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书名 | 将光打结——将拓扑学应用于光学 |
分类 | 教育考试-外语学习-英语 |
作者 | (美)大卫·S.西蒙 |
出版社 | 哈尔滨工业大学出版社 |
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简介 | 内容推荐 本书主要介绍了将拓扑学应用于光学的问题,旨在以简明的形式提供必要的数学背景,以理解拓扑的发展过程,并给出在光学应用中出现的一些拓扑问题的调查结果。全书共分九章,包括介绍、量子动力学、原子势、激光脉冲、原子算符的矩阵元素、密度矩阵元素方程、向量态、拓扑和物理历史概述、电磁学和光学、特征空间、纤维束、曲率和完整、拓扑不变量、漩涡、奇异的光束、光孤子、几何和拓扑相、物质和光的拓扑状态等内容。在叙述方面,本书力求易于数学、物理和相关领域的高年级本科生及相关专业教师阅读。 目录 Preface Acknowledgements Author biography 1 Topology and physics: a historical overview 1.1 Introduction: searching for holes in fields of light 1.2 Topology and physics 1.2.1 Dirac monopoles 1.2.2 Aharonov-Bohm effect 1.2.3 Topology in optics References 2 Electromagnetism and optics 2.1 Electromagnetic fields 2.2 Electromagnetic potentials and gauge invariance 2.3 Linear and nonlinear optical materials 2.4 Polarization and the Poincaré sphere References 3 Characterizing spaces 3.1 Loops, holes, and winding numbers 3.2 Homotopy classes References 4 Fiber bundles, curvature, and holonomy 4.1 Manifolds 4.2 Vectors and forms 4.3 Curvature 4.3.1 One dimension: curves 4.3.2 Two dimensions and beyond 4.4 Connections and covariant derivatives 4.5 Fiber bundles 4.6 Connection and curvature in electromagnetism and optics References 5 Topological invariants 5.1 Euler characteristic 5.2 Winding number 5.3 Index 5.4 Chern numbers 5.5 Linking number and other invariants References 6 Vortices and corkscrews: singular optics 6.1 Optical singularities 6.2 Optical angular momentum 6.3 Vortices and dislocations 6.4 6.5 Polarization singularities 6.6 Optical M?bius strips References 7 Optical solitons 7.1 Solitary waves 7.2 Solitons in optics References 8 Geometric and topological phases 8.1 The Pancharatnam phase 8.2 Berry phase in quantum mechanics 8.3 Geometric phase in optical fibers 8.4 Holonomy interpretation References 9 Topological states of matter and light 9.1 The quantum hall effect 9.2 Topological phases and localized boundary states 9.3 Topological photonics References Appendices 编辑手记 |
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