光子晶体光学

表7． 光学与电子信息 学院（系、所） 研究生课程简介 课程名称：光子晶体光学 英文名称：Optics of Photonic Crystals 课程类型：讲授课程 □实践（实验、实习）课程 □研讨课程 □专题讲座 □其它 考核方式： 开卷考查 教学方式：双语教学 适用专业：理工文医各专业 开课学期：第二学期 适用层次： 硕士 博士 总学时/讲授学时： 32 / 32 学分：2 先修课程要求：几何光学，物理光学 课程组教师姓名 竺子民 职 称 教授 专 业 光学 年 龄 57 学术专长 光学 课程教学目标： 掌握光子晶体的结构特点、描述方法，光波在折射率周期性变化的介质中的传播规律，分析方法和计算方法。重点掌握布洛赫定理，矩阵法、平面波展开法和时域差分法在带结构计算、本征态密度计算中的应用，掌握带结构的显示技术，计算结果与实验结果的对比分析方法。在理论学习的同时，还进行Matlab编程实践，要求掌握光子晶体数值模拟的基本方法。 教学大纲（章节目录）： 第一章 Introduction to Photonic Crystals §1.1 Introduction: What are Photonic Crystals? §1.2 Photonic Crystal Lattice §1.3 Basic Terminology §1.4 Historical Notes §1.5 Problems and Questions 第二章 Fundamentals of Wave Optics §2.1 What is an Optical Medium? – Theoretical Models 2.1.1 Wave Optics 2.1.2 Geometric Optics §2.2 Wave Propagation: Maxwell’s Equations §2.3 Wave Equation in Vacuum §2.4 Waves in Dielectric Media 2.4.1 Refractive Index of Dielectric Medium 2.4.2 Lossy Dielectric Medium §2.5 Group Velocity §2.6 Summary §2.7 Problems and Questions 第三章 Fundamentals of Computation of Photonic Crystal Characteristics §3.1 Computation of the Field Distribution in One-Dimensional (1D) Photonic Crystal §3.2 Applications of the Field Distribution Computation §3.3 Summary §3.4 MATLAB Program Reflectance Spectrum Computation of 1D PhC §3.5 Problems and Questions 第四章 Band Structure Computation of 1D Photonic Crystals §4.1 Problem Definition §4.2 Unit Cell §4.3 Lattice Vectors §4.4 Reciprocal Lattice §4.5 Reciprocal Lattice Vectors and Brillouin Zone §4.6 Band Structure Computation §4.7 Eigen-Values and Eigen-Vectors of a Matrix §4.8 Computation Results §4.9 Fourier Expansion of the Dielectric Function §4.10 The Eigen-Value Problem for Electric Field §4.11 Algorithm of PWE Method §4.12 Off-Axis Band Structure of 1D PhC §4.13 Summary §4.14 MATLAB Program for 1D PhC Band Structure Computation by Means of PWE Method §4.15 Problems and Questions 第五章 Band Structure Computation of 2D and 3D Photonic Crystals §5.1 Problem Definition for 3D Photonic Crystal §5.2 Problem Definition for 2D Photonic Crystal §5.3 Fourier Expansion of the Dielectric Function 5.3.1 Dielectric Spheres 5.3.2 Dielectric Rods 5.3.3 Fourier Expansion Coefficient of an Arbitrary Dielectric Function 5.3.4 Validation of the Fourier Expansion §5.4 Wave Vectors Set §5.5 Reciprocal Lattice Vectors Set §5.6 Results of the Band Structure Computation §5.7 Analysis of the Band Structure §5.8 Photonic Band Gap Maps §5.9 Photonic Density of States §5.10 Off-Plane Band Structure for 2D Photonic Crystal §5.11 Band Structure Computation of the PhC with Defect §5.12 Experimental Verification of the PWE Method

§5.13 Advantages and Disadvantages of the Plane Wave Expansion Method §5.14 Summary §5.15 MATLAB Program for Band Structure Computation of 2D PhC by Means of PWE Method §5.16 Problems and Questions 第六章 Finite-Difference Time-Domain Method for PhC Devices Modeling §6.1 Problem Formulation for the Field Distribution Computation: Finite-Difference Time-Domain Method §6.2 Maxwell’s Equations Discretization §6.3 Definition of the Dielectric Function §6.4 Definition of Initial and Boundary Conditions §6.4.1 Initial Conditions §6.4.2 Conditions at the Boundaries of Computation Region §6.5 FDTD Method Stability §6.6 FDTD Method Application for Experimentaly Obtained PhC with Hexagonal Lattice Structure §6.7 Summary §6.8 Problem Solution Example §6.9 MATLAB Program for Computation of Field Distribution in Nonuniform Optical Medium §6.10 Problems and Questions 第七章 Photonic Crystal Optical Fibers §7.1 Photonic Crystal Fibers: New Class of Optical Waveguides §7.2 Modes in Conventional Optical Fibers §7.3 Solution of Helmholtz Equation in Axial-Symmetric System §7.4 Hybrid Modes in Fibers and Mode Parameters 7.4.1 Fundamental Mode Distribution in Weakly Guiding Fibers 7.4.2 Effective Mode Index and Cutoff Conditions 7.4.3 bV Diagram §7.5 Single-Mode Fibers 7.5.1 Single-Mode Condition §7.6 Microstructured Fibers 7.6.1 Computation of Eigen-States of Microstructured Fibers 7.6.2 Computation of the Mode Field Distribution in Microstructured Fibers §7.7 Index-Guided Microstructured Fibers §7.8 Photonic Band Gap Fibers §7.9 Band Gap Diagram of the PBG Fiber 7.9.1 Coupling Losses of the PhC Fiber §7.10 Summary §7.11 MATLAB Program for Computation of the Fundamental Mode Distribution in Microstructured Fiber by Means of Plane Wave Expansion Method §7.12 Problems and Questions 第八章 FDTD Method for Band Structure Computation

§8.1 Problem Definition §8.2 Computation Region Definition §8.3 Boundary Conditions Definition §8.4 Initial Conditions §8.5 Structure Response Analysis §8.6 Summary §8.7 MATLAB Program for Band Structure Computation of 1D PhC by Means of FDTD Method §8.8 Problems and Questions 第九章 Photonic Crystal Waveguides §9.1 Conventional Planar Waveguides §9.2 Weakly Guiding Slabs §9.3 Kinds of PhC Waveguides §9.4 PWE Method for PhC Waveguides §9.5 Analysis of the Dispersion Diagram §9.6 FDTD Modeling of the PhC Waveguides §9.7 Summary §9.8 MATLAB Program for Computation of Dispersion Diagrams of 2D PhC Waveguide §9.9 Problems and Questions 第十章 Application for Design and Simulation of Optical WDM Demultiplexer §10.1 Problem Formulation §10.2 Band Structure Analysis §10.3 Temporal Response of DEMUX §10.4 Summary §10.5 MATLAB Program for the Computation of the PBG Map of PhC by Means of PWE Method §10.6 Problems and Questions 教材： Igor A. Sukhoivanov and Igo r V. Guryev, Photonic Crystals: Physics and Practical Modeling, Springer-Verlag,2009 主要参考书： 1. Kazuaki Sakoda, Optical Properties of Photonic Crystals, 2nd Edition, Springer ,2005 2. John D. Joannopoulos, Steven G. Johnson, Joshua N. Winn, and Robert D. Meade, Photonic Crystals_Molding the flow of light, 2nd edition, Princeton University Press, 2008 注：每门课程都须填写此表。本表不够可加页