Two-dimensional isotropic scattering in a semi-infinite cylindrical medium

Beginning with the integral equation for the source function, the solutions for the source function, flux and intensity at the boundary of a two-dimensional, isotropically scattering cylindrical medium are found. The incident radiation is collimated and normal to the surface of the medium and depends only on the radial coordinate. For a Bessel function boundary condition, separation of variables is used to reduce the source function integral equation to a one-dimensional equation. The resulting integral equation is shown to be the same as that for the two-dimensional planar case. Solutions for other boundary conditions are then shown to be superpositions of the Bessel function solution. Numerical results are presented for a Gaussian distribution of incident radiation which closely models a laser beam. These multiple scattering results are compared to the single scattering approximation. Also, the solution for a strongly anisotropic phase function which is made up of a spike in the forward direction superimposed on an otherwise isotropic phase function is expressed in terms of the isotropic results.     

Two-dimensional rayleigh scattering in a semi-infinite cylindrical medium exposed to a laser beam

A modification of Ambarzumian's method is used to develop the integro-differential equations for the source function, flux, and intensity at the boundary of a two-dimensional, semi-infinite cylindrical medium with second order Legendre phase function scattering. The incident radiation is collimated, normal to the top surface, and is dependent only on the radial coordinate. Boundary conditions which vary as a Bessel function and as a Gaussian distribution are investigated. The Gaussian distribution approximates a laser beam. Numerical results are presented in graphical and tabular forms for a Rayleigh scattering medium. The results are compared with those of isotropic scattering.     

Two-dimensional linearly anisotropic scattering in a semi-infinite cylindrical medium exposed to a laser beam

A modification of Ambarzumian's method is used to develop the integro-differential equations for the source function, flux, and intensity at the boundary of a two-dimensional, semi-infinite cylindrical medium which scatters linearly. The incident radiation is collimated, normal to the top surface of the medium, and is dependent only on the radial coordinate. The radial variation is assumed to be a Bessel function or a Gaussian distribution. The Gaussian boundary condition is used to simulate a laser beam. Numerical results are presented in graphical and tabular forms for both boundary conditions. Results for forward and backward scattering phase functions are compared with those for isotropic scattering. A method is presented for extending these results to the problem of a strongly anisotropic phase function which is made up of a spike in the forward direction superimposed on a linear phase function.     

Comparison of the high-aperture Bessel and Gaussian beams

The diffraction broadening of the high-aperture freely propagating (vector) Bessel and Gaussian beams is considered. The dependences of the degree of transverse concentration of light in such beams on their axial and radial coordinates are obtained. It is shown that if the initial degree of the transverse localization of total power of these beams is the same, the diffraction broadening of a Gaussian beam is smaller than that of a Bessel beam, and the only advantage of the latter is the specific radial distribution of the field amplitude.     

A closed form of a kurtosis parameter of a hypergeometric-Gaussian type-Ⅱ beam

Based on the irradiance moment definition and the analytical expression of waveform propagation for hypergeometricGaussian type-Ⅱ beams passing through an ABCD system, the kurtosis parameter is derived analytically and illustrated numerically. The kurtosis parameters of the Gaussian beam, modified Bessel modulated Gaussian beam with quadrature radial and elegant Laguerre–Gaussian beams are obtained by treating them as special cases of the present treatment. The obtained results show that the kurtosis parameter depends on the change of the beam order m and the hollowness parameter p, such as its decrease with increasing m and increase with increasing p.     

贝塞尔光束与激光打孔

当高斯激光束用于打小孔时，焦深很小。截断的贝塞尔光束的主极大具有很长的焦深，可降低调焦精度，用于打小孔时优于高斯光束，但是分析表明两者的成孔质量和所能实现的深径比差不多。本文通过计算指出环状分布的光束经透镜后可在焦平面产生适用于激光打孔的贝塞尔－高斯光束，这是一种高效、简单实用的方法。     

Multiscale Bessel beams generated by a tunable acoustic gradient index of refraction lens

A beam that resembles a Bessel beam on two scales is generated using a tunable acoustic gradient index of refraction (TAG) lens. The minor scale of the TAG-generated Bessel beam is nondiffracting and self-healing. The major scale of the beam diffracts while still forming a Bessel pattern due to the specific geometry of the TAG lens. The acoustic and optical theory behind the TAG lens is outlined, and the experimental beam itself is presented. The major and minor rings are explained, and the TAG beam is compared with both axicon-generated and conventionally focused Gaussian beams.     

Propagation and transformation of Bessel beam through the fractional Fourier transform system with two hard-edged apertures

The propagation properties of Bessel beam is a meaningful research. In this paper, based on the expanding the hard-edged circular aperture as a finite sum of complex Gaussian functions and the scalar diffraction theory, an approximate analytical solution for Bessel beam propagating through a fractional Fourier transform system is derived in the cylindrical coordinates. Then, the detailed numerical calculation for Bessel beam is presented. The simulation also shows that the beam parameter and the order of fractional Fourier transform result in the change of field distribution, including location, intensity and width.     

