【作者】 李华星；

【导师】 林机；

【作者基本信息】 浙江师范大学 ， 凝聚态物理， 2011， 硕士

【摘要】 近年来,光声相互作用成为人们关注的热点问题,其中布拉格光栅中光波和声波耦合形成光声孤立子是典型代表。我们知道,布拉格光栅具有周期性变化的中心折射率,及较大的群速度色散和非线性效应,光波在其中传播时,可以形成光孤子。此外,在布拉格光栅中,电致伸缩效应表现为：光强的变化可以改变介质的密度,从而对声波产生影响,相反,声波也能够通过介质折射率的变化作用于光波,因此,在考虑电致伸缩的情况下,光孤子可以与声波耦合形成光声孤立子。Tasgal[1]首先提出了光声孤立子的概念,并给出了光声在布拉格光栅中传播所遵循的祸合方程组。然而,其只给出了单光声孤立子解析解,用数值方法分析了孤子的稳定性。为了进一步研究光声相互作用,找到更多的解析解,同时由于光声耦合方程组是不可积的,直接寻找方程组的解析解有很大的困难,而多重尺度方法是寻找这些不可积方程的近似解析解行之有效的方法。因此,本论文研究工作主要集中于运用多重尺度方法约化光声耦合方程组。本文中我们用多重尺度方法来研究光声耦合方程组,发现该方程可以约化为一些简单的模型：如非线性薛定谔方程等。并且由于这些简单模型的孤子解已经有很好的研究,我们得到该耦合方程组的一系列孤子解：单光声孤子解、二光声孤子解等。在约化过程中我们分别在忽略声波粘滞系数和考虑声波粘滞系数的情况下,研究了该耦合方程组的性质。更多还原

【Abstract】 The interaction of acoustic and optical signals are under intensive studies these years, One of the typical examples is the coupling of optical wave and acoustic wave in the the Bragg gratings. As we know, Bragg gratings have periodic variation of the refractive index, a very large group velocity dispersion and nonlinear effects. optical waves propagating in the Bragg gratings may form optical solitons. Moreover, light may drive sound through compressing the medium due to variations of the intensity of light, conversely, acoustic waves react into the optical wave through the dependence of the refractive index on the material density. So, considering the electrostriction, optical gap solitons may couple to acoustic waves, generate the optoacoustic solitons.Optoacoustic solitons were first found by Richard S. Tasgal in the Bragg gratings. And the optoacoustic coupled mode equations were given. But, Richard S. Tasgal only gave out the single-soliton solutions and tested solitons stability by numerical simulation. For the sake of completely investigating the properties of optoacoustic solitons, meanwhile because the coupled mode equations are non-integrable, and the multiple-scales method is effective to find the approximate solutions of non-integrable equations. So, In this paper, we use the multiple-scales method to discuss the optoacoustic coupled mode equations in the Bragg gratings.In this paper, using the multiple-scales method, we find that the optoacoustic coupled mode equations can be reduced to some simple models, such as the nonlinear Schrodinger equation. Then, from the solutions of the simple models, we obtain the approximate solutions of the optoacoustic coupled mode equations, such as the single-soliton solutions and two-soliton solutions. And that, we discuss the properties of the optoacoustic coupled mode equations in two aspects, such as neglecting phonon viscosity and considering phonon viscosity.更多还原