ZHI HAO JIANG, PHD, is Professor at the State Key Laboratory of Millimeter Waves and Associate Dean of the School of Information Science and Engineering, Southeast University. He is the co-editor of Electromagnetics of Body-Area Networks: Antennas, Propagation, and RF Systems. DOUGLAS H. WERNER, PhD, is Director of the Computational Electromagnetics and Antennas Research Lab, as well as a faculty member of the Materials Research Institute at Penn State. He is also Editor for the IEEE Press Series on Electromagnetic Wave Theory & Applications.

• About the Editors xvList of Contributors xviiPreface xxiPart I Fundamentals and Basics of Electromagnetic Vortices 11 Fundamentals of Orbital Angular Momentum Beams: Concepts, Antenna Analogies, and Applications 3Anastasios Papathanasopoulos and Yahya Rahmat-Samii1.1 Electromagnetic Fields Carry Orbital Angular Momentum 31.2 OAM Beams; Properties and Analogies with Conventional Beams 41.2.1 Laguerre–Gaussian Modes 51.3 Communicating Using OAM: Potentials and Challenges 101.3.1 OAM Communication Link Scenarios and Technical Barriers 111.3.2 OAM Emerging Applications and Perspectives 141.3.2.1 Free-space Communications 141.3.2.2 Optical Fiber Communications 171.4 OAM Generation Methods 201.5 Summary and Perspectives 22Appendix 1.A OAM Far-field Calculation 23References 262 OAM Radio – Physical Foundations and Applications of Electromagnetic Orbital Angular Momentum in Radio Science and Technology 33Bo Thidé and Fabrizio Tamburini2.1 Introduction 332.2 Physics 342.2.1 The Classical Electromagnetic Field 342.2.2 Electrodynamic Observables 362.2.2.1 Behavior at Very Long Distances 412.3 Implementation 452.3.1 Wireless Information Transfer with Linear Momentum 462.3.2 Wireless Information Transfer with Angular Momentum 482.3.2.1 Spin Angular Momentum vs. Orbital Angular Momentum 502.3.2.2 Angular Momentum Transducers 502.3.2.3 Electric Hertzian Dipoles 522.3.3 Astronomy Applications 58Appendix A 612.A.1 Theory 612.A.1.1 Classical Majorana-Oppenheimer Formalism and Its Affinity to First Quantization Formalism 612.A.1.1.1 Riemann–Silberstein Electromagnetic Potentials and Fields 63A.1.1.1 Purely Electric Sources 66A.1.1.2 Useful Approximations 67A.1.2.1 The Paraxial Approximation 68A.1.2.2 The Far-Zone Approximation 702.A.2 Poincaré Invariants and Conserved Quantities of the EM Field 74A.2.1 Energy 74A.2.2 Linear Momentum 76A.2.2.1 Gauge Invariance 78A.2.2.2 First Quantization Formalism 79A.2.3 Angular Momentum 80A.2.3.1 Gauge Invariance 82A.2.3.2 First Quantization Formalism 83References 84Part II Physical Wave Phenomena of Electromagnetic Vortices 973 Generation of Microwave Vortex Beams Using Metasurfaces 99Jia Yuan Yin and Tie Jun Cui3.1 Introduction 993.2 Metasurfaces for Vortex-beam Generation 1003.2.1 Reflective Metasurfaces for Vortex-beam Generation 1013.2.2 Transmission Metasurfaces for Vortex-beam Generation 1083.2.3 Planar Metasurfaces for Vortex-beam Generation 1103.2.4 Metasurfaces for Modified Vortex-beam Generation 1123.2.5 One-dimensional Metasurface for Vortex-beam Generation 1133.3 Conclusion 114Acknowledgments 114References 1154 Application of Transformation Optics and 3D Printing Technology in Vortex Wave Generation 121Jianjia Yi, Shah Nawaz Burokur, and Douglas H. Werner4.1 Introduction 1214.2 Theoretical Basis of Transformation Optics and 3D Printing 1214.2.1 The Concept and Development of Transformation Optics 1214.2.2 An Overview of 3D Printing Techniques 1254.3 Several Applications of Transformation Optics in Vortex Waves 1284.3.1 All-Dielectric Transformed Material for the Generation of OAM Beams 1284.3.2 All-dielectric Metamaterial Medium for Collimating OAM Vortex Waves 1374.3.3 A Transformation Optics-Based Lens for Horizontal Radiation of OAM Vortex Waves 1474.4 Conclusions 153References 1545 Millimeter-Wave Transmit-Arrays for High-Capacity and Wideband Generation of Scalar and Vector Vortex