Area scintillations of Bessel Gaussian and modified Bessel Gaussian beams of zeroth order

As an extension of our previous study, the area scintillation aspects of Bessel Gaussian and modified Bessel Gaussian beams of zeroth order are investigated. The analysis is carried out on the basis of equal source sizes and equal source powers. It is found that, when compared on equal source size basis, modified Bessel Gaussian beams always have less area scintillations than a Gaussian beam, while Bessel Gaussian beams exhibit more area scintillations. Comparison on equal source power basis, however, removes the advantage of modified Bessel Gaussian beams, that is, their area scintillations become nearly the same as those of the Gaussian beam. On the other hand, for the case of equal source powers, Bessel Gaussian beams with larger width parameters continue to have higher area scintillations than the Gaussian beam. We provide graphical illustrations for profiles of equal source size beams, equal source power beams and the curves to aid the selection of equal source power beams.     

Second-harmonic generation of the nth-order Bessel beam

We investigate the second-harmonic generation of the nth-order Bessel beam in the nonlinear medium. The analysis is based on the Khokhlov-Zabolotskaya-Kuznetsov wave equation under the second-order approximation in nonlinear acoustics. The theory indicates that for an nth-order Bessel beam, the second-harmonic beam is nearly diffraction-free in the radial direction and behaves as a Bessel beam of the order 2n, and that the axial pressure amplitude is proportional to the square root of propagation distance. A variety of applications in many fields of nonlinear acoustics and nonlinear optics is expected.     

贝塞尔光束中瑞利粒子所受横向力的参数理论分析

基于电磁模型,数值计算了瑞利粒子在贝塞尔光束中所受横向光阱力,给出了粒子所受横向力与粒子的半径、折射率和波长的关系。结果表明,与高斯光束形成的光阱相比,贝塞尔光束既能捕获高折射率粒子也能捕获低折射率粒子,并且有多个平衡位置,因此应用更为广泛。     

Slant path average intensity of finite optical beam propagating in turbulent atmosphere

The average intensity of finite laser beam propagating through turbulent atmosphere is calculated from the extended Huygens Fresnel principle. Formulas are presented for the slant path average intensity from an arbitrarily truncated Gaussian beam. The new expressions are derived from the modified von Karman spectrum for refractive-index fluctuations, quadratic approximation of the structure function,and Gaussian approximation for the product of Gaussian function and Bessel function. It is shown that the form of average intensity is not a Gaussian function but a polynomial of the power of the binomial function, Gaussian function, and the incomplete gamma function. The results also show that the mean irradiance of a finite optical beam propagating in slant path turbulent atmosphere not only depends on the effective beam radius at the transmitting aperture plane, propagation distance, and long-term lateral coherence length of spherical wave, but also on the radius of emit aperture.     

小瓣数贝塞尔声束的二次谐波

采用高斯展开法,研究了具有三个瓣的小瓣数贝塞尔声束的基波和二次谐波的传播性质.根据准线性近似下Khokhlov-Zabolotskaya-Kuznetsov方程的积分形式解,分析了媒质的声吸收(声衰减)对波束形状的影响.结果表明:吸收参量对二次谐波径向分布有很大的影响.当瓣数较少时,实际的有限孔径贝塞尔声束二次谐波仍然具有理想无限大孔径贝塞尔声束的主要特征,在近场无衍射区,径向几乎无衍射. 关键词： 二次谐波 贝塞尔声束 声吸收 有限孔径声束     

A high-efficient method for generating radially and azimuthally polarized Bessel beams using biaxial crystals

As was shown previously, in propagation of a circularly polarized Bessel light beam along the optical axes of a biaxial crystal, there takes place the conversion of the order of Bessel function. In this paper, a new result is presented which is obtained by varying the polarization state of an input beam. Namely, a linearly polarized beam can be transformed into a beam with the radial or azimuthal polarization state. At that the order-transformation also occurs. The switching between radial and azimuthal polarization states of the output beam is performed by the proper switching between two orthogonal linear polarization states of the input beam. The efficiency of polarization conversion is high and can be practically full at an appropriate choice of the cone angle of the input beam or crystal length.     

