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.     

Probing of liquids by Bessel light beams under conditions of acousto-optical interactions

The acousto-optical interactions of Bessel and Gaussian light beams with the ultrasonic field in liquids under the condition of Raman-Nath diffraction for the standing-wave mode are experimentally investigated. The main differences of acousto-optical interactions for Bessel and Gaussian light beams are revealed. The various phenomena of refraction and focusing of Bessel beam in liquids owing to sound-field spatial modulation are demonstrated.     

Theoretical conversion of the hypergeometric-Gaussian beams family into a high-order spiraling Bessel beams by a curved fork-shaped hologram

Based on the process of the Fresnel diffraction, the possibility of generating a new type of laser beams family by illuminating a curved fork-shaped hologram, with an input hypergeometric-Gaussian beams family of orders n and m is studied in this paper. The theoretical and the numerical results showed that, at the output plane, a high order spiraling Bessel vortex beam is produced. This vortex beam is divergence or non-divergence depending upon the waist position of the input hypergeometric-Gaussian beams, regarding the plane where the curved fork-shaped hologram is situated. Analytical expressions of the amplitude and the intensity distribution of the diffracted wave field are calculated and deduced using the stationary phase method. The actual work generalizes also the Fresnel diffraction study of some subfamilies of the hypergeometric-Gaussian beams family, such as: fundamental Gaussian, hollow Gaussian, modified quadratic Bessel–Gaussian and elegant Laguerre–Gaussian beams.     

Pulsed single-photon Bessel beams propagation in non-Kolmogorov turbulent atmosphere

The analytic expressions are derived for the turbulent broadening, the long-term temporal broadening, the acquisition probability of single-pulse and the transmittance probability density of a pulsed space-time Bessel photon-beam propagating along a slant path in weak non-Kolmogorov atmospheric turbulence, based on the assumption of a pulsed Bessel beam with the initial Gaussian temporal shape of pulse and diffraction-free spatial distribution. It is shown that the turbulent broadening and the long-term temporal broadening are the nolinear-increase functions of the index of non-Kolmogorov turbulence and the effect of non-Kolmogorov index on the acquisition probability of single-pulse can be approximatively described by a Gaussian function with a peak value at non-Kolmogorov index close to 3.7 for the case of the input half-pulse width greater than picosecond (ps). The transmittance of probability density is decreasing as the increasing of the structure constant of the index of refraction, the zenith angle of communication channel, the propagation path and the pulse broadening. There is turbulent diffraction for Bessel beam propagation in turbulent atmosphere, but its free-space diffraction-free characteristic is reservation.     

Generation of Bessel Beams at mm- and Sub mm-wavelengths by Binary Optical Elements

In this paper, binary optical elements (BOE’s) are designed for generating Bessel beams at mm- and sub mm- wavelengths. The design tool is to combine a genetic algorithm (GA) for global optimization with a two-dimension finite-difference time-domain (2-D FDTD) method for rigorous electromagnetic computation. The design process for converting a normally incident Gaussian beam into a Bessel beam is described in detail. Numerical results demonstrate that the designed BOE’s can not only successfully produce arbitrary order Bessel beams, but also have higher diffraction efficiencies when compared with amplitude holograms.     

Fresnel diffraction of truncated Gaussian beam

We study the Fresnel diffraction of Gaussian beam truncated by one circular aperture, and give the general analytic expression of the Fresnel diffraction of truncated Gaussian beam denoted by Bessel functions. Then the characteristic of the axial diffraction fluctuation and the influence of the caliber of the circular aperture and the wave waist of Gaussian beam on the diffraction distributions are discussed, respectively. Through the numerical calculations, the characteristics of the transverse diffraction are presented and the relationship of the fluctuation of the transverse diffraction profile and the position of the axial point is shown. The physical origin of the fluctuation of Fresnel diffraction intensities of truncated Gaussian beam is expressed in terms of Fresnel half-zone theory. These phenomena and the conclusions are important for the measurement of the parameters of the beam and its applications.     

