Discover the most recent advances in electromagnetic vortices In Electromagnetic Vortices: Wave Phenomena and Engineering Applications, a team of distinguished researchers delivers a cutting-edge treatment of electromagnetic vortex waves, including their theoretical foundation, related wave properties, and several potentially transformative applications. The book is divided into three parts. The editors first include resources that describe the generation, sorting, and manipulation of vortex waves, as well as descriptions of interesting wave behavior in the infrared and optical regimes with custom-designed nanostructures. They then discuss the generation, multiplexing, and propagation of vortex waves at the microwave and millimeter-wave frequencies. Finally, the selected contributions discuss several representative practical applications of vortex waves from a system perspective. With coverage that incorporates demonstration examples from a wide range of related sub-areas, this essential edited volume also offers: Thorough introductions to the generation of optical vortex beams and transformation optical vortex wave synthesizers Comprehensive explorations of millimeter-wave metasurfaces for high-capacity and broadband generation of vector vortex beams, as well as orbital angular momentum (OAM) detection and its observation in second harmonic generations Practical discussions of microwave SPP circuits and coding metasurfaces for vortex beam generation and OAM-based structured radio beams and their applications In-depth examinations and explorations of OAM multiplexing for wireless communications, wireless power transmission, as well as quantum communications and simulations Perfect for students of wireless communications, antenna/RF design, optical communications, and nanophotonics, Electromagnetic Vortices: Wave Phenomena and Engineering Applications is also an indispensable resource for researchers in academia, at large defense contractors, and in government labs.

Table of Contents:
About the Editors xv List of Contributors xvii Preface xxi Part I Fundamentals and Basics of Electromagnetic Vortices 1 1 Fundamentals of Orbital Angular Momentum Beams: Concepts, Antenna Analogies, and Applications 3 Anastasios Papathanasopoulos and Yahya Rahmat-Samii 1.1 Electromagnetic Fields Carry Orbital Angular Momentum 3 1.2 OAM Beams; Properties and Analogies with Conventional Beams 4 1.2.1 Laguerre–Gaussian Modes 5 1.3 Communicating Using OAM: Potentials and Challenges 10 1.3.1 OAM Communication Link Scenarios and Technical Barriers 11 1.3.2 OAM Emerging Applications and Perspectives 14 1.3.2.1 Free-space Communications 14 1.3.2.2 Optical Fiber Communications 17 1.4 OAM Generation Methods 20 1.5 Summary and Perspectives 22 Appendix 1.A OAM Far-field Calculation 23 References 26 2 OAM Radio – Physical Foundations and Applications of Electromagnetic Orbital Angular Momentum in Radio Science and Technology 33 Bo Thidé and Fabrizio Tamburini 2.1 Introduction 33 2.2 Physics 34 2.2.1 The Classical Electromagnetic Field 34 2.2.2 Electrodynamic Observables 36 2.2.2.1 Behavior at Very Long Distances 41 2.3 Implementation 45 2.3.1 Wireless Information Transfer with Linear Momentum 46 2.3.2 Wireless Information Transfer with Angular Momentum 48 2.3.2.1 