Moments of intensity distribution of super-Gauss beam in turbulent atmosphere

Moment of intensity distribution is one of the most important parameters in studying the propagation of a beam in turbulent atmosphere. With the help of Wigner transform and the expansion of mutual coherence function (MCF) of turbulence, a relation between the moment of intensity distribution and the moment of power spectrum of refractive index fluctuations is found. The study shows that the jth-order moment of beam intensity distribution is only affected by the moment of power spectrum of refractive index fluctuations which order is not larger than j. Meanwhile, the expressions for the moment of beam intensity distribution, in which order is not larger than the fourth order are given. As a special case, the moments of the super-Gaussian beam (SGB) in turbulence are studied. The evolution of the kurtosis parameters of SGB under different condition is investigated in detail.     

Definition and measurements of high-power laser beam parameters

Three definitions of the beam quality, characterized by waist radius and far-field divergence, of high average power laser beams are investigated. The beam parameters can be defined by their second moments, the power content profile and the power content area. The methods of measurement are described in detail and compared with respect to their suitability for two high-power laser systems: a cw Nd:YAG-rod laser and an annular system. The validity of theABCD law was checked experimentally. Additionally, third and fourth-order intensity moments were used to characterize the laser field in more detail.     

谱合成光束特性的模拟分析

建立了光束谱合成的传输模型.应用光线追迹方法，将闪耀光栅引起的相位变化用槽间光程差和槽内光程差来表示，建立了光束倾斜入射到光栅时相位变化的计算模型.利用衍射积分方法，给出了阵列光源各子光束经谱合成系统后输出光场的解析表达式.依据光束非相干叠加的原理，计算得到合成光束的光强分布.在此基础上，利用强度二阶矩方法，分别计算了阵列光束和合成光束的M²因子，并定量分析了谱合成系统参数对合成光束特性的影响.研究结果表明：通过谱合成系统合成光束的M²关键词： 光束谱合成 阵列光源 闪耀光栅 光束质量     

Determination of the ten second order intensity moments

The general astigmatic beam can be characterized by its ten second order moments in first order approach. Most intensity moments, except the beam twist, can be determined by measuring the intensity in a reasonable number of positions around the waist of the beam. The beam twist is determined by applying a rotated cylindrical lens. The ten intensity moments of two kinds of astigmatic beam were determined: a simple astigmatic TEM_8,0 Hermite–Gaussian beam and a twisted beam generated from the TEM_8,0 mode. The experimental results were compared with the theoretical calculations and demonstrate that the ten second order moments of a beam can be determined in a rather simple way.     

Kurtosis parameters of super Lorentzben Gauss beams through a paraxial and real ABCD optical system

Based on the propagation equation of higher-order intensity moments, analytical propagation expressions for the kurtosis parameters of a super Lorentz-Gauss (SLG) SLG₀₁ beam through a paraxial and real ABCD optical system are derived. By replacing the parameters in the expressions of the kurtosis parameters of the SLG₀₁ beam, the kurtosis parameters of the SLG₁₀ and SLG₁₁ beams through a paraxial and real ABCD optical system can be easily obtained. The kurtosis parameters of an SLG₀₁ beam through a paraxial and real ABCD optical system depend on two ratios. One is the ratio of the transfer matrix element B to the product of the transfer matrix element A and the diffraction-free range of the super-Lorentzian part. The other is the ratio of the width parameter of the super-Lorentzian part to the waist of the Gaussian part. As a numerical example, the properties of the kurtosis parameters of an SLG₀₁ beam propagating in free space are illustrated. The influences of different parameters on the kurtosis parameters of an SLG₀₁ beam are analysed in detail.     

Joint moments of the wave beam amplitude and inverse power in an absorbing random medium with lens properties

Abstract

This paper presents a derivation of a system of closed equations for joint moments of the amplitude and inverse power of a wave beam propagating in a regularly inhomogeneous dissipative random medium. The radiation transfer in the medium is characterized by non-conservation of the total radiation energy flux and by the existence of power fluctuations. The statistics of the wave beam power fluctuations have been studied. Information on the power statistical characteristics is applied to close the system of equations for joint moments. For task parameters which are not very strict (an effective radius of the wave beam should be considerably less than the outer scale of the turbulence) a system of independent equations for arbitrary joint moments has been obtained. The equations for the first two lower joint moments of the beam intensity and inverse power have been solved analytically. With the solutions obtained the effective wave beam parameters were calculated, i.e. the beam mean displacement, effective broadening and tremble variance (the beam wandering variance) for the propagation of radiation in the refractive channel of an absorbing turbulent medium. Radically new characteristics of the behaviour of the effective parameters in random absorbing and transparent media have been revealed.     

