【作者】 卓辉；

【导师】 范滇元；

【作者基本信息】 湖南大学 ， 计算机应用技术， 2008， 博士

【摘要】 光子代替电子作为信息的载体是人们的一个共识,因为光子技术具有高传输速度、高密度及高容错性等优点。然而,由于光子不像电子一样易于控制,光子器件远不如电子器件成熟,致使光信息技术仅仅在信息传输中得到应用,而且是最基本的信息功能。研究光波与新型光子材料的相互作用,探索利用光子材料对光子的操纵和控制,是发展新型光子器件的基础,对光计算、全光通信等领域具有重要的理论和实际意义。周期性微结构光子材料,如布拉格光栅、光子晶体、光学格子、超常介质等,使人们操纵和控制光子的梦想成为可能,是发展全光器件的理想材料。本论文着重研究最近几年发展的两种新型的周期性微结构光子材料即光学格子和超常介质中光波的非线性传输特性,进行了如下的工作:第一,光学格子是指具有横向周期性调制折射率的光学介质。光束在非线性光学格子中传输时展现出丰富的令人感兴趣的现象,特别是,横向折射率的周期性调制深刻地影响空间孤子的形成和传输特性。我们利用变分法和数值方法研究了克尔型非线性光学格子中光束的传输,求出了光束宽度、振幅、频率啁啾参量随传播距离的演化形式,揭示了光学格子的调制周期和调制深度对光波非线性传输的影响,得到了格子孤子的形成和稳定传输的条件。发现光束宽度与调制周期的比值必须小于一定的值才能形成孤子的传输,周期性格子有类似于非线性的良好特性,从而为更好地控制格子孤子的形成和传输提供了另一个自由度。第二,损耗是所有系统的固有属性,光学格子也不例外。为有效克服损耗对光学格子孤子的影响,我们借鉴色散渐变光纤中利用色散的缓变来补偿因光纤中的损耗而导致非线性效应减弱的方案,首次提出通过控制光格子的调制深度和调制周期来补偿光学格子介质的损耗效应,以在实际有损耗的光学格子介质中实现稳定的孤子传输。为论证该方案,利用解析和数值方法研究了空间光孤子在具有损耗的Bessel光格子中的传输,通过变分法得到了光束宽度、振幅和波面曲率的动力学方程,结果表明,通过适当地增加光格子的折射率调制深度,介质的损耗效应能得到精确的补偿,从而达到稳定的空间孤子的传输。第三,超常材料通常是指人工构造的、具有自然材料所不具备的特性的材料,是当今重大科学前沿之一。我们结合最新的超常介质和传统的非线性光学原理研究了超常介质中光波的非线性传输特性。超常介质与常规光学介质的一个最重要的区别是前者具有色散磁导率。将色散磁导率合并到非线性极化项中,借鉴常规介质中超短脉冲传输方程的推导方法,得到了非线性超常介质中超短脉冲的传输方程。在Drude色散模型下,根据脉冲中心频率的不同在传输方程中出现了可正、可负、可为零的自陡峭系数,以及高阶非线性色散项。此外,利用矩方法对得到的传输方程进行分析,得到了超常介质中超短脉冲传输方程的能量守恒定律表达式,揭示了色散磁导率导致的超短脉冲传输的新特性,发现二阶非线性色散使超短脉冲的能量、脉冲频移、脉冲宽度、中心位置和啁啾都随传输距离呈现振荡式变化。第四,基于我们得到的非线性超常介质中超短脉冲的传输方程,研究了完全相干和部分相干超短脉冲在超常介质中传输的调制不稳定性,着重讨论了由超常介质中色散磁导率导致的非线性色散项对调制不稳定性的影响。推导了部分相干超短脉冲的Wigner–Moyal传输方程,以及发生调制不稳定性的色散关系。首次发现二阶非线性色散在调制不稳定性中的作用在某种程度上与群速度色散的作用是等效的,因此,由于二阶非线性色散的作用,调制不稳定性可以发生在其他不可能发生的情况,例如在正常色散情况下。更多还原

