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.

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。

Effects of the frequency chirp on the fields of a chirped Gaussian pulse passing through a hard-edged aperture

Based on the Huygens-Fresnel diffraction integral and Fourier transform, propagation expression of a chirped Gaussian pulse passing through a hard-edged aperture is derived. Intensity distributions of the pulse with different frequency chirp in the near-field and far-field are analyzed in detail by numerical calculations. In the near-field, amplitudes of the intensity peaks generated by the modulation of the hard-edged aperture decrease with increasing the frequency chirp, which results in the improving of the beam uniformity. A physical explanation for the smoothing effect brought by increasing the frequency chirp is given. The smoothing effect is achieved not only in the pulse with Gaussian transverse profile but also in the pulse with Hermite-Gaussian transverse profile when the frequency chirp increases. (C) 2005 Elsevier B.V. All rights reserved.

厄米-高斯光束中带宽对横向强度分布均匀性的影响

使用惠更斯-菲涅耳衍射积分和傅里叶变换，推导了横向模式为厄米高斯的激光束通过硬边光阑的传输表达式。利用所得公式通过数值计算详细分析了光束的频带宽度对光束横向强度分布的影响。分析发现激光束通过硬边光阑后会出现大量的强度尖峰，引起近场的强度分布不均匀。然而，当带宽增加时，强度尖峰的数量减少，幅度减小，光束的均匀性得到改善。在远场，光束的横向强度分布没有强度尖峰出现，但宽度随带宽的增加而减小。因此带宽增加会带来近场强度匀滑化和远场光束宽度变窄的效应。另外，数值结果表明带宽对模指数为1和2的厄米-高斯光束的强度分

Transverse mode formation in longitudinally pumped miniature slab lasers

The formation of transverse modes in longitudinally pumped miniature slab lasers is investigated theoretically and experimentally. The longitudinally non-uniform gain-guiding is studied by expanding the electric field into the Hermite-Gaussian functions that satisfy boundary conditions of the resonator. Non-Gaussian transversal beam profiles in the near field are found and the beam diameter is reduced when the pump spot becomes smaller. The experimental observation agrees with the theoretical calculation.

Research on the influence of fabrication parameters on the performance of buried ion-exchanged glass waveguides using the variational method

The variational method is proposed to analyze the influence of the fabrication parameters on the performance of buried K+-Na+ ion-exchanged Er3+-Yb3+ ions co-doped glass waveguide. The unknown parameters of the Hermite-Gaussian functions as the trial field distribution are determined based on the scalar variational principle. It is demonstrated that the results calculated in this paper agree with those measured in the experiment. The mode dimensions, the effective refractive index, and the overlap factor as the functions of the fabrication parameters are investigated. These results of the variational analysis are useful for the design and optimization of Er3+-Yb3+ ions co-doped waveguides.