Intensity Moments of Hermite-Cosh-Gaussian Laser Beams

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Intensity Moments of Hermite-Cosh-Gaussian Laser Beams

In this paper,attention is focused on the intensity moments of the Hermite-Cosh-Gaussian (HChG) laser beams from the zero-order to the fourth-order.The frequently used parameters such as the power in bucket (PIB),the beam width,the curvature radius,the far field divergence,the M2-factor,the Rayleigh length and the kurtosis are calculated in terms of the intensity moments.Figures show the influence of the mode index and the decentered parameter,which are the critical parameters of the HChG beams.Moreover,the center of the gravity of the radiation field and the symmetry are discussed along with the propagation axis.Finally,the power fraction within the beam width defined by the second moments is illustrated with numerical method.     

Propagation of flat-topped beams

The propagation of flat-topped beams passing through paraxial ABCD optical system is investigated based on the propagation formulas of Gaussian beam. The focal shift of focused coherent flat-topped beam is also studied in detail. Analytical expressions of the M² factor and the far-field intensity distribution for flat-topped beams are derived on the basis of second-order moments.     

Moments of the intensity of a non-circular Gaussian laser speckle pattern in the diffraction field

Statistics of the intensity of a non-circular Gaussian speckle field that arises in imaging and propagation geometries was analyzed in the past but no general expressions for the moments of intensity were given. In this paper general expressions for the moments of the intensity of a non-circular speckle field are derived and their dependence on the path and beam parameters is discussed.     

Joint moments of the wave beam amplitude and inverse power in an absorbing random medium with lens properties

This paper presents a derivation of a system of closed equations for joint moments of the amplitude and inverse power of a wave beam propagating in a regularly inhomogeneous dissipative random medium. The radiation transfer in the medium is characterized by non-conservation of the total radiation energy flux and by the existence of power fluctuations. The statistics of the wave beam power fluctuations have been studied. Information on the power statistical characteristics is applied to close the system of equations for joint moments. For task parameters which are not very strict (an effective radius of the wave beam should be considerably less than the outer scale of the turbulence) a system of independent equations for arbitrary joint moments has been obtained. The equations for the first two lower joint moments of the beam intensity and inverse power have been solved analytically. With the solutions obtained the effective wave beam parameters were calculated, i.e. the beam mean displacement, effective broadening and tremble variance (the beam wandering variance) for the propagation of radiation in the refractive channel of an absorbing turbulent medium. Radically new characteristics of the behaviour of the effective parameters in random absorbing and transparent media have been revealed.     

Propagation properties of partially coherent modified Bessel–Gauss beams

Starting from the propagation law of partially coherent light, the analytical propagation equations of partially coherent modified Bessel–Gauss beams (MBGBs) through a paraxial optical ABCD system are derived and illustrated with typical application examples. Furthermore, by using the intensity moments method and integral transformation technique, the important characteristic parameters, including the beam width, far-field divergence angle, M² factor and kurtosis parameter of partially coherent MBGBs, are expressed in a closed and simple form. As a result, some basic properties of MBGBs and the dependence of the M² factor and kurtosis parameter on the spectral degree of coherence and beam order are illustrated both analytically and numerically.     

Moment and kurtosis parameter of partially coherent cosh-Gaussian beam in turbulent atmosphere

An analytical expression for arbitrary moments of the cosh-Gaussian–Shell beam in turbulent atmosphere is derived. As a special case, kurtosis parameters of collimated and focused cosh-Gaussian beam with and without turbulent atmosphere are studied in detail. It can be seen from the study that the kurtosis parameters of Gaussian beam do not remain constant in turbulent atmosphere. Similar to the kurtosis parameters of a cosh-Gaussian beam at source plane, the kurtosis parameters at focal plane without turbulent atmosphere are independent of the propagation distance and vary with the parameters of the beam. But the variation of the kurtosis parameters at focal plane is different from that at source plane. However, the kurtosis parameters of collimated and focused cosh-Gaussian beam both vary with the propagation distance and gradually converge to 3 along the z-axis in turbulent atmosphere. Compared with a collimated beam, the kurtosis parameters of a focused beam converge more quickly.     