【Abstract】 It is a consensus to replace electron with photon as the carrier of information because photonic technology has several advantages, such as high transmission speed, high density and high fault tolerance. However, photons are not so prone to be controlled as electrons, and the photonic devices are far from mature compared to electronic component, which result in that optical information technonlogy has been only applied to information transmission, further more, the basic information function. Thus, the research on the interaction between light wave and new type photonic material and the exploration of technologies of controlling photon by using photonic material are the basis of the development of novel photonic devices and are very important in optical calculation and all optical communication, both theoretically and practically. Periodically microstructure photonic material as Bragg gratings, photonic crystal, optical lattice, and metamaterials et al, are ideal material for all-optical devices because of their ability in manipulating and controlling photons. In this thesis, we investigate the properties of nonlinear propagation in two kinds of new type periodically microstructure optical material, i.e. optical lattice and metamaterials. Our work and results are mainly follows:Firstly, optical lattice is an optical media with transverse periodic lattice modulation refractive index. Beams appear plenty of interesting phenomena when they propagate in the nonlinear optical lattice, especially periodic modulation with transverse refractive index can affect deeply the form and transmission characteristic of spacial solition. Using the variational principle and numerical method, we study the beam evolution of Kerr nonlinear optical lattice, and obtain the forms for the evolution during propagation of beam width, beam amplitude and frequency chirp, and post the influence of modulation period and modulation depth of optical lattice on the light-wave’s nonlinear propagation. The following, we find the conditions for lattice soliton formation and stabile propagation. We find that solitions can propagate only if the ratio of beam width and modulation period are less than a certain numerical value. With the good characteristic similar to nonlinearity, periodic lattice can offer a better method to control the lattice soliton formation and propagation.Secondly, attenuation is an intrinsic property of any practical system, including optical lattice. Therefore, it is important to compensate the medium loss for maintaining the propagation of the spatial soliton in the system. We first propose and demonstrate a scheme to compensate medium loss for spatial soliton propagation, i.e., controlling the modulation depth of a Bessel lattice along the light propagation direction to compensate the loss effect. Here, we investigated the propagation of a spatial soliton in a dissipative modulated Bessel optical lattice, both analytically and numerically. The dynamic evolution equations for beam width, amplitude, and curvature wavefront are obtained by a variational approach. It is shown that by properly increasing the modulation depth of refractive index of the optical lattice, the loss effect can be compensated exactly to fulfill stable spatial soliton propagation.Thirdly, metamaterials are artificial materials which have anomalous properties not possessed by natural materials. The research about metamaterials is one of the important frontline in modern scientific domain. One of the most important differences between metamaterials and conventional materials is that the magnetic permeabilities of metamaterials are dispersive. Combining the properites of metamatirials and the related principles of nonlinear optics, we have investigated the propagation properties of light wave in metamatirals. It is shown that, under the Drude dispersive model, the dispersive permeability results in a self-steepening parameter which can be negative, positive or zero depending on the central frequency of the pulse, and a series of higher-order nonlinear dispersion terms in the propagation equation. Furthermore, the propagation equation is analyzed by using the moment method, an explicit expression for power conservation for the propagation equation is obtained, and the unique propagation properties of ultrashort pulse in metamaterials are disclosed. It is found that due to the role of the second-order nonlinear dispersion, the characteristic parameters of the ultrashort pulse, including energy, frequency shift, duration, center position, and chirp, all oscillate with propagation distance.Fourthly, on the basis of the propagation equation obtained for ultrashort pulse in nonlinear metamaterials we have investigated the modulational instability in metamaterials of the propagation of both coherent and incoherent ultrashort pulses. The combination of dispersive magnetic permeability with nonlinear polarization leads to a series of nonlinear dispersion terms in the propagation equations for ultrashort pulses in metamaterials. Here we present an investigation of modulation instability (MI) of both coherent and partially coherent ultrashort pulses in metamaterials to identify the role of nonlinear dispersion in pulse propagation. The Wigner–Moyal equation for partially coherent ultrashort pulses and the nonlinear dispersion relation for MI in metamaterials are derived. Combining the standard MI theory with the unique properties of the metamaterial, the influence of the controllable first-order nonlinear dispersion, namely self-steepening, and the second-order nonlinear dispersion on both coherent and partially coherent MI, in both negative-index and positive-index regions of the metamaterial for all physically possible cases is analyzed in detail. For the first time to our knowledge, we demonstrate that the role of the second-order nonlinear dispersion in MI is equivalent to that of group-velocity dispersion (GVD) to some extent, and thus due to the role of the second-order nonlinear dispersion, MI may appear in the otherwise impossible cases, such as in the normal GVD regime.更多还原