Spin Angular Momentum vs. Orbital Angular Momentum 50 2.3.2.2 Angular Momentum Transducers 50 2.3.2.3 Electric Hertzian Dipoles 52 2.3.3 Astronomy Applications 58 Appendix A 61 2.A.1 Theory 61 2.A.1.1 Classical Majorana-Oppenheimer Formalism and Its Affinity to First Quantization Formalism 61 2.A.1.1.1 Riemann–Silberstein Electromagnetic Potentials and Fields 63 A.1.1.1 Purely Electric Sources 66 A.1.1.2 Useful Approximations 67 A.1.2.1 The Paraxial Approximation 68 A.1.2.2 The Far-Zone Approximation 70 2.A.2 Poincaré Invariants and Conserved Quantities of the EM Field 74 A.2.1 Energy 74 A.2.2 Linear Momentum 76 A.2.2.1 Gauge Invariance 78 A.2.2.2 First Quantization Formalism 79 A.2.3 Angular Momentum 80 A.2.3.1 Gauge Invariance 82 A.2.3.2 First Quantization Formalism 83 References 84 Part II Physical Wave Phenomena of Electromagnetic Vortices 97 3 Generation of Microwave Vortex Beams Using Metasurfaces 99 Jia Yuan Yin and Tie Jun Cui 3.1 Introduction 99 3.2 Metasurfaces for Vortex-beam Generation 100 3.2.1 Reflective Metasurfaces for Vortex-beam Generation 101 3.2.2 Transmission Metasurfaces for Vortex-beam Generation 108 3.2.3 Planar Metasurfaces for Vortex-beam Generation 110 3.2.4 Metasurfaces for Modified Vortex-beam Generation 112 3.2.5 One-dimensional Metasurface for Vortex-beam Generation 113 3.3 Conclusion 114 Acknowledgments 114 References 115 4 Application of Transformation Optics and 3D Printing Technology in Vortex Wave Generation 121 Jianjia Yi, Shah Nawaz Burokur, and Douglas H. Werner 4.1 Introduction 121 4.2 Theoretical Basis of Transformation Optics and 3D Printing 121 4.2.1 The Concept and Development of Transformation Optics 121 4.2.2 An Overview of 3D Printing Techniques 125 4.3 Several Applications of Transformation Optics in Vortex Waves 128 4.3.1 All-Dielectric Transformed Material for the Generation of OAM Beams 128 4.3.2 All-dielectric Metamaterial Medium for Collimating OAM Vortex Waves 137 4.3.3 A Transformation Optics-Based Lens for Horizontal Radiation of OAM Vortex Waves 147 4.4 Conclusions 153 References 154 5 Millimeter-Wave Transmit-Arrays for High-Capacity and Wideband Generation of Scalar and Vector Vortex Beams 157 Zhi Hao Jiang, Lei Kang, Wei Hong, and Douglas H. Werner 5.1 Introduction 157 5.2 Vector Vortex Beams and Hybrid-Order PSs 159 5.3 Millimeter-Wave Transmit-Array Unit Cell Designs 161 5.3.1 Ka-Band CP Unit Cell Design 161 5.3.2 Q-Band CP Unit Cell Design 165 5.3.3 K-Band Dual-CP Unit Cell Design 166 5.4 Millimeter-Wave Transmit-Arrays for Vortex Beam Multiplexing 171 5.4.1 Far-Field Pattern Calculation for Transmit-Arrays 171 5.4.2 Multiplexing of Scalar Vortex Beams 172 5.4.3 Multiplexing of Vector Vortex Beams with Symmetry Constraints 176 5.4.4 Multiplexing of Vector Vortex Beams with Broken Symmetry 182 5.5 Conclusion 183 Acknowledgment 183 References 184 6 Twisting Light with Metamaterials 189 Natalia M. Litchinitser 6.1 Introduction 189 6.2 OAM Beams on the Nanoscale 194 6.3 Active OAM Sources 201 6.4 OAM Light in Engineered Nonlinear Colloidal Systems 206 6.5 Conclusion 214 References 214 7 Generation of Optical Vortex Beams 223 Yuanjie Yang and Cheng-Wei Qiu 7.1 Introduction 223 7.2 Basic Theory of Optical Vortex 224 7.3 Generation of Optical Vortex 225 7.3.1 Generation of