书籍详情
将光打结：将拓扑学应用于光学（英文版）
作者：（美）大卫·S.西蒙
出版社：哈尔滨工业大学出版社
出版时间：2021-07-01
ISBN：9787560394640
定价：¥68.00
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内容简介
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。
作者简介
大卫·S.西蒙（David S.Simon）教授。他在俄亥俄州立大学获得数学和物理学学士学位，接着又获得理论物理学博士学位（约翰·霍普金斯大学）和工程学博士学位（波士顿大学）。他最初学习数学物理和量子场论，现在主要从事量子光学和相关领域的工作。在劳德代尔堡的诺瓦东南大学任教十多年后，他目前是石山学院物理与天文学系的物理学教授，也是波士顿大学的访问研究员。
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
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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