Non-paraxial Propagation of Gaussian Beam Rays in Active Graded-index Waveguides with Gain or Losses

Non-paraxial propagation of Gaussian beam rays in active multi-mode graded-index waveguides with polynomial refractive index profile is investigated analytically using algebraic perturbation theory and the generalized coherent states formalism. Explicit expressions are obtained for the beam ray trajectories and widths in a waveguide with gain or losses. The influence of the gain or losses of the waveguide on the recently found effect of large-scale periodical revival (reconstruction) of initial beam field distribution is investigated in detail. The results obtained may be useful for large distance image transmission through optical fibres.     

环形孔径高斯光束的远场特性

讨论环形孔径高斯光束的远场光斑能量分布，并给出拟合表达式。首先推导光束没有抖动时远场光斑的光能分布表达式，然后研究各种不同中心遮拦和不同光束截断比，在有以及没有激光束抖动的情况下，对高斯光束的远场环围能量分布变化的影响。     

Light Propagation in Singly and Doubly Periodic Planar Waveguides

Abstract

Light propagation in singly and doubly periodic planar waveguides is investigated with respect to future applications in integrated optics. The waveguides used in our experiments reveal, in the vicinity of Bragg reflection, a strong difference between the directions of phase and group velocities, the beam steering. A clear graphical representation of the observable propagation effects is given in wave-vector diagrams, showing the directional dispersion of the elementary waves in periodic structures, the Floquet-Bloch waves. The dispersion phenomena were measured with high accuracy, using selective wave excitation. In conjunction with straight tapered transitions to smooth planar waveguides, the periodic structures show a great variety of strong frequency and direction-dependent effects such as lateral beam shifting and focusing with a frequency-variant focal length. Ray optics of Floquet-Bloch waves is used to describe these phenomena. Complex interference patterns observable in the vicinity of Bragg reflection in doubly periodic structures are explained by the superposition of Floquet-Bloch waves. Examples of applications of planar periodic structures as highly selective frequency filters, optical multiplexers as well as frequency-tunable beam narrowing, focusing and expanding devices are given together with measured data.     

Propagation of a Gaussian Beam in Planar and Cylindrically Inhomogeneous Media: Comparison of Modal Analysis and Approximate Approaches

This work presents a study on the propagation of electromagnetic waves in media, characterized by k = k₀ m k₂ y ² and k = k₀ m k₂ r². A vector theory based on Maxwell's equations is used to derive linear homogeneous second-order equations satisfied by the transverse electric and magnetic field components. The various modes of propagation and the corresponding propagation constants have been determined. These are used to study the propagation and focusing of waves which have an intensity distribution along their wavefront. An alternative method for the study of the propagation and focusing of electromagnetic waves has been discussed. This is based on an approximate solution of the wave equation given in previous communications. For parameters of interest, the results obtained from the approximate solution are in excellent agreement with the solution obtained from the modal analysis of the problem. The present study should be of relevance in tropospheric communication and focusing of laser beams in selfoc fibres, gas lenses, etc.     

轴向初压力和横向初偏移对梁非线性振动的影响

本文应用摄动法对受轴向初压力、并具有一定初偏移的梁的非线性自由振动进行了研究.结果表明:初压力和初偏移的不同组合,能够影响梁非线性振动的频率.这对动态环境下压力杆件的设计有一定的工程意义.另外文中通过数值结果对一次摄动解进行了误差分析.     

Propagation and focusing of Gaussian beams generated by Gaussian mirror resonators

The propagation and focusing properties of a class of Gaussian beams generated by optical resonators with Gaussian reflectivity mirrors are investigated. Attention is concentrated on the following two beams in this class: (a) the annular Gaussian beam (the Gaussian doughnut mode) and (b) the flat-topped Gaussian beam. A class of flat-topped Gaussian beams is introduced. All analysis is limited to a coherent superposition scheme of the lowest-order Gaussian modes (TEM00) that have different parameters.     

Propagation of Gaussian Schell-model Beams in Dispersive and Absorbing Media

Abstract

The spectral properties and the coherence properties of Gaussian Schell-model beams, propagating in dispersive and absorbing media, are discussed. Unlike in free space, the ratio of the transverse spectral correlation length to the beam width is found to increase on propagation. Consequently upon propagation the beam becomes spatially more coherent at each frequency. Numerical results for the spectrum and for the degrees of spectral and of temporal coherence of the field are presented for some selected values of the beam parameters and for several values of the propagation distance. Propagation in a gain medium is also briefly discussed.     

考虑电子热初速分布计算磁聚焦强流电子注的新方法

电子的热初速对强流电子注磁聚焦系统的性能具有重大的影响.本文提出了一种新方法,系统地考虑电子热初速分布和空间电荷效应计算非层流强流电子注聚焦系统;导出了局部正交曲线坐标系中电流密度分布的演化方程;编写了强流电子注磁聚焦的软件,研究了热初速分布对周期磁聚焦电子注电流密度分布及其演化的影响.     