Beams 157Zhi Hao Jiang, Lei Kang, Wei Hong, and Douglas H. Werner5.1 Introduction 1575.2 Vector Vortex Beams and Hybrid-Order PSs 1595.3 Millimeter-Wave Transmit-Array Unit Cell Designs 1615.3.1 Ka-Band CP Unit Cell Design 1615.3.2 Q-Band CP Unit Cell Design 1655.3.3 K-Band Dual-CP Unit Cell Design 1665.4 Millimeter-Wave Transmit-Arrays for Vortex Beam Multiplexing 1715.4.1 Far-Field Pattern Calculation for Transmit-Arrays 1715.4.2 Multiplexing of Scalar Vortex Beams 1725.4.3 Multiplexing of Vector Vortex Beams with Symmetry Constraints 1765.4.4 Multiplexing of Vector Vortex Beams with Broken Symmetry 1825.5 Conclusion 183Acknowledgment 183References 1846 Twisting Light with Metamaterials 189Natalia M. Litchinitser6.1 Introduction 1896.2 OAM Beams on the Nanoscale 1946.3 Active OAM Sources 2016.4 OAM Light in Engineered Nonlinear Colloidal Systems 2066.5 Conclusion 214References 2147 Generation of Optical Vortex Beams 223Yuanjie Yang and Cheng-Wei Qiu7.1 Introduction 2237.2 Basic Theory of Optical Vortex 2247.3 Generation of Optical Vortex 2257.3.1 Generation of Vortex Beams using Optical Elements 2257.3.1.1 Spiral Phase Plate 2257.3.1.2 Fork-grating Hologram 2267.3.1.3 Spiral Zone Plate Holograms 2267.3.2 Generation of Vortex Beams Using Digital Devices 2277.3.3 Generation of Vortex Beams Based on Mode Conversion 2297.3.4 Generation of Vortex Beams Based on the Superposition of Waves 2307.3.5 Generation of Vortex Beams Based on Metasurfaces 2317.4 Generation of Novel Vortex Beams 2337.4.1 Perfect Vortex Beam 2337.4.2 Fractional Vortex Beams 2357.4.3 Anomalous Vortex Beam 2377.4.4 Vortex Beams with Varying OAM 2397.5 Conclusion 241References 2418 Orbital Angular Momentum Generation, Detection, and Angular Momentum Conservation with Second Harmonic Generation 245Menglin L. N. Chen, Xiaoyan Y. Z. Xiong, Wei E. I. Sha, and Li Jun Jiang8.1 Orbital Angular Momentum Generation and Detection 2458.1.1 OAM Generation 2468.1.1.1 Complementary Metasurfaces 2478.1.1.2 Quasi-Continuous Metasurfaces 2478.1.1.3 Photonic Crystals 2508.1.2 OAM Detection 2528.1.2.1 Modified Dynamic Mode Decomposition 2528.1.2.2 Holographic Metasurfaces 2548.2 AM Conservation: Nonlinear Optics 2568.2.1 BEM for Nonlinear Optics 2568.2.2 Verification of the Algorithm 2588.2.3 Mixing of Spin and OAM 2598.2.4 General Angular Momenta Conservation Law 2618.3 Conclusion 263References 264Part III Engineering Applications of Electromagnetic Vortices 2699 Orbital Angular Momentum Based Structured Radio Beams and its Applications 271Xianmin Zhang, Shilie Zheng, Wei E. I. Sha, Li Jun Jiang, Xiaowen Xiong, Zelin Zhu, Zhixia Wang, Yuqi Chen, Jiayu Zheng, Xinyue Wang, and Menglin L. N. Chen9.1 Introduction 2719.2 PS–OAM Based Structured Beams 2729.2.1 Plane Spiral OAM 2729.2.2 Structured Radio Beam 2739.3 Antennas for Structured Beams 2769.3.1 Antennas for PS–OAM Waves 2769.3.2 SIW-based Compact Antenna 2799.3.3 Partial Arc Transmitting Scheme 2849.4 Potential Applications 2869.4.1 Radar Detection 2869.4.2 MIMO System 2879.4.3 Spatial Field Digital Modulation 2899.5 Conclusion 291References 29110 OAM Multiplexing Using Uniform Circular Array and Microwave Circuit for Short-range Communication 295Kentaro Murata and Naoki Honma10.1 Introduction 29510.2 OAM Multiplexing System and its Mechanism 29710.2.1 Coaxial UCA Configuration 29710.2.2 Circulant Channel Matrix 29810.2.3 DFT/IDFT Beamformers 29910.3 OAM Multiplexing for Short-range Communications 30010.3.1 Achievable Rate 30010.3.2 Array Topology 30110.3.3 Optimal Array Radius 30410.3.4 Butler Matrix 30910.3.5 Performance Evaluation 31210.4 Conclusion and Key Challenges 317References 31811 OAM Communications in Multipath Environments 321Xiaoming Chen and Wei Xue11.1 Introduction 32111.1.1 Fading in Wireless Propagation 32111.1.1.1 Pass Loss 32211.1.1.2 Large-Scale Fading 32211.1.1.3 Small-Scale Fading 32211.1.2 Diversity and Multiplexing 32311.1.3 MIMO