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。     

Transformation of nonlinear sawtooth waves in a medium with refractive inhomogeneities

Theexact solutions of intensive sawtooth waves and beams in a medium with a sound speed inhomogeneity have been found. It has been shown that the focusing on the medium inhomogeneity is strongly pronounced for a single pulse, resulting in the formation of narrow high-amplitude areas. It has been determined that the refractive infomogeneity can lead to a shift of the amplitude maximum of the initial focused beam and the transformation of the converging beam into a dispersing one.     

多脉冲激光对碳纳米管悬浮液光限幅特性影响

利用实验的方法研究了碳纳米管悬浮液对脉宽8 ns,波长532 nm多脉冲激光的光限幅效应.分析了直径分布为10~20 nm的多壁碳纳米管悬浮液对重复频率分别为1 Hz、 3 Hz、 5 Hz、 10 Hz情况下532 nm激光的光限幅效应,分析计算了不同重复频率下碳纳米管悬浮液的限幅阈值,比较了不同焦距的透镜会聚入射光束情况下对碳纳米管悬浮液光限幅效果的影响.实验结果表明：碳纳米管悬浮液对不同重复频率的532 nm 激光都具有较强的光限幅特性;碳纳米管悬浮液对激光在不同重复频率入射情况下的光限幅阈值变化很大,当入射激光的重复频率为5 Hz时,碳纳米管悬浮液的光限幅阈值比单脉冲激光入射时的限幅阈值低了2倍,重复频率为10 Hz时的限幅阈值比单脉冲时的限幅阈值低了近3倍;碳纳米管在紧焦系统中的光限幅效果更好.     

强非局域正交偏振双厄米高斯光束的传输特性

依据非局域非线性介质中双光束传输时遵循的非局域非线性薛定谔耦合方程,在强非局域情形下,通过把响应函数作泰勒展开近似取到二阶,运用变分法求出了正交偏振、中心重合的双厄米高斯光束在强非局域介质中传输时各参量演化规律和一个临界功率,并运用分步傅里叶算法数值模拟出了束宽和相位的演化规律。当两光束以临界功率入射时,得到了正交偏振、中心重合的双厄米高斯空间光孤子及其大相移演化规律。当两光束以总临界功率入射,但两束光的入射功率不等时,光束可以形成呼吸子,但随着阶数的增加呼吸子将越来越不稳定。对于各阶呼吸子,功率大的束宽都作周期性压缩振荡变化,功率小的束宽都作周期性展宽振荡变化,且两呼吸子中功率大的相移随传输距离增加更快。在厄米高斯光束阶数小于5时,变分解得到的结果与数值解吻合较好。     

Acoustic radiation force on a sphere in standing and quasi-standing zero-order Bessel beam tweezers

Starting from the exact acoustic scattering from a sphere immersed in an ideal fluid and centered along the propagation axis of a standing or quasi-standing zero-order Bessel beam, explicit partial-wave representations for the radiation force are derived. A standing or a quasi-standing acoustic field is the result of propagating two equal or unequal amplitude zero-order Bessel beams, respectively, along the same axis but in opposite sense. The Bessel beam is characterized by the half-cone angle β of its plane wave components, such that β = 0 represents a plane wave. It is assumed here that the half-cone angle β for each of the counter-propagating acoustic Bessel beams is equal. Fluid, elastic and viscoelastic spheres immersed in water are treated as examples. Results indicate the capability of manipulating spherical targets based on their mechanical and acoustical properties. This condition provides an impetus for further designing acoustic tweezers operating with standing or quasi-standing Bessel acoustic waves. Potential applications include particle manipulation in micro-fluidic lab-on-chips as well as in reduced gravity environments.     

Acoustic beam scattering and excitation of sphere resonance: Bessel beam example

The exact partial wave series for the scattering by a sphere centered on an ideal Bessel beam was recently given by Marston ["Scattering of a Bessel beam by a sphere," J. Acoust. Soc. Am. 121, 753-758 (2007)]. That series is applied here to solid elastic spheres in water and to an empty spherical shell in water. The examples are selected to illustrate the effect of varying the beam's conical angle so as to modify the coupling to specific resonances in the response of each type of sphere considered. The backscattering may be reduced or increased depending on properties of the resonance and of the specular contribution. Changing the conical angle is equivalent to changing the beamwidth. Some applications of the Van de Hulst localization principle to the interpretation of the partial wave series and to the interpretation of the scattering dependence on the beam's conical angle are discussed. Some potential applications to the analysis of the scattering by spheres of more general axisymmetric beams are noted.     

