光子晶体非线性光学效应产生和增强的数值算法及其结构最优设计研究

发布时间：2018-03-10 23:38

本文选题：光子晶体　切入点：非线性　出处：《北京邮电大学》2017年博士论文　论文类型：学位论文

【摘要】：光子晶体概念自提出以来,得到了国内外学者的广泛关注。这是由于其独特周期结构性质,使其具有了光子带隙,间接有了操控光波的能力:利用带隙产生光子局域并控制电磁波自发辐射。这一特性使它具有较强的实际应用前景,光学材料中的非线性效应具有非常广泛的应用背景。因此,利用非线性光子晶体产生非线性效应也是重要的研究方向之一。本文正是在这一大背景下,考虑介质的非线性,研究光子晶体结构中非线性光学特性的产生和增强及结构最优设计问题。本文的研究工作以Maxwell方程组为理论基础,利用物质方程和非线性极化来建立非线性光学效应的数学模型,进而研究非线性光子晶体中的若干非线性光学效应问题。利用有限元理论和方法研究了光子晶体的非线性效应问题,设计了基于固定点迭代的高效求解算法,解决现有方法收敛速度慢甚至发散的问题。本文研究工作主要涉及光子晶体结构中二次谐波、三次谐波等光学效应的若干物理问题的限元模型构造、有限元离散格式的设计、有限元误差理论分析、高效算法的设计、算法的实现、结果的分析、光子晶体结构的设计研究等。本文重点研究了光子晶体中的非线性光学效应,分别对二阶非线性极化X(2)过程中的二倍频产生二次谐波;X(2)过程中的二倍频、和频、差频耦合产生三次谐波;三阶非线性极化X(3)过程中的三倍频产生三次谐波等做了详细的理论研究并给出了相应的光子晶体优化结构。对于一维非线性光子晶体结构,首先基于各类非线性问题抽象出非线性效应的数学模型,进而建立相应的光子晶体数值分析模型,利用固定点迭代方法、连续性方法等设计高效的有限元求解算法。其次,构建了非线性光子晶体光学效应优化的数学模型,利用高效数值算法设计了增强光子晶体非线性光学效应的材料结构。由于光子晶体具有光子禁带,利用带边相位匹配技术,可显著提高非线性效应的转换效率;同时利用光子晶体的缺陷模也可增强结构的非线性效应。我们利用该技术可设计产生较高非线性转换效率的光子晶体结构,进而设计了高效数值算法,并通过数值算例验证了设计新算法的正确性及收敛效果。本文还对光子晶体的另一广泛应用——光子晶体弯曲波导——进行了建模及其优化。对120°以及60°弯曲波导进行建模,并针对两种弯曲角度数值上分别设计了高透低损、宽频带的高效光子晶体弯曲波导。通过在硅基板上腐刻圆形空气孔来获得光子晶体波导,并对空气孔形状、大小、位置调整来优化波导效率,进而获得了在1550nm波长附近的宽频带、高透射低损耗的光子晶体波导结构。本文所有数值实验结果均验证了我们设计新算法的正确性,同时也表明新算法具有较快的收敛速度。这些都可为实验研究和应用设计提供参考、帮助、指导。
[Abstract]:Since the concept of photonic crystal has been proposed, has received wide attention from scholars at home and abroad. This is due to its unique periodic structure properties, it has a photonic band gap, the ability to manipulate the indirect light photons generated by the band gap and control the electromagnetic wave of spontaneous emission. This feature is that it has a strong practical the application prospect of nonlinear effect in optical materials has very wide applications. Therefore, the use of nonlinear photonic crystals to produce nonlinear effect is one of the important research direction. This article is in this background, considering the nonlinear medium, produce nonlinear optical properties of photonic crystal structure and enhanced and the optimum design of structures the research work in this dissertation. The Maxwell equation as the theoretical basis, mathematical model of material equations and nonlinear polarization to establish nonlinear optical effect by the further study Some problems of nonlinear optical effects in nonlinear photonic crystals. The nonlinear effect of photonic crystal based on finite element theory and method, the design of efficient algorithm based on fixed point iterations, solve the existing method of slow convergence or even divergence. This research work mainly involves two harmonic photonic crystal structure, structural finite element model of some physical problems three harmonic optical effect, the design of finite element discretization, error analysis of finite element theory, efficient algorithm design, algorithm implementation, results analysis, research and design of photonic crystal structure. This paper focuses on the research of nonlinear optical effect in photonic crystals, respectively for the two order nonlinear polarization X (2) in the process of the two generation two harmonic; X (2) in the process of the two frequency, sum frequency, difference frequency coupling three harmonic generation; three order nonlinear polarization X (3) three times in the process of three harmonic generation were given detailed research and theory to optimize the photonic crystal structure. The corresponding one-dimensional nonlinear photonic crystal structure, based on all kinds of nonlinear problems of abstract mathematical model of nonlinear effects, and then establish the corresponding numerical analysis model of photonic crystal, using fixed point iteration method of finite element algorithm for continuous method of designing efficient. Secondly, build a mathematical model of nonlinear photonic crystal optical effect optimization, using efficient numerical algorithm to design the reinforced material structure photonic crystal non linear optical effect. The photonic crystal with photonic band gap, the band edge phase matching technology, can significantly improve the conversion of nonlinear the effect of efficiency; while using the defect mode of photonic crystals can also enhance nonlinear effects of structure. We use this technology can produce design The higher conversion efficiency of nonlinear photonic crystal structure, and an effective numerical algorithm is presented, and the numerical results verify the correctness and convergence effect of the new algorithm design. The photonic crystal is another widely used photonic crystal waveguide of modeling and optimization. By modeling the 120 degrees and 60 degrees bend waveguide, and for the two bending angle of numerical separately designed high permeability and low loss, high efficiency photonic crystal waveguide broadband. To obtain the photonic crystal waveguide on a silicon substrate by etching circular air holes, and air holes in the shape, size, position adjustment to optimize the waveguide efficiency, and then obtained in broadband the wavelength of 1550nm with high transmission, low loss photonic crystal waveguide structure. In this paper, all the numerical experimental results verify the correctness of our design of the new algorithm, and also show that the new algorithm has The speed of convergence is faster. These can provide reference, help and guidance for experimental research and application design.

【学位授予单位】：北京邮电大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：O734

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