Comparison of SRS thresholds under pumping by Gaussian and Bessel beams

In the paraxial approximation, it has been shown that the quasi-stationary SRS amplification coefficient in the near-threshold region is determined by the product of the pump intensity in the beam center and the overlap integral of the transverse structure of the pump and the Stokes component. Expressions for the overlap integral and the scattering powers have been obtained and analyzed for the following cases: the pump and the Stokes field are Gaussian beams; the pump and the Stokes field are Bessel beams; the pump is a Bessel beam and the Stokes field is an axial Gaussian beam. Relations between the SRS excitation thresholds in different cases have been found.Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 71, No. 6, pp. 778–787, November–December, 2004.This revised version was published online in April 2005 with a corrected cover date.     

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.     

Bessel光束经椭圆环形孔径后的衍射光场

基于菲涅耳衍射积分理论及硬边孔径的复高斯函数展开法导出了Bessel光束经椭圆环形孔径后的光场表达式, 数值模拟了其光场的强度分布. 研究了Bessel光束经椭圆环形孔径后的光场变化及其传播过程; 在实验上利用轴棱锥输出的近似无衍射Bessel光, 通过椭圆环形孔径, 使用电荷耦合器件拍摄得到不同传播距离处的光强分布. 理论结果和实验结果均表明无衍射光束经椭圆环形孔径后会产生空心光束.     

CONCEPTUAL DESIGN OF BESSEL BEAM CAVITY FOR FREE-ELECTRON LASER

The conventional cavity for a free-electron laser (FEL) oscillator usually forms an optical beam of Gaussian mode, which undergoes transverse spread along the interaction region. The transverse divergence of an optical beam will induce reduction of the FEL gain from three aspects: degenerating filling factor, causing diffraction loss and limiting the effective interaction distance. Bessel optical beam has been experimentally demonstrated diffraction-free characteristics in its propagation, which provides a possibility of improvement of FEL gain. In this paper, we present a conceptual design of a Bessel beam cavity for the free-electron laser oscillator. This cavity generates nondiffracting optical beam in the wiggler, resulting in improving the filling factor, decreasing the diffraction loss and elongating the effective interaction distance.     

贝塞尔-高斯涡旋光束相干合成研究

基于相干合成技术,提出了对特定离散空间分布的高斯光束阵列加载离散涡旋相位生成二阶贝塞尔-高斯(Bessel-Gaussian,BG)涡旋光束的方案.利用干涉法、桶中功率和相关系数对合成BG涡旋光束的拓扑荷、光束质量进行了定量评价及参数优化.结果表明:基于相干合成技术能够产生特定的目标BG涡旋光束,阵列子光束紧密排布时合成BG光束的光束质量更高.该方法的提出对于其他涡旋光束的产生或者涡旋光束功率的提高具有一定的参考意义.     

无衍射贝塞尔光束相干的理论与实验

分别使用两种不同底角的轴棱锥产生无衍射贝塞尔光束。理论分析了单束贝塞尔光及两束贝塞尔光相干叠加后光场的光强分布,分析了产生的局域空心光束在一个完整周期内的特性。数值模拟了光沿纵向传播时光场的横向光强分布,并给出了相关的实验。对单束贝塞尔光及两束贝塞尔光干涉后的中心光斑的大小进行了测量,测量结果与理论计算结果吻合。     

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。     

一种含时贝塞尔光束的理论性质研究

本文从理论角度提出了一种"含时贝塞尔光束"的概念.在非傍轴和非时谐条件下,直接从麦克斯韦方程出发,借鉴半贝塞尔光束的处理方法,同时引入第四维虚数坐标,由此获得了完整的"含时贝塞尔光束"的解析表达式.并从无衍射性质和时空特性两个方面对其进行了探讨和研究,发现该光束具有如下性质:符合贝塞尔光束类型的无衍射特征;在时空双曲线上强度保持不变;光波时空特性的临界条件类似于相对论中的光锥."含时贝塞尔光束"的概念为无衍射自加速光束的研究开拓了新的思路和方向.     

Ultrasonic diffraction of Bessel light beams in uniaxial gyrotropic crystals

Specific features of the acousto-optic diffraction of Bessel light beams propagating in the vicinity of the optical axis of a uniaxial gyrotropic crystal have been investigated. The dependences of the diffraction efficiency on the acousto-optic interaction length, ultrasound power, and polarization state of the incident Bessel light beam have been analyzed using the coupled-wave equations and the overlap-integral method. It is shown that polarization-independent diffraction of Bessel light beams is observed in paratellurite crystals, when the Bragg diffraction efficiency is independent of the polarization state of the incident beam. The physical reason for this diffraction has been established (both theoretically and experimentally) to be simultaneous implementation of two processes of anisotropic scattering, at which the Bragg synchronism conditions are satisfied for orthogonal polarized Bessel beams with elliptical polarization.     