Propagation of elliptical Gaussian beams in apertured and misaligned optical systems

On the basis of the fact that a hard-edged elliptical aperture can be expanded approximately as a finite sum of complex Gaussian functions in tensor form, an analytical propagation expression for an elliptical Gaussian beam (EGB) through a misaligned optical system with an elliptical aperture is derived by use of vector integration. The approximate analytical results provide more convenience for studying the propagation and transformation of EGBs than the usual way by using a diffraction integral directly, and the efficiency of numerical calculation is improved. Some numerical simulations are illustrated for the propagation properties of EGBs through apertured optical transforming systems with misaligned thin lenses.     

Propagation of a Non-Gaussian Laser Beam in SELFOC Fibres

In this communication we have presented an analysis of the propagation of a laser beam operating in a TEM₀₁ mode, in a medium of varying dielectric constant. The cylindrical and conical optical fibre guides have been considered. The results have been put in a form suitable for numerical computation.     

Propagation of decentered elliptical Gaussian beams in apertured and nonsymmetrical optical systems

A hard-edged elliptical aperture is described approximately by a tensor form, which can be expanded as a finite sum of complex Gaussian functions. An analytical propagation expression for a decentered elliptical Gaussian beam (DEGB) through an axially nonsymmetrical optical system with an elliptical aperture is derived by using vector integration. The approximate analytical results are compared with numerically integral ones, and it is shown that this method can significantly improve the efficiency of numerical calculation. Some numerical simulations are illustrated for the propagation properties of DEGBs through apertured and nonsymmetrical optical transforming systems.     

Propagation of four-petal Gaussian beams in apertured fractional Fourier transforming systems

Based on the Collins diffraction integral formula and the fact that a hard-edged-aperture function can be expanded into a finite sum of complex Gaussian functions, the propagation of a four-petal Gaussian beam passing through an apertured fractional Fourier transform (FRFT) optical system has been studied in detail. Some typical numerical examples are given to illustrate the properties of the four-petal Gaussian beam in the FRFT plane. The results indicate that the intensity distributions of the beam in the FRFT plane are closely related to not only the fractional order but also the beam parameters and the aperture parameters.     

Wave Propagation Model in a Human Long Poroelastic Bone under Effect of Magnetic Field and Rotation

This article is aimed at describing the way rotation and magnetic field affect the propagation of waves in an infinite poroelastic cylindrical bone. It offers a solution with an exact closed form. The authors got and examined numerically the general frequency equation for poroelastic bone. Moreover, they calculated the frequencies of poroelastic bone for different values of the magnetic field and rotation. Unlike the results of previous studies, the authors noticed little frequency dispersion in the wet bone. The proposed model will be applicable to wide-range parametric projects of bone mechanical response. Examining the vibration of surface waves in rotating cylindrical, long human bones under the magnetic field can have an impact. The findings of the study are offered in graphs. Then, a comparison with the results of the literature is conducted to show the effect of rotation and magnetic field on the wave propagation phenomenon. It is worth noting that the results of the study highly match those of the literature.     

Propagation of partially coherent twisted anisotropic Gaussian Schell-model beams in dispersive and absorbing media

By adopting a new tensor method, we derived an analytical propagation formula for the cross-spectral density of partially coherent twisted anisotropic Gaussian Schell-model (GSM) beams through dispersive and absorbing media. Using the derived formula, we studied the evolution properties and spectrum properties of twisted anisotropic GSM beams in dispersive and absorbing media. The results show that the dispersive and absorbing media have strong influences on the propagation properties of twisted anisotropic GSM beams and their spectrum evolution. Our method provides a simple and convenient way to study the propagation of twisted anisotropic GSM beams in media with complex refractive index.     

Effects of the Binomial Field Distribution on Collapse and Revival Phenomena in the Jaynes-Cummings Model

Abstract

The dynamical properties of a two-level atom interacting with a single non-decaying mode of an electromagnetic field in a binomial state are studied. The statistical aspects of the field, such as intensity-intensity correlation and squeezing, are also investigated. The binomial state reduces to a pure number state and a pure coherent state in different limits. Hence it enables us to study how the sinusoidal Rabi oscillations in a pure number state develop to give rise to the phenomenon of collapse and revival which has been studied extensively in the coherent-state field. In addition, the binomial state exhibits squeezing for certain values of parameters, but it is not a minimum-uncertainty-product state.     

激光大气传输光斑统计概率接收孔径效应

本文综合考虑湍流大气对激光斑纹强度、光束传输方向的调制作用和有限接收孔径的光强起伏、相位起伏平滑作用等因素,从理论上研究了激光斑纹强度、相位起伏概率密度函数和孔径平滑作用,求得了高阶强度矩的孔径平滑因子。