【作者】 吴锦花；

【导师】 范滇元； 文双春；

【作者基本信息】 湖南大学 ， 计算机应用技术， 2006， 硕士

【摘要】 研究周期性光学结构中传输和控制光信息流的方法和技术,具有重要的科学意义和应用价值。特别是,由于周期性光学格子独特的性质,使得它可以制作全新原理或以前所不能制作的高性能器件,在光通讯上有重要的用途。本文利用解析和数值方法研究了在具有横向折射率周期性调制的克尔型非线性光学格子中孤子的传输和控制,做出了一些创新性的研究结果:首次得出了高斯光束形成格子孤子的条件和两种稳定传输形式。根据三阶非线性光学格子孤子传输所遵循的偏微分方程,利用矩方法推导出了格子孤子主要参量的演化方程,进一步分析得出了格子孤子的形成与稳定传输的条件。研究发现:光束的初始功率和入射角度是格子孤子形成和稳定传输的重要因素,当光束的初始功率与光束宽度满足一定条件时,可以维持传输过程中衍射和非线性效应的精确平衡,从而形成稳定的三阶非线性格子孤子。由于入射角度的取值不同,格子孤子具有两种不同的传输方式:当光束入射角小于某临界角度时,光束可被类似波导形式的路径俘获,转而沿该路径向前传输;当光束入射角大于该临界角时,孤子则不会被俘获,而是沿着光束的入射方向直线传输。从理论上得到了该临界角的表达式,它随折射率调制周期、调制深度的增加而增大,且光束越窄临界值越大。首次提出利用初始啁啾实现对格子孤子传输的控制。我们得到了在光束具有线性空间啁啾的条件下高斯光束形成孤子的条件以及传输过程中光束啁啾的演化方程。结果表明:线性空间啁啾虽然对光束传输的中心位置没有任何影响,但它打破了衍射与非线性效应的平衡,导致光束发散,从而破坏了孤子形成的条件。为此,我们提出采用特定功率取值与啁啾作用互补以形成格子孤子的方案。数值模拟直观地反映了三阶非线性格子孤子的传输特性,同时也验证了我们的理论解析结果。更多还原

【Abstract】 It is of great scientific importance and practical value to study methods and techniques of propagation and control of the flow of light in periodic photonic structures. Especially,because of the unique features of the periodic photonic lattice, it can be effectively used to make high-performance devices based on bran-new theories and those would have been otherwise impossible. Therefore, it has important uses in the field of optics communication. The propagation and control of soliton in nonlinear Kerr optical lattice with harmonic modulation of refractive index are investigated analytically and numerically in this paper. And some innovative research results have been worked out.The forming conditions of lattice soliton from Gauss beam and the two modes of its stable propagation are obtained for the first time. According to the nonlinear Schr?dinger equations, by which propagation of optic lattice soliton is governed, the moment method is applied to deduce the evolution equations of lattice soliton’s primary parameters. And conditions of formation and stable transmission of lattice soliton are found by further analysis. It is show that the initial power and the incident angle of the beam are important factors of formation and stable propagation of soliton. When the initial power matches with the beam width, a balance of diffraction and nonlinearity effects in propagation will be maintained and therefore the stable nonlinear lattice soliton comes into being. Due to the different values of incident angle, there are two different propagation formats. One case is that the beam is finally trapped in a guide-like channel and propagates stably along the channel when the launching angle is smaller than a critical value. Otherwise, it will propagate along the incident direction all along. The theoretical expression of the critical angle is acquired, showing that it rises with the increase of the depth and period of modulation of refractive index. Also, it increases as the beam width decreases.The method that initial chirp is used to control the propagation of lattice soliton is put forward for the first time. Under the condition that the beam is chirped, demands for soliton formation from Gauss beam and the evolution equations of the beam chirp in the propagation are obtained. The results show that linear spatial chirp upsets the balance between diffraction and nonlinearity, leading to radiation and thus destroying the condition for the formation of soliton, although it doesn’t affect the central更多还原