted into modified Bessel–Gaussian beams at intermediate propagation ranges eventually ending up as Gaussian profiles. The impacts of order and turbulence levels on beam profile are analysed. Focusing effects and beam size change along the propagation axis are studied. PACS 41.85.Ew; 42.68.Bz     

Propagation of elegant Hermite cosine Gaussian laser beams

In this paper, a more generalized beam containing an elegant Hermite Gaussian beam and a cosine Gaussian beam, which is called elegant Hermite cosine Gaussian (EHcoG) beam, is introduced and studied. The propagation properties of the EHcoG laser beams through a first-order paraxial optical system are demonstrated analytically and numerically. The recurrence propagation equations of the EHcoG beams through a first-order paraxial optical system with and without aperture are derived, from which the analytical propagation expression for EHcoG beams of any order can be obtained by means of the recursive procedures. The validity of the analytical results is confirmed by the numerical results.     

Gyrator transform of Gaussian beams with phase difference and generation of hollow beam

The optical expression of Gaussian beams with phase difference, which is caused by gyrator transform (GT), has been obtained. The intensity and phase distribution of transform Gaussian beams are analyzed. It is found that the circular hollow vortex beam can be obtained by overlapping two GT Gaussian beams with π phase difference. The effect of parameters on the intensity and phase distributions of the hollow vortex beam are discussed. The results show that the shape of intensity distribution is significantly influenced by GT angle α and propagation distance z. The size of the hollow vortex beam can be adjusted by waist width ω₀. Compared with previously reported results, the work shows that the hollow vortex beam can be obtained without any model conversion of the light source.     

Characterizing the divergence properties of the laser diode beams propagation through collimator and aperture ABCD optical system

The propagation properties of Gaussian laser beams through a complete optical path including free space and the optics of transmitter and receiver containing a collimator, an aperture and a lens is studied. Based on the Collins integral and using the second order moment method, analytical formulas for intensity distribution and Power In Bucket (PIB) along the propagation path are derived. The effects of initial beam divergence, collimator–source separation distance and beam width deviation on laser beams properties are investigated. Obtained results are confirmed and illustrated with numerical examples and resulted graphs.     

洛伦兹光束经光阑失调傍轴光学系统的传输

基于广义衍射积分公式和光阑函数的复高斯展开,导出了一洛伦兹光束经一个带圆形光阑失调傍轴光学系统的近似解析传输公式.作为一般公式的特例,还给出了洛伦兹光束经一无光阑失调傍轴光学系统的解析传输式.作为数值计算的例子,运用所得到的公式分析了洛伦兹光束经带光阑失调薄透镜的传输特性.结果表明：不同强度的衍射即圆形光阑半径的大小明显影响衍射光束的归一化强度分布及其传输变化规律. 关键词： 洛伦兹光束 失调傍轴光学系统 光束传输     

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.     

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.     

柱坐标下光波场在垂直光轴方向的参考面上的复振幅表示

在柱坐标下从微分波动方程推导柱面光波和高斯球面波的场分布，并利用远场近似条件导出在垂直光轴方向的参考面上这两种光波的复振幅表示。     

Convergence of general beams into Gaussian intensity profiles after propagation in turbulent atmosphere

It is shown that a general shaped laser beam will eventually approach a Gaussian average intensity profile after propagation in turbulent atmosphere. In our formulation, source field at the exit plane of the laser is taken as the product of arbitrary functions of source transverse coordinates with Gaussian exponential modulations. Following the expansion of the arbitrary functions in terms of Hermite polynomials, the average receiver intensity expression is derived using the extended Huygens-Fresnel principle and the conditions for the intensity profile to assume a Gaussian shape are stated. The results are illustrated by simulating various source field distributions.