Generalized periodically focused beams and multiple on-axis lens imaging

A class of periodically focused propagation-invariant monochromatic beams with sharp central peak is extended to the beams, of which the patterns of intensity at discrete transverse planes regularly spaced along the propagation axis may have an arbitrary, but the same, form. It is shown that the wave field of such beams in free space may be represented as a discrete set of nonuniform phase-distorted spherical wavelets converging to the vicinities of axial points at the indicated transverse planes and possessing the property of mutual similarity. High-order azimuth angular constituents of these wavelets are shown to have phase singularities appearing in the transverse planes as dark coaxial spots with bright rims. Hybrid refractive–diffractive systems are proposed, which are suited both for the direct high efficient production of the beams considered and for the multiple imaging of arbitrary plane objects. The results of numerical simulations are given for two cases of multiple reproduction of rings with large and small radii.     

球形粒子在聚焦拉盖尔-高斯光束中的散射特性研究

研究了球形粒子在聚焦拉盖尔-高斯光束中的散射特性. 根据广义Mie理论, 推导出球形粒子在聚焦拉盖尔-高斯光束中散射系数的解析公式. 针对光束的电场分布及粒子散射强度进行了数值仿真, 讨论了散射强度随散射角、散射球粒子半径和拓扑荷的变化特性, 并通过散射系数解释了散射强度分布的振荡现象. 结果表明, 在聚焦拉盖尔-高斯光束照射下, 球形粒子的后向散射强度随着粒子半径的增大而逐渐增大; 后向散射强度开始增大时对应的粒子半径与拓扑荷有关. 通过与高斯光束的对比, 可以看出球形粒子在聚焦拉盖尔-高斯光束中散射特性的差异, 使其在粒径测量、光通信和大气后向散射探测等方面具有潜在应用价值.     

Aberrated diffraction patterns of off-axis Gaussian beams

Fraunhofer diffraction patterns of off-axis Gaussian beams passing through an optical system having primary spherical aberration are investigated. The resultant diffraction patterns show a nearly elliptical form with a transverse focal shift which depends on the incident position of the Gaussian beams on the pupil and on their radius.     

Effect of aberrations on off-axis gaussian beams

The effect of aberrations of an optical system on gaussian beams is analyzed. If an incident position of the beams of the optical system does not coincide with the center of its pupil, the beams suffer from aberrations differently in accordance with the various incident positions. The Strehl definition of the beams is studied as a function of the incident position of the beams and the kind of abberations present in the optical system.     

Fractional Fourier transform for off-axis dark-hollow beams

Based on the definition of fractional Fourier transform (FRT) in the rectangular coordinate system, the FRT for off-axis circular and elliptical dark-hollow beams (DHB) is studied in detail, and analytical formulae are derived for the FRT for off-axis circular and elliptical DHB. The properties of off-axis DHB in the FRT plane are illustrated numerically by use of the derived formulae. The results show that the properties of the off-axis DHB in the FRT plane are closely related with the parameters of the beam and fractional order. The derived formula provides a convenient way for analyzing and calculating the FRT of off-axis DHBs.     

Fractional Fourier transform for off-axis elliptical Gaussian beams

The fractional Fourier transform (FRT) is applied to off-axis elliptical Gaussian beam (EGB). An analytical formula is derived for the FRT of off-axis EGB in terms of the tensor method. The corresponding tensor ABCD law for performing the FRT of off-axis EGB is also obtained. By using the derived formulae, numerical examples are given. The derived formulae provide a convenient way for analyzing and calculating the FRT of off-axis EGB.     

Floquet states of a periodically kicked particle

We present explicit expressions for the Floquet states of a periodically kicked particle in coordinate and momentum representations. These states have been used to evaluate the energy of the particle after an arbitrary number of kicks.     

Indistinguishability limit for off-axis vortex beams in uniaxial crystals

The circular polarization components of a vortex beam in a uniaxial crystal exhibit complex propagation characteristics. We demonstrate how the amount of splitting may be distinguished by use of a vortex beam. We predict and experimentally verify a threshold angle subtending the crystal and beam axes, below which the splitting is indistinguishable.     

1维线阵离轴高斯光束的分数傅里叶变换

 为研究非相干的1维线阵离轴高斯光束通过分数傅里叶变换(FRFT)系统的传输特性,利用Collins积分公式,导出了其在FRFT面上的光强分布解析式,并利用此解析式作数值计算和分析。研究表明：非相干的1维线阵离轴高斯光束在FRFT面上的光强分布由FRFT的阶数和子光束数目共同决定,其归一化的光强分布随FRFT的阶数周期性变化,周期为2;子光束数目的大小及其奇偶性对归一化光强分布的影响取决于FRFT的阶数;轴上归一化光强分布也随FRFT的阶数周期性变化,变化周期也为2。     

1维线阵离轴高斯光束的分数傅里叶变换

为研究非相干的1维线阵离轴高斯光束通过分数傅里叶变换(FRFT)系统的传输特性,利用Collins积分公式,导出了其在FRFT面上的光强分布解析式,并利用此解析式作数值计算和分析。研究表明：非相干的1维线阵离轴高斯光束在FRFT面上的光强分布由FRFT的阶数和子光束数目共同决定,其归一化的光强分布随FRFT的阶数周期性变化,周期为2;子光束数目的大小及其奇偶性对归一化光强分布的影响取决于FRFT的阶数;轴上归一化光强分布也随FRFT的阶数周期性变化,变化周期也为2。     