Vortex Beams using Optical Elements 225 7.3.1.1 Spiral Phase Plate 225 7.3.1.2 Fork-grating Hologram 226 7.3.1.3 Spiral Zone Plate Holograms 226 7.3.2 Generation of Vortex Beams Using Digital Devices 227 7.3.3 Generation of Vortex Beams Based on Mode Conversion 229 7.3.4 Generation of Vortex Beams Based on the Superposition of Waves 230 7.3.5 Generation of Vortex Beams Based on Metasurfaces 231 7.4 Generation of Novel Vortex Beams 233 7.4.1 Perfect Vortex Beam 233 7.4.2 Fractional Vortex Beams 235 7.4.3 Anomalous Vortex Beam 237 7.4.4 Vortex Beams with Varying OAM 239 7.5 Conclusion 241 References 241 8 Orbital Angular Momentum Generation, Detection, and Angular Momentum Conservation with Second Harmonic Generation 245 Menglin L. N. Chen, Xiaoyan Y. Z. Xiong, Wei E. I. Sha, and Li Jun Jiang 8.1 Orbital Angular Momentum Generation and Detection 245 8.1.1 OAM Generation 246 8.1.1.1 Complementary Metasurfaces 247 8.1.1.2 Quasi-Continuous Metasurfaces 247 8.1.1.3 Photonic Crystals 250 8.1.2 OAM Detection 252 8.1.2.1 Modified Dynamic Mode Decomposition 252 8.1.2.2 Holographic Metasurfaces 254 8.2 AM Conservation: Nonlinear Optics 256 8.2.1 BEM for Nonlinear Optics 256 8.2.2 Verification of the Algorithm 258 8.2.3 Mixing of Spin and OAM 259 8.2.4 General Angular Momenta Conservation Law 261 8.3 Conclusion 263 References 264 Part III Engineering Applications of Electromagnetic Vortices 269 9 Orbital Angular Momentum Based Structured Radio Beams and its Applications 271 Xianmin 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. Chen 9.1 Introduction 271 9.2 PS–OAM Based Structured Beams 272 9.2.1 Plane Spiral OAM 272 9.2.2 Structured Radio Beam 273 9.3 Antennas for Structured Beams 276 9.3.1 Antennas for PS–OAM Waves 276 9.3.2 SIW-based Compact Antenna 279 9.3.3 Partial Arc Transmitting Scheme 284 9.4 Potential Applications 286 9.4.1 Radar Detection 286 9.4.2 MIMO System 287 9.4.3 Spatial Field Digital Modulation 289 9.5 Conclusion 291 References 291 10 OAM Multiplexing Using Uniform Circular Array and Microwave Circuit for Short-range Communication 295 Kentaro Murata and Naoki Honma 10.1 Introduction 295 10.2 OAM Multiplexing System and its Mechanism 297 10.2.1 Coaxial UCA Configuration 297 10.2.2 Circulant Channel Matrix 298 10.2.3 DFT/IDFT Beamformers 299 10.3 OAM Multiplexing for Short-range Communications 300 10.3.1 Achievable Rate 300 10.3.2 Array Topology 301 10.3.3 Optimal Array Radius 304 10.3.4 Butler Matrix 309 10.3.5 Performance Evaluation 312 10.4 Conclusion and Key Challenges 317 References 318 11 OAM Communications in Multipath Environments 321 Xiaoming Chen and Wei Xue 11.1 Introduction 321 11.1.1 Fading in Wireless Propagation 321 11.1.1.1 Pass Loss 322 11.1.1.2 Large-Scale Fading 322 11.1.1.3 Small-Scale Fading 322 11.1.2 Diversity and Multiplexing 323 11.1.3 MIMO Systems 324 11.2 OAM Communication in Line-of-sight Environment 325 11.2.1 Conventional OAM Multiplexing 325 11.2.2 OAM Multiplexing with Spatial Equalization 329 11.3 OAM Multiplexing in Multipath Environment 337 11.3.1 Specular Reflection 337 11.3.1.1 Intra-channel Interference 338 11.3.1.2 Inter-channel Interference 341 11.3.2 Indoor Environment 343 11.3.2.1 Inter-Symbol Interference (ISI) 343 11.3.2.2 Antenna misalignment 346 11.3.3 Highly Reverberant