Focal switch in unapertured converging Hermite-cosh-Gaussian beams

Based on the Huygens-Fresnel diffraction integral, analytical representation of unapertured converging Hermite-cosh-Gaussian beams is derived. Focal switch of Hermite-cosh-Gaussian beams is studied detailedly with numerical calculation examples and a physical interpretation of focal switch is presented. It is found that decentered parameter is the dominant factor for the emergence of focal switch, and Fresnel number affects the amplitude of focal switch and the value of critical decentered parameter to determine emergence of focal switch. Physically, the emergence of focal switch of Hermite-cosh-Gaussian beams is resulted from competition between two major maximum intensities and switch of the absolute maximum intensity from a point to another when decentered parameter increases. (C) 2005 Elsevier Ltd. All rights reserved.

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. (c) 2005 Elsevier GmbH. All rights reserved.

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.(c) 2006 Elsevier Ltd. All rights reserved.

Spatiotemporal behaviors and singularity of ultrashort pulsed Elegant Hermite-Gaussian beams

Analytical propagation expressions of ultrashort pulsed Elegant Hermite-Gaussian beams are derived and spatiotemporal properties of the pulses with different transverse modes are studied. Singularity of the complex amplitude envelope solution of the pulses obtained under slowly varying envelope approximation is analyzed in detail. The rigorous analytical solution of the pulse is deduced and no singularity emerges in the solution. The obtained results indicate that the transverse mode affects not only the spatiotemporal properties but also the singularity of the pulses. Time delay of the off-axis maximum intensity is more obvious and the singularity is located nearer to the z-axis for the pulse with higher transverse modes. (C) 2007 Elsevier GmbH. All rights reserved.

Propagation properties of off-axis Hermite-cosh-Gaussian beam combinations through a first-order optical system

Based on the Collins integral formula, the analytic expressions of propagation of the coherent and the incoherent off-axis Hermite-cosh-Gaussian (HChG) beam combinations with rectangular symmetry passing through a paraxial first-order optical system are derived, and corresponding numerical examples are given and analysed. The resulting beam quality is discussed in terms of power in the bucket (PIB). The study suggests that the resulting beam cannot keep the initial intensity shape during the propagation and the beam quality for coherent mode is not always better than that for incoherent mode. Reviewing the numerical simulations of Gaussian, Hermite-Gaussian (HG) and cosh Gaussian (ChG) beam combinations indicates that the Hermite polynomial exerts a chief influence on the irradiance profile of composite beam and far field power concentration.

Hierarchy of structure functions for passive scalars advected by turbulent flows

A hierarchical model is proposed for the joint moments of the passive scalar dissipation and the velocity dissipation in fluid turbulence. This model predicts that the joint probability density function (PDF) of the dissipations is a bivariate log-Poisson. An analytical calculation of the scaling exponents of structure functions of the passive scalar is carried out for this hierarchical model, showing a good agreement with the results of direct numerical simulations and experiments.

Interactions of Penny-Shaped Cracks in Three-Dimensional Solids

The interaction of arbitrarily distributed penny-shaped cracks in three-dimensional solids is analyzed in this paper. Using oblate spheroidal coordinates and displacement functions, an analytic method is developed in which the opening and the sliding displacements on each crack surface are taken as the basic unknown functions. The basic unknown functions can be expanded in series of Legendre polynomials with unknown coefficients. Based on superposition technique, a set of governing equations for the unknown coefficients are formulated from the traction free conditions on each crack surface. The boundary collocation procedure and the average method for crack-surface tractions are used for solving the governing equations. The solution can be obtained for quite closely located cracks. Numerical examples are given for several crack problems. By comparing the present results with other existing results, one can conclude that the present method provides a direct and efficient approach to deal with three-dimensional solids containing multiple cracks.

Static Study of Cantilever Beam stiction under Electrostatic Force Influence

The model and analysis of the cantilever beam adhesion problem under the action of electrostatic force are given. Owing to the nonlinearity of electrostatic force, the analytical solution for this kind of problem is not available. In this paper, a systematic method of generating polynomials which are the exact beamsolutions of the loads with different distributions is provided. The polynomials are used to approximate the beam displacement due to electrostatic force. The equilibrium equation offers an answer to how the beam deforms but no information about the unstuck length. The derivative of the functional with respect to the unstuck length offers such information. But to compute the functional it is necessary to know the beam deformation. So the problem is iteratively solved until the results are converged. Galerkin and Newton-Raphson methods are used to solve this nonlinear problem. The effects of dielectric layer thickness and electrostatic voltage on the cantilever beamstiction are studied.The method provided in this paper exhibits good convergence. For the adhesion problem of cantilever beam without electrostatic voltage, the analytical solution is available and is also exactly matched by the computational results given by the method presented in this paper.

迟滞系统随机响应问题基于函数级数的解法

本文提出了一个三次多项式的迟滞模型,并用Wiener-Hermite函数级数展开的方法求解,得到了不同阻尼及不同的非线性强度时系统响应的均方值σ(t)。不仅从理论上而且通过实验证实了用这种方法求解迟滞系统的响应是行之有效的、简便的。