聚焦贝塞尔-高斯光束的焦开关效应

详细研究了贝塞尔-高斯光束被无光阑透镜聚焦后的焦开关效应。推导出了轴上最大光强位置满足的一元三次方程和相对跃迁量公式,并用数值计算对理论结果作了说明。研究表明,当光束参数大于2时,聚焦贝塞尔-高斯光束会有焦开关现象出现。相对跃迁量随着光束参数的增大而增大,轴上归一化光强最小值随着光束参数的增大而减小,并且当光束参数大于3.9时,轴上归一化光强最小值为零。     

聚焦贝塞尔-高斯光束的焦开关效应

 详细研究了贝塞尔-高斯光束被无光阑透镜聚焦后的焦开关效应。推导出了轴上最大光强位置满足的一元三次方程和相对跃迁量公式,并用数值计算对理论结果作了说明。研究表明,当光束参数大于2时,聚焦贝塞尔-高斯光束会有焦开关现象出现。相对跃迁量随着光束参数的增大而增大,轴上归一化光强最小值随着光束参数的增大而减小,并且当光束参数大于3.9时,轴上归一化光强最小值为零。     

Gaussian representation of high-intensity focused ultrasound beams

A method for fast numerical simulation of high-intensity focused ultrasound beams is derived. The method is based on the frequency-domain representation of the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation, and assumes for each harmonic a Gaussian transverse pressure distribution at all distances from the transducer face. The beamwidths of the harmonics are constrained to vary inversely with the square root of the harmonic number, and as such this method may be viewed as an extension of a quasilinear approximation. The technique is capable of determining pressure or intensity fields of moderately nonlinear high-intensity focused ultrasound beams in water or biological tissue, usually requiring less than a minute of computer time on a modern workstation. Moreover, this method is particularly well suited to high-gain simulations since, unlike traditional finite-difference methods, it is not subject to resolution limitations in the transverse direction. Results are shown to be in reasonable agreement with numerical solutions of the full KZK equation in both tissue and water for moderately nonlinear beams.     

矢量非傍轴离轴高斯光束的传输

基于矢量瑞利-索末菲衍射积分公式，得出了波动方程的一个解，它代表矢量非傍轴离轴高斯光束，其在自由空间的传输方程表示为解析的结果.矢量非傍轴离轴高斯光束的轴上和远场公式，矢量非傍轴高斯光束的传输方程，以及傍轴的结果都可作为一般表达式的特例而得出.研究表明，f参数对光束的非傍轴特性有重要影响，而离心参数也影响非傍轴行为.与共轴情况不同的是，对离轴情况，在y方向存在场的纵向分量. 关键词： 激光光学 矢量非傍轴离轴高斯光束 瑞利-索末菲衍射积分 f参数 离轴参数     

Response of infinite length rods and beams with periodically varying area

This paper develops a solution method for the longitudinal motion of a rod or the flexural motion of a beam of infinite length whose area varies periodically. The conventional rod or beam equation of motion is used with the area and moment of inertia expressed using analytical functions of the longitudinal (horizontal) spatial variable. The displacement field is written as a series expansion using a periodic form for the horizontal wavenumber. The area and moment of inertia expressions are each expanded into a Fourier series. These are inserted into the differential equations of motion and the resulting algebraic equations are orthogonalized to produce a matrix equation whose solution provides the unknown wave propagation coefficients, thus yielding the displacement of the system. An example problem of both a rod and beam are analyzed for three different geometrical shapes. The solutions to both problems are compared to results from finite element analysis for validation. Dispersion curves of the systems are shown graphically. Convergence of the series solutions is illustrated and discussed.     

Multiple off-axis acoustic vortices generated by dual coaxial vortex beams

As a kind of special acoustic field, the helical wavefront of an acoustic vortex(AV) beam is demonstrated to have a pressure zero with phase singularity at the center in the transverse plane. The orbital angular momentum of AVs can be applied to the field of particle manipulation, which attracts more and more attention in acoustic researches. In this paper,by using the simplified circular array of point sources, dual coaxial AV beams are excited by the even-and odd-numbered sources with the topological charges of l_E and l_O based on the phase-coded approach, and the composite acoustic field with an on-axis center-AV and multiple off-axis sub-AVs can be generated by the superimposition of the AV beams for|l_E| ≠ |l_O|. The generation of edge phase dislocation is theoretically derived and numerically analyzed for l_E=-l_O. The numbers and the topological charges as well as the locations of the center-AV and sub-AVs are demonstrated, which are proved to be determined by the topological charges of the coaxial AV beams. The proposed approach breaks through the limit of only one on-axis AV with a single topological charge along the beam axis, and also provides the feasibility of off-axis particle trapping with multiple AVs in object manipulation.     

Focal shift in focused truncated gaussian beams

It is known that under certain circumstances the point of maximum intensity in a focused aberration-free wave is not at the geometrical focus, but is closer to the focusing lens. In the present note such a focal shift is analyzed for the case of a gaussian beam, focused by a thin lens, which fills a circular aperture of any prescribed radius, the waist of the beam being assumed to be located in the aperture plane. Many previously known results follow as limiting cases of our analysis.     

Focal shifts in focused Hermite-cosh-Gaussian laser beams

A closed-form propagation equation of Hermite-cosh-Gaussian beams passing through an unapertured thin lens is derived. Focal shifts are analyzed by means of two different methods according to the facts that the axial intensity of some focused Hermite-cosh-Gaussian beams are null and that of some others are not null but the principal maximum intensity may be located on the axis or off the axis. Optimal focusing for the beams is studied, and the condition of optimal focusing ensuring the smallest beam width is also given.