Systems 32411.2 OAM Communication in Line-of-sight Environment 32511.2.1 Conventional OAM Multiplexing 32511.2.2 OAM Multiplexing with Spatial Equalization 32911.3 OAM Multiplexing in Multipath Environment 33711.3.1 Specular Reflection 33711.3.1.1 Intra-channel Interference 33811.3.1.2 Inter-channel Interference 34111.3.2 Indoor Environment 34311.3.2.1 Inter-Symbol Interference (ISI) 34311.3.2.2 Antenna misalignment 34611.3.3 Highly Reverberant Environments 34911.4 Conclusion 354References 35412 High-capacity Free-space Optical Communications Using Multiplexing of Multiple OAM Beams 357Alan E. Willner, Runzhou Zhang, Kai Pang, Haoqian Song, Cong Liu, Hao Song, Xinzhou Su, Huibin Zhou, Nanzhe Hu, Zhe Zhao, Guodong Xie, Yongxiong Ren, Hao Huang, and Moshe Tur12.1 Introduction 35712.2 Challenges for an OAM Multiplexing Free-space Optical Communication System 35912.2.1 Beam divergence 36012.2.2 Misalignment 36112.2.3 Atmospheric Turbulence Effects 36212.2.4 Obstruction 36412.2.5 Summary 36412.3 Free-space Optical OAM Links 36412.3.1 High-capacity OAM Multiplexed Communication Link Under Laboratory Conditions 36512.3.2 OAM-based FSO Link Beyond Laboratory Distances 36812.3.3 Summary 37112.4 Inter-channel Crosstalk Mitigation Methods in OAM-multiplexed FSO Communications 37112.4.1 Adaptive Optics for Crosstalk Mitigation 37112.4.1.1 AO Using a Wavefront Sensor (WFS) and a Gaussian Probe Beam 37212.4.1.2 AO Using WFS and Gaussian Probe Beam in a Quantum Communication Link 37412.4.1.3 AO Using a Camera for Beam Intensity Measurement 37612.4.2 Spatial Modes Manipulation for Crosstalk Mitigation 37812.4.2.1 Turbulence Precompensation by OAM Mode Combination 37812.4.2.2 Simultaneous Orthogonalizing and Shaping of Multiple LG Beams 38012.4.3 Digital Signal Processing for Crosstalk Mitigation 38112.4.3.1 MIMO Equalization for Crosstalk Mitigation in Laboratory 38212.4.3.2 Turbulence-Resilient Beam Mixing for Crosstalk Mitigation 38312.4.4 Summary 38412.5 OAM Multiplexing for Unmanned Aerial Vehicle (UAV) Platforms 38512.5.1 OAM System Design and Demonstrations for UAV Platforms 38612.5.2 Multiple-Input-Multiple-Output (MIMO) Mitigation for Atmospheric Turbulence in UAV Platforms 38912.5.3 Summary 39012.6 OAM Multiplexing in Underwater Environments 39112.6.1 Underwater Effects for OAM Beam Propagation 39212.6.2 OAM Multiplexing Demonstrations in Underwater Environments 39212.6.3 Multiple-Input-Multiple-Output (MIMO) Mitigation for Inter-Channel Crosstalk in Underwater Environments 39412.6.4 Summary 39412.7 Summary of this Chapter 394Acknowledgment 396References 396Part IV Multidisciplinary Explorations of Electromagnetic Vortices 40113 Theory of Vector Beams for Chirality and Magnetism Detection of Subwavelength Particles 403Mina Hanifeh and Filippo Capolino13.1 Characterization of Azimuthally and Radially Polarized Beams 40313.2 Circular Dichroism for a Particle of Subwavelength Size 40713.2.1 Helicity of an Azimuthally Radially Polarized Vector Beam 40913.3 Photoinduced Force Microscopy at Nanoscale 41113.3.1 Magnetic Photoinduced Force Microscopy by Using an APB 41213.3.2 Chirality Photoinduced Force Microscopy 41513.4 Conclusion 418References 41814 Quantum Applications of Structured Photons 423Alessio D’Errico and Ebrahim Karimi14.1 Introduction 42314.2 Photonic Degrees of Freedom 42414.3 Single Photon Source: SPDC 42614.4 Generation and Detection of Structured Photon Quantum States 43014.4.1 Generation of Structured Photon States 43014.4.2 Detection of Structured Photons 43314.5 Quantum Key Distribution 43414.5.1 BB84 Protocol 43614.5.2 Alignment-free QKD 43714.5.3 High-dimensional QKD 43814.6 Quantum Simulation with Quantum Walks 44214.6.1 Quantum Walks in the OAM Space 44314.6.2 Shaping the Walker Space: Cyclic Walks and Walks on 2D Lattices 44414.6.3 Applications: Wavepacket Dynamics and Detection of Topological Phases 44614.7 Outlook 450References 450Index 457