Environments 349 11.4 Conclusion 354 References 354 12 High-capacity Free-space Optical Communications Using Multiplexing of Multiple OAM Beams 357 Alan 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 Tur 12.1 Introduction 357 12.2 Challenges for an OAM Multiplexing Free-space Optical Communication System 359 12.2.1 Beam divergence 360 12.2.2 Misalignment 361 12.2.3 Atmospheric Turbulence Effects 362 12.2.4 Obstruction 364 12.2.5 Summary 364 12.3 Free-space Optical OAM Links 364 12.3.1 High-capacity OAM Multiplexed Communication Link Under Laboratory Conditions 365 12.3.2 OAM-based FSO Link Beyond Laboratory Distances 368 12.3.3 Summary 371 12.4 Inter-channel Crosstalk Mitigation Methods in OAM-multiplexed FSO Communications 371 12.4.1 Adaptive Optics for Crosstalk Mitigation 371 12.4.1.1 AO Using a Wavefront Sensor (WFS) and a Gaussian Probe Beam 372 12.4.1.2 AO Using WFS and Gaussian Probe Beam in a Quantum Communication Link 374 12.4.1.3 AO Using a Camera for Beam Intensity Measurement 376 12.4.2 Spatial Modes Manipulation for Crosstalk Mitigation 378 12.4.2.1 Turbulence Precompensation by OAM Mode Combination 378 12.4.2.2 Simultaneous Orthogonalizing and Shaping of Multiple LG Beams 380 12.4.3 Digital Signal Processing for Crosstalk Mitigation 381 12.4.3.1 MIMO Equalization for Crosstalk Mitigation in Laboratory 382 12.4.3.2 Turbulence-Resilient Beam Mixing for Crosstalk Mitigation 383 12.4.4 Summary 384 12.5 OAM Multiplexing for Unmanned Aerial Vehicle (UAV) Platforms 385 12.5.1 OAM System Design and Demonstrations for UAV Platforms 386 12.5.2 Multiple-Input-Multiple-Output (MIMO) Mitigation for Atmospheric Turbulence in UAV Platforms 389 12.5.3 Summary 390 12.6 OAM Multiplexing in Underwater Environments 391 12.6.1 Underwater Effects for OAM Beam Propagation 392 12.6.2 OAM Multiplexing Demonstrations in Underwater Environments 392 12.6.3 Multiple-Input-Multiple-Output (MIMO) Mitigation for Inter-Channel Crosstalk in Underwater Environments 394 12.6.4 Summary 394 12.7 Summary of this Chapter 394 Acknowledgment 396 References 396 Part IV Multidisciplinary Explorations of Electromagnetic Vortices 401 13 Theory of Vector Beams for Chirality and Magnetism Detection of Subwavelength Particles 403 Mina Hanifeh and Filippo Capolino 13.1 Characterization of Azimuthally and Radially Polarized Beams 403 13.2 Circular Dichroism for a Particle of Subwavelength Size 407 13.2.1 Helicity of an Azimuthally Radially Polarized Vector Beam 409 13.3 Photoinduced Force Microscopy at Nanoscale 411 13.3.1 Magnetic Photoinduced Force Microscopy by Using an APB 412 13.3.2 Chirality Photoinduced Force Microscopy 415 13.4 Conclusion 418 References 418 14 Quantum Applications of Structured Photons 423 Alessio D’Errico and Ebrahim Karimi 14.1 Introduction 423 14.2 Photonic Degrees of Freedom 424 14.3 Single Photon Source: SPDC 426 14.4 Generation and Detection of Structured Photon Quantum States 430 14.4.1 Generation of Structured Photon States 430 14.4.2 Detection of Structured Photons 433 14.5 Quantum Key Distribution 434 14.5.1 BB84 Protocol 436 14.5.2 Alignment-free QKD 437 14.5.3 High-dimensional QKD 438 14.6 Quantum Simulation with Quantum Walks 442 14.6.1 Quantum Walks in the OAM Space 443 14.6.2 Shaping the Walker Space: Cyclic Walks and Walