Spectral shifts and spectral switches in diffraction of ultrashort pulsed beams passing through a circular aperture

Based on the Fourier transform method, a simple closed-form expression for the on-axis power spectrum of ultrashort Gaussian pulsed beams in diffraction at a circular aperture is derived, which permits us to study spectral changes both analytically and numerically. It is shown that for diffracted pulsed beams there exist spectral red and blue shifts, spectral narrowing, and spectral switches in the near field. The aperture diffraction plays an important role in spectral switching, but both the truncation parameter and bandwidth (or equally, Fourier transform limited pulse duration) affect the behavior of spectral switches.     

高功率激光驱动器中小尺度自聚焦和噪声模型

 建立了一套线性的近似分析方法，研究高功率激光驱动器中强激光传输的小尺度自聚焦效应和相位噪声对光束传输和光束质量的影响，给出了系统噪声强度、B积分值与光束近场调制对比度之间的定量关系。研究表明,为保证输出光束质量，即近场调制对比度小于给定值，系统内的噪声强度必须符合一定的谱分布。     

On parabolic equations with a small parameter

A singularly perturbed parabolic equation with a nonlinear right-hand side of a special form is examined. A numerical analytical study of such equations is performed.     

Persistence of Floquet invariant tori for a class of non-conservative dynamical systems

In this paper we consider a class of non-conservative dynamical system with small perturbation. By the KAM method we prove existence of Floquet invariant tori under the weakest non-resonant conditions.

     

Novel methods and universal software for HRXRD, XRR and GISAXS data interpretation

Several novel methods for evaluation and interpretation of X-ray data from modern nanostructures are presented along with their applications. The background of methods and their relations to fundamental problems of X-ray analysis is shortly described. The key features of LEPTOS software, which is designed for the analysis of X-ray data measured with various geometries and setups and implements all discussed techniques, are discussed.     

等效可变孔径远场法测量单模光纤模场半径

本文提出等效远场的可变孔径方法,由测量光纤远场累积分布求得模场半径。并且利用Petermann关于模场半径的新定义,推出了一种对非高斯模场分布也适用的求模场半径的方法。实验表明,这种测量方法简便可靠,在不同的制备端面下,重复测量的标准误差小于0.04μm。     

Propagation of elegant Laguerre–Gaussian beams through an annular apertured paraxial ABCD optical system

Based on the generalized Huygens–Fresnel diffraction integral and the expansion of the hard aperture function into a finite sum of complex Gaussian functions, the approximate analytical expression of elegant Laguerre–Gaussian beams passing through a paraxial ABCD optical system with an annular aperture is derived. Meanwhile, the corresponding closed-forms for the unapertured, circular apertured or circular black screen cases are also given. The obtained results provide more convenience for studying their propagation and transformation than the usual way by using diffraction integral formula directly. Some numerical examples are given to illustrate the propagation properties of elegant Laguerre–Gaussian beams.     

斐索型光学合成孔径系统近轴成像条件研究

从几何光学理论出发，详细推导了斐索型光学合成孔径成像系统的近轴非相干成像条件，即子望远系统的角放大率等于系统的线性缩放因子。对于焦平面上的像点而言，合成孔径成像系统可等效为一个带有特殊形状孔径光阑的望远系统，这要求该孔径光栏的开口形状和位置分布与合成孔径成像系统各子系统孔径大小和位置分布相一致。我们由此得到了斐索型合成孔径成像系统的主要约束条件。     

Recurrence propagation equation of Hermite-Gaussian beams through a paraxial optical ABCD system with hard-edge aperture

Based on the generalized Huygens-Fresnel diffraction integral, a recurrence propagation equation of Hermite-Gaussian (H-G) beams through a paraxial optical ABCD system with hard-edge aperture is derived, which permits us to obtain the analytical propagation expression for H-G beams of any order. The advantages of our analytical results are analyzed, and the application is illustrated with numerical examples.