Coherence and intensity moments of laser light

Taking the modal behaviours of the laser field into account, the coherence properties of laser light can be characterized by mode coherence functions (MCFs) and mode coherence coefficients (MCCs). Changes in laser light properties due to optical operations can be described by transformation laws for the MCFs and the MCCs. The transformation laws as well as transformation matrices for propagation in free space, phase transformations, spatial amplitude modulations and aperturizing are given. Furthermore, intensity distributions and intensity moments in the spatial and in the spatial frequency domains are expressed in terms of the MCCs. General expressions for the beam quality factors,M ²s, obtained using the intensity moments and some useful expressions for intensity moments of higher order are discussed.     

激光光束传输因子M2的一些问题

本文讨论与M²因子有关的一些问题,指出在近轴近似条件下由光束的二阶强度矩定义的M²因子满足M²≥1,其中只有对基模高斯光束等式才成立.由光束的功率通量值定义的M²因子(M_pc²)有可能小于1,M_pc²的大小取决于所定义的光斑半径内包含的光功率的百分数.通过计算光场的二阶矩,我们获得了轴向相干叠加的高斯光束的M²因子的解析解.     

Does the beam width affect the generalized M factor of hard-edged diffracted beams?

A detailed study of the generalized M² factor of hard-edged diffracted beams based on the truncated second-order moments method, asymptotic analysis and self-convergent beam width approach is performed. The dependence of the generalized M² factor on the parameters characterizing the spatial profile, and beam truncation, etc. is analyzed.     

M2-factor of a truncated electromagnetic Gaussian Schell-model beam

Based on the extended Huygens–Fresnel integral and the second-order moments of the Wigner distribution function, analytical expression for the M ²-factor of a truncated electromagnetic Gaussian Schell-model (EGSM) beam in turbulent atmosphere is derived by expanding the hard-aperture function into a finite sum of complex Gaussian functions. It is found that the evolution properties of the normalized M ²-factor of a truncated EGSM beam are closely determined by the truncation parameter, the parameters of the source beam and the parameters of the turbulent atmosphere together. The advantage of the EGSM beam for overcoming the turbulence-induced degradation disappears gradually as the truncation parameter decreases.     

大气湍流中光束的高阶强度矩

研究了光束通过大气湍流传输的高阶强度矩, 提出了大气湍流中光束高阶强度矩的推导方法, 并推导出了一至四阶光束强度矩传输的解析表达式. 所得结果具有一般性,任意某一光束在自由空间和大气湍流中传输的高阶强度矩均可作为本文结果的特例. 另一方面, 以高斯光束为例, 研究了其K参数在湍流大气中的传输规律. 研究表明,高斯光束在大气湍流中其K参数并不是一个传输不变量,它与传输距离、束腰半径、湍流内外尺度以及湍流强度均有关.这个结论与采用Rytov相位结构函数二次近似或强湍流近似下的结论不同,本文给出了合理解释. 关键词： 高阶强度矩 大气传输 大气湍流 K参数')" href="#">K参数     

HL-2A托卡马克中性束辐射光谱的数值模拟

采用数值模拟的方法研究中性束辐射光谱(BES)对开展与中性束相关的光谱诊断与实验有重要的指导意义.本文在HL-2A托卡马克装置上利用ADAS数据库（Atomic Data and Analysis Structure,1998）计算有效束辐射系数和有效束衰减系数,分析了束辐射光谱强度与等离子体运行参数和中性束参数的关系,并在不同的中性束注入能量、等离子体密度分布和等离子体温度分布的情况下,获得了束辐射光谱强度的空间分布.在n_e=2×10¹³ cm< 关键词： 中性束 束辐射光谱 束衰减     

On the different definitions of laser beam moments

The analytical relationship between the different reported definitions of beam moments, extended to the general partially coherent case, is established. Explicit equivalence formulae between both families of beam moments are given. The validity of the corresponding propagation laws through ABCD optical systems is thus confirmed.