超常介质中高阶色散对高斯脉冲传输的影响

发布时间：2018-01-23 08:45

本文关键词： 超常介质色散非线性薛定谔方程脉冲传输色散补偿　出处：《华东师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：作为一种人造材料,超常介质具有独特的色散特性。与常规介质相比,其介电常数和磁导率都是色散的。它是由金属或塑料材料共同组合而成的一种复合材料,其微观结构通常是周期性排列的阵列结构,且单元尺寸一般小于作用其上的电磁波(光波)的波长尺度。正是这种周期性阵列结构使得超常介质的色散很大,我们的研究发现超常介质的各阶色散比常规介质相应色散大约3个数量级(2.5节)。这使得超常介质不仅具有很强的群速度色散,同时也具有很强的高阶色散。因为色散限制了光脉冲的传输距离和系统的比特率,导致通信容量下降,所以在高阶色散作用下的信号传输问题中研究并控制色散是很有必要的。近来纳米制造技术的飞快发展和超常材料制造技术的突破使得人们有可能根据需求获得想要的介质特性[4-6],并发展出新的色散补偿技术。这是因为超常介质的色散特性依赖于电和磁的等离子频率,所以这种可重构特性使得调制电、磁等离子频率、色散的管理和控制成为可能。本文以超常介质在通信领域的应用为背景,研究了高阶色散作用下脉冲在超常介质中的传输问题及色散补偿问题。采用的方法步骤以及研究得出的主要结果如下:(1)从麦克斯韦方程组和无损耗Drude模型出发,推导了单光束脉冲在超常介质中传输所满足的非线性薛定谔方程,并对比了超常介质中色散与常规介质中色散,发现超常介质中各阶色散均比常规介质大约3个数量级。(2)采用分步傅里叶方法求解脉冲在超常介质中的传输问题,分析了超常介质中各阶色散以及啁啾参量对脉冲传输的影响,发现:(i)群速度色散不仅会引起脉冲的展宽,而且它的符号还会影响由三阶色散引起的脉冲分裂峰的位置,并使四阶色散具有不同的影响效果;(ii)啁啾参量也会加剧脉冲的分裂。(3)研究了色散系数对超常介质中结构参数的依赖关系,找到了两种具有完全相反的群速度色散、而三阶色散却十分相近的超常介质,使得脉冲在三阶色散明显起作用前获得了近乎完美的二阶色散补偿。
[Abstract]:As a kind of artificial material, supernormal medium has unique dispersive property. Compared with conventional medium, its dielectric constant and permeability are dispersive. It is a composite composed of metal or plastic materials. The microstructures are usually array structures arranged periodically, and the cell size is generally smaller than the wavelength scale of electromagnetic waves (light waves) acting on them. It is this periodic array structure that makes the dispersion of supernormal medium very large. We find that the dispersion of supernormal medium is about 3 orders of magnitude and 2.5 knots than that of conventional medium, which makes the supernormal medium not only have strong group velocity dispersion. At the same time, it also has strong high-order dispersion, because dispersion limits the transmission distance of optical pulse and the bit rate of the system, which leads to the decrease of communication capacity. Therefore, it is necessary to study and control dispersion in the signal transmission problem under the action of high order dispersion. The recent rapid development of nanofabrication technology and the breakthrough of supernormal material manufacturing technology make it possible for people to obtain according to the demand. Desired dielectric properties. [This is because the dispersion characteristic of the supernormal medium depends on the plasma frequency of the electricity and magnetism, so the reconfigurable characteristic makes the modulation electricity and the magnetic plasma frequency. It is possible to manage and control dispersion. This paper is based on the application of supernormal media in the field of communication. In this paper, the propagation and dispersion compensation of pulse in supernormal medium under the action of higher order dispersion are studied. The main results are as follows: 1: 1). Based on Maxwell equations and lossless Drude model. The nonlinear Schrodinger equation for the propagation of a single beam pulse in a supernormal medium is derived, and the dispersion in a supernormal medium is compared with that in a conventional medium. It is found that the dispersion of each order of order in the supernormal medium is about 3 orders of magnitude than that in the conventional medium) the fractional Fourier method is used to solve the problem of pulse propagation in the supernormal medium. The effects of the order dispersion and chirp parameters on the pulse propagation in supernormal medium are analyzed. It is found that the dispersion of the group velocity in the 1: 1 group will not only cause the broadening of the pulse. Moreover, its symbol will also affect the position of the split peak caused by third-order dispersion, and make the fourth-order dispersion have different effects. The dependence of dispersion coefficient on structural parameters in supernormal medium is studied. Two kinds of dispersion with completely opposite group velocity dispersion are found. But the third order dispersion is very similar to the supernormal medium, which makes the pulse obtain almost perfect second order dispersion compensation before the third order dispersion is obvious.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TB33

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