一类新平顶光束的束传播因子

 基于迭加原理，引入了利用双曲余弦-高斯光束的相干迭加而得的新光束，结果表明这类迭加光场的场强分布在适当参数条件下可具有平顶结构，并且分析了这类迭加所得的平顶光束的束传播因子与束参数的关系。     

一类新平顶光束的束传播因子

基于迭加原理,引入了利用双曲余弦-高斯光束的相干迭加而得的新光束,结果表明这类迭加光场的场强分布在适当参数条件下可具有平顶结构,并且分析了这类迭加所得的平顶光束的束传播因子与束参数的关系。     

Density Transition Based Self-Focusing of cosh-Gaussian Laser Beam in Plasma with Linear Absorption

Density transition based self-focusing of cosh-Gaussian laser beam in plasma with linear absorption has been studied. The field distribution in the plasma is expressed in terms of beam width parameter, decentered parameter, and linear absorption coefficient. The differential equation for the beam width parameter is solved by following Wentzel—Kramers—Brillouin (WKB) and paraxial approximation through parabolic wave equation approach. The behaviour of beam width parameter with dimensionless distance of propagation is studied at optimum values of plasma density, decentered parameter and with different absorption levels in the medium. The results reveal that these parameters can affect the self-focusing significantly.     

Virtual source for a Hermite-Gauss beam

A virtual source that generates a Hermite-Gauss wave of mode numbers m and n is introduced. An expression is obtained for this Hermite-Gauss wave. From this expression, the paraxial approximation and the first 3 orders of nonparaxial corrections for the corresponding paraxial Hermite-Gauss beam are determined. When both m and n are even, leading to maximum amplitude along the axis, the number of orders of nonvanishing nonparaxial corrections is found to be equal to (m + n)/2.     

First-order approximation in studying beam spreading of cosh-Gaussian and cos-Gaussian beam in Kolmogorov turbulence

With the help of extended Huygens–Fresnel principle and the expansion of the mutual coherence function in a Taylor series, the analytical expression of the first-order approximation for the average intensity of a cosh-Gaussian and cos-Gaussian beam in Kolmogorov turbulence has been obtained. Based on the analytical expression of the first-order approximation, the variation of average intensity in Kolmogorov turbulence has been examined. Comparing with numerical integration, the relative error due to the quadratic structure function and first-order approximation of the mutual coherence function is studied and discussed. It is shown that the analytical expression of the first-order approximation provides a more precise approach to study the beam spreading of the cosh-Gaussian and cos-Gaussian beam in Kolmogorov turbulence, no matter whether the effect of turbulence is weak or strong.     

复宗量双曲余弦高斯光束的束腰及其位置

 由复宗量双曲余弦高斯光束通过近轴-ABCD-光学系统传输公式，推导出了基于二阶矩定义的光斑尺寸的解析表达式，给出了复宗量双曲余弦高斯光束在自由空间传输和通过薄透镜时的光斑尺寸、束腰宽度及其位置的解析表达式，并进行了数值计算，对计算结果进行了分析和讨论，该方法可用于其它光束通过近轴ABCD光学系统的类似计算。     

Virtual source for rotational symmetric Lorentz-Gaussian beam

The virtual source for generation of rotational symmetric Lorentz-Gaussian (RLG) wave whose propagating dynamics present the rotational symmetry is identified. Closed-form expressions, including integral and differential representations, are derived for this kind of Lorentz-Gaussian (LG) wave, thereby yieldingparaxial approximation of the RLG beam in the appropriate regime. From the spectral representation of this wave, the first three order corrections of nonparaxial approximations are determined for a corresponding paraxial RLG beam. Moreover, the relationship between the RLG beam and the Hermite-Gaussian beam is revealed.     

Virtual source for the Bessel-Gauss beam

The virtual source for generation of the fundamental scalar Bessel-Gauss wave is identified. An expression is derived for the Bessel-Gauss wave, which, in the appropriate limit, yields the paraxial approximation for the fundamental Bessel-Gauss beam. For the azimuthally symmetric beam, the first-order nonparaxial correction to the on-axis field is also determined. This nonparaxial correction reduces correctly to that of the fundamental Gaussian beam in the appropriate limit.     

Cross focusing of two coaxial cosh-Gaussian laser beams in a parabolic medium

In this paper authors have presented the cross focusing of two coaxial cosh-Gaussian laser beams of different frequencies in a parabolic medium. Starting from the expression for field distribution of cosh-Gaussian beams, differential equations for beam-width parameters of two beams have been established through parabolic wave equation approach and analytical solution for weak beam has been obtained. The effect of decentred parameter of strong beam on the behavior of beam-width parameter with the normalized distance of propagation for weak beam has been specifically considered. The results have been presented graphically and discussed.     

Paraxial waves in the far-field region

By investigating the changes suffered by a paraxial beam propagating in the near-field and in the far-field regions, it has been found a set of wave equations valid for points gradually closer to the near field. A relevant expression for the validity of the far-field approximation is given from the paraxial Helmholtz equation. It is pointed out that the well-known Fresnel number associated with every transverse diffraction pattern can be interpreted as a magnitude that measures the relative standard deviation of the Fraunhofer pattern and a first-order field, thus reporting on an integral expression suitable for a general case. Finally, the Rayleigh range of the optical beam is deduced from the previously inferred Fresnel number, what has been applied for the cases of a spherical Gaussian beam and a uniform-illuminated circular aperture.     

Effect of Critical Beam Radius on Self-focusing of cosh-Gaussian Laser Beams in Collisionless Magnetized Plasma

Effect of critical beam radius on self-focusing of cosh-Gaussian laser beams in collisionless magnetized plasma under ponderomotive nonlinearity forms the main core of present work. To investigate propagation dynamics of cosh-Gaussian laser beams in collisionless magnetized plasma, well established parabolic equation approach under WKB and paraxial approximations is employed. Our study is crucially pivoted on the concept of critical curve and subsequent determination of numerical interval for decentered parameter to sustain the competition between diffraction and self-focusing during the propagation of laser beam. Additionally, in the present study an interesting feature in the self-focusing region of the critical curve has been attempted for different values of decentered parameter.     

Effect of Critical Beam Radius on Self-focusing of cosh-Gaussian Laser Beams in Collisionless Magnetized Plasma

Effect of critical beam radius on self-focusing of cosh-Gaussian laser beams in collisionless magnetized plasma under ponderomotive nonlinearity forms the main core of present work. To investigate propagation dynamics of cosh-Gaussian laser beams in collisionless magnetized plasma, well established parabolic equation approach under WKB and paraxial approximations is employed. Our study is crucially pivoted on the concept of critical curve and subsequent determination of numerical interval for decentered parameter to sustain the competition between diffraction and self-focusing during the propagation of laser beam. Additionally, in the present study an interesting feature in the self-focusing region of the critical curve has been attempted for different values of decentered parameter.     

Relativistic self-focusing of cosh-Gaussian laser beams in a plasma

In the present paper, we have proposed to exploit an analysis of a self-consistent, steady state, theoretical model, which explains the propagation of cosh-Gaussian laser beams in a plasma. The nonlinearity we have considered is of relativistic type. Using the expression for the dielectric function, we have setup the differential equation for beam-width parameter using the WKB and paraxial approximations. The effect of decentred parameter of the beam on the critical curve and the dependence of the beam-width on the distance of propagation have been specifically considered. The results have been presented in the form of graphs and discussed.     

Effect of turbulent atmosphere on the on-axis average intensity of Pearcey–Gaussian beam

The propagation characteristics of the Pearcey–Gaussian(PG) beam in turbulent atmosphere are investigated in this paper.The Pearcey beam is a new kind of paraxial beam,based on the Pearcey function of catastrophe theory,which describes diffraction about a cusp caustic.By using the extended Huygens–Fresnel integral formula in the paraxial approximation and the Rytov theory,an analytical expression of axial intensity for the considered beam family is derived.Some numerical results for PG beam propagating in atmospheric turbulence are given by studying the influences of some factors,including incident beam parameters and turbulence strengths.     

双层界面下非近轴近似多元高斯模型的相控阵声场模拟

非近轴近似多元高斯模型克服了近轴近似条件的限制,能保证较大偏转角度下模拟声场的精确度和效率。根据双层介质的瑞利积分模型和单层介质的非近轴近似多元高斯模型,推导出双层介质中基于非近轴近似多元高斯模型的单阵元辐射声场计算模型。并在得到各阵元声束偏转聚焦的延迟时间基础上,累加得到基于非近轴近似高斯模型的超声相控阵横波检测辐射声场计算模型。模拟计算带丙烯酸树脂楔块的超声相控阵探头在钢中横波检测的声束偏转与偏转聚焦辐射声场,并与近轴近似多元高斯模型的横波检测声束的偏转聚焦辐射声场进行比较分析。对比分析结果表明非近轴近似多元高斯模型计算速度更快,用时约为近轴近似多元高斯模型的1/13。此外,非近轴近似高斯模型方法横波检测的聚焦声束覆盖区域更大,能量更集中,更适于远场区域检测。     

非近轴近似多高斯声束模型的相控阵换能器声场计算

针对近轴近似的多高斯声束模型无法准确计算离轴区域声场的问题,我们提出了一个矩形源的非近轴近似多高斯声束模型,用于计算偏转聚焦时线性相控阵换能器辐射的声场。利用该方法计算了由矩形阵元组成的相控线阵的辐射声场,并与瑞利积分、近轴近似方法及夫琅和费近似方法进行了分析和对比,计算结果表明该方法克服了常规近轴近似条件的限制,可以准确、快速地计算较大偏转范围内的换能器辐射声场,在计算相控阵换能器偏转聚焦声场中具有独特的优势。     

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。     

光在类锥形梯度折射率纤维中的传播——波动光学研究

本文从近轴波动方程出发,寻求光在类锥梯度折射率纤维中传播的解析解。研究了在纤维中传播的高斯光束光斑半径、波面曲率半径、光束强度分市的变化规律,并讨论了准锥形近似及准几何光学传播条件。     

非傍轴高斯光束传输方程解的探讨

由洛伦兹规范下光场满足的矢势和标势方程出发, 探讨了初始光场具有任意对称性的一般非傍轴光束在空间的传输情况。利用角频谱并结合傅里叶变换处理得到了非傍轴光束的传输方程。利用扰动方法并结合新近似取法得到了非傍轴横向光场的扰动形式解, 该解对于近场弱非傍轴情况下的效果比强非傍轴条件下要好。给出了光束非傍轴传输高阶(八阶)修正解。对于零阶情况, 非傍轴光束退化为傍轴光束, 传输方程也相应退化为傍轴传输的模型方程。高斯解为扰动参量的零阶修正解。