Structural stability of a nonparaxial singular mode beam

The exact explicit solution of the Maxwell equations for nonparaxial singular beams propagating in free space or in a homogeneous isotropic medium is considered. It is shown that, in the paraxial approximation, such solutions for mode beams of both lower and higher orders may turn into the solutions for guided modes or vortices of optical fibers. It is found that a variation of the Rayleigh length for a mode beam does not change the structure of phase and polarization singularities; it merely transforms their coordinates. In the paraxial limit, the singularities are shifted off the axis to regions with negligible light fluxes.     

Theoretical comparison of optical traps created by standing wave and single beam

We used generalised Lorenz–Mie scattering theory (GLMT) to compare submicron-sized particle optical trapping in a single focused beam and a standing wave. We focus especially on the study of maximal axial trapping force, minimal laser power necessary for confinement, axial trap position, and axial trap stiffness in dependency on trapped sphere radius, refractive index, and Gaussian beam waist size. In the single beam trap (SBT), the range of refractive indices which enable stable trapping depends strongly on the beam waist size (it grows with decreasing waist). On the contrary to the SBT, there are certain sphere sizes (non-trapping radii) that disable sphere confinement in standing wave trap (SWT) for arbitrary value of refractive index. For other sphere radii we show that the SWT enables confinement of high refractive index particle in wider laser beams and provides axial trap stiffness and maximal axial trapping force at least by two orders and one order bigger than in SBT, respectively.     

Effective interaction between two giant spheres suspended in a size polydisperse hard-sphere fluid

Analytic expressions for the Laplace transform of the interaction energy and force between two exceedingly large hard spheres at infinite dilution in a polydisperse hard-sphere suspending fluid are presented. The equations are based on the Percus–Yevick approximation for the many-component suspending fluid, supplemented by the hypernetted chain approximation for the correlation function of the suspended spheres. By applying the Derjaguin approximation, the energy and force results for two spheres are related to the energy per unit area and the disjoining pressure between two flat walls suspended in a polydisperse fluid. Numerical results for the representative Schultz distributions of the diameters of the species comprising the suspending fluid are presented and discussed.     

Anomalies in the field of a gaussian beam near focus

A theoretical analysis of the electromagnetic field of a focused gaussian beam, like that produced by some lasers, indicates anomalies in the field distribution over the focal region. The transverse component of the electric field is shown graphically in this region using data obtained through the numerical integration of an expression that is exact according to Maxwell's equations. These data agree with the standard paraxial theories used to describe gaussian beams only asymtotically, in the limit of zero beam divergence about focus. As the divergence is increased, so that the beam is brought more sharply to focus, the gaussian beam evolves toward a dipole field from which all evanescent plane waves have been removed. Gaussian beams observed in nature should show some evidence of the associated anomalies, even if the beam is almost collimated.     

大气湍流中部分相干聚焦涡旋光束的传输特性

基于广义惠更斯-菲涅耳原理和相位结构函数的平方近似,研究了部分相干高斯-谢尔模型涡旋光束被聚焦后在大气湍流中的传输特性,得到了焦平面上光强解析表达式.利用该表达式,详细研究了该类光束在大气湍流中传输焦平面上的光强分布特性.结果表明：在大气湍流中,随着传输距离的增加,涡旋光束的奇异性逐渐降低.对于拓扑荷大的以及空间相干长度较长的涡旋光束,光束奇异性的保持相对要好.在一定的焦距长度和湍流大气条件下,我们可以通过调整光源的拓扑荷和相干长度控制焦面光强分布和焦斑大小.另外,有一定拓扑荷的涡旋光束可以在一定程度上降低大气湍流对传输光束焦面光强分布的影响.     

An efficient algorithm for strongly focused optical beams propagating in Kerr media

Due to the lens-induced quadratic phase factor from converging lens, the beam-propagation method (BPM) is computationally expensive in simulations by the sampling theorem for lens-induced strongly focused beams propagating in nonlinear media. In the paper, we present a modified approach (MA) based on the separate envelope and lens-induced phase to only compute the envelope in the whole focal region. Then we demonstrate the correctness of MA analytically by the propagation of focused Gaussian beam and numerically by that of focused Super-Gaussian beam in linear media. Numerical simulations of strongly focused beams based on MA are in good agreement with those of BPM when propagating in Kerr media. The sampling requirement of MA which is similar with no lens-induced phase beam is lower than that of BPM which increases with the lens-induced chirp parameter and the propagation distance. Thus the computational efficiency can be greatly improved.