Generation of TE- and TH-polarized Bessel beams using one-dimensional photonic crystal

Based on the matrix method, a theory of propagation of TE- and TH-polarized Bessel light beams (BLBs) in a one-dimensional photonic crystal (1DPC) is developed. The transmission through a 1DPC (with and without a defect impurity) of a quasi-circularly-polarized incident Bessel beam generated by an axicon from a circularly-polarized Gaussian beam has been calculated and analyzed. Also a solution of the problem on the transmission of BLBs through crystalline plate (layer of a uniaxial crystal with the orientation of the optical axis orthogonally to its interfaces) and reflection from it has been presented.Based on this, a new method of formation of TE- and TH-polarized Bessel light beams has been proposed. It has been shown that it is possible to control this process by changing the cone angle of an incident Bessel light beam. The effect of generation of a coherent superposition of two Bessel beams with different cone angles in the case of a high birefringence of defect layer has been predicted theoretically.     

基于光克尔效应的径向光束匀滑新方案

针对惯性约束聚变装置中提高靶面辐照均匀性的要求, 提出了一种基于光克尔效应的径向光束匀滑方案, 其基本原理是利用光克尔介质和周期性高斯脉冲光束相互作用实现对激光束透射波前附加周期性的球面位相调制, 以周期性地改变激光束远场焦斑尺寸, 进而引起远场焦斑内部散斑的快速径向扫动, 从而在积分时间内抹平靶面焦斑的强度调制, 实现径向方向的光束匀滑. 通过建立基于光克尔效应的径向光束匀滑的理论模型, 分析了焦斑形态及其径向匀滑特性, 并讨论了光克尔介质的选取和径向扫动特性. 结果表明, 基于光克尔效应的径向光束匀滑方案可以有效地实现远场焦斑内部散斑的周期性径向扫动, 从而在积分时间内快速改善靶面辐照均匀性.     

Distribution regimes of intense laser beam in a self-consistent plasma channel

In the present work, we investigate the distributed regimes of an intense laser beam in a self-consistent plasma channel. As the intensity of the laser beam increases, the relativistic mass effect as well as the ponderomotive expulsion of electrons modifies the dielectric function of the medium due to which the medium exhibits nonlinearity. Based on Wentzel–Kramers–Brillouin and paraxial ray theory, the steady-state solution of an intense, Gaussian electromagnetic beam is studied. A differential equation of the beamwidth parameter with the distance of propagation is derived, including the effects of relativistic self-focusing (SF) and ponderomotive self-channeling. The nature of propagation and radial dynamics of the beam in plasma depend on the power, width of the beam, and Ω _p, the ratio of plasma to wave frequency. For a given value of Ω _p (<1), the distribution regimes have been obtained in beampower–beamwidth plane, characterizing the regimes of propagation as steady divergence, oscillatory divergence, and SF. The related focusing parameters are optimized introducing plasma density ramp function, and spot size of the laser beam is analyzed for inhomogeneous plasma. This results in overcoming the diffraction and guiding the laser beam over long distance. Numerical computations are performed for typical parameters of relativistic laser–plasma interaction studies.     

Focal shift of radially polarized axisymmetric Bessel modulated Gaussian beam with radial variance phase plate

Focal shift of the radially polarized axisymmetric QBG beam with radial variance phase plate is investigated theoretically by vector diffraction theory. Axisymmetric Bessel modulated Gaussian beam with quadratic radial dependence (QBG beam) has attracted much attention recently. Calculation results show that focus shifts considerably by changing the phase parameter C that indicates the radial phase variance speed. Under condition of beam parameter μ of radially polarized axisymmetric QBG beam, there is one focal spot that shifts far away from optical aperture on increasing C. When increases the value of beam parameter, there may occur two focal peaks that also shift remarkably on increasing C.     

Exact partial wave expansion of optical beams with respect to an arbitrary origin

Using an analytical expression for an integral involving Bessel and Legendre functions, we succeed in obtaining the partial wave decomposition of a general optical beam at an arbitrary location relative to the origin. We also showed that solid angle integration will eliminate the radial dependence of the expansion coefficients. The beam shape coefficients obtained are given by an exact expression in terms of single or double integrals. These integrals can be evaluated numerically on a short time scale. We present the results for the case of a linear-polarized Gaussian beam.     

非偏振贝塞尔高斯光束的球散射

无衍射光束球散射性质的研究目前一般采用贝塞尔光束,但是贝塞尔光束在物理上是不可实现的。贝塞尔高斯光束作为近似无衍射光束,是亥姆霍兹方程在傍轴条件下的解,并且可以用激光振荡器直接产生,但其光束宽是有限的。应用傅里叶变换,平面波谱展开和球面矢量波函数展开法,推导了非偏振贝塞尔高斯光束的球散射远场的无量纲散射函数。通过数值模拟,对非偏振的贝塞尔高斯光束与贝塞尔光束,高斯光束的球散射远场进行了比较,比较发现:当球散射体偏离光轴时,非偏振贝塞尔高斯光束跟贝塞尔光束散射远场的差异主要是散射强度的差异,但是散射极点所在的方向基本保持不变;贝塞尔高斯光束和贝塞尔光束的散射在光束圆锥角方向上比较显著,但高斯光束的前向散射比较显著。