Propagation of modified Bessel-Gaussian beams in turbulence

We investigate the propagation characteristics of modified Bessel-Gaussian beams traveling in a turbulent atmosphere. The source beam formulation comprises a Gaussian exponential and the summation of modified Bessel functions. Based on an extended Huygens–Fresnel principle, the receiver plane intensity is formulated and solved down to a double integral stage. Source beam illustrations show that modified Bessel-Gaussian beams, except the lowest order case, will have well-like shapes. Modified Bessel-Gaussian beams with summations will experience lobe slicing and will display more or less the same profile regardless of order content. After propagating in turbulent atmosphere, it is observed that a modified Bessel-Gaussian beam will transform into a Bessel-Gaussian beam. Furthermore it is seen that modified Bessel-Gaussian beams with different Bessel function combinations, but possessing nearly the same profile, will differentiate during propagation. Increasing turbulence strength is found to accelerate the beam transformation toward the eventual Gaussian shape.     

Fields of apertured polychromatic laser beams with Gaussian and Hermite–Gaussian transverse modes

Starting from the Huygens–Fresnel diffraction integral, the field expressions of apertured polychromatic laser beams with Gaussian and Hermite–Gaussian transverse modes are derived. Influence of the bandwidth on the intensity distributions of the laser beams is analyzed. It is found that when the bandwidth increases, the amplitudes and numbers of the intensity spikes decrease and beam uniformity is improved in the near field and the width of transverse intensity distribution of the apertured beams decreases in the far field. Thus, the smoothing and narrowing effects can be achieved by increasing the bandwidth. Also, these effects are found in the laser beams with Hermite–Gaussian transverse modes as the bandwidth increases.     

瑞利粒子在贝塞尔光束中的横向受力

 为寻找捕获瑞利粒子的最佳光场,利用电磁模型推导了贝塞尔光束捕获粒子的最小半径的表达式,并数值计算了瑞利粒子在贝塞尔光束和高斯光束中所受的横向力和势阱的深度。结果表明:当激光功率为4 W时,贝塞尔光束仅能在光轴处稳定地捕获瑞利粒子;当激光功率达到6 W时,贝塞尔光束能够在光轴和次极大位置捕获瑞利粒子。在相同的激光参数条件下,高斯光束无法克服布朗运动的影响稳定地捕获瑞利粒子,贝塞尔光束更有利于捕获瑞利粒子。     

瑞利粒子在贝塞尔光束中的横向受力

为寻找捕获瑞利粒子的最佳光场,利用电磁模型推导了贝塞尔光束捕获粒子的最小半径的表达式,并数值计算了瑞利粒子在贝塞尔光束和高斯光束中所受的横向力和势阱的深度。结果表明:当激光功率为4 W时,贝塞尔光束仅能在光轴处稳定地捕获瑞利粒子;当激光功率达到6 W时,贝塞尔光束能够在光轴和次极大位置捕获瑞利粒子。在相同的激光参数条件下,高斯光束无法克服布朗运动的影响稳定地捕获瑞利粒子,贝塞尔光束更有利于捕获瑞利粒子。     

Improvement of optical trapping effect by using the focused high-order Laguerre-Gaussian beams

We investigate the optical trapping effect of high-order Laguerre-Gaussian (LG) beams acting on a dielectric sphere in Rayleigh regime. For LG beams with the azimuthal mode index l=0, it is found that under the same input power, the transverse trapping effect can be enhanced several times with increasing the radial mode index p, compared with that of the Gaussian beam; while its axial trapping effect is exactly the same as that of Gaussian beam, although the central trapping region reduces as p increases. For LG beams with l≥1, we find that the maximal transverse gradient forces increase with the increasing of p and the axial radiation forces reduces slightly, therefore an optimal choose on p and l is necessary for obtaining an optimal optical guiding. Our result is useful for analyzing the trapping efficiency of LG beams applied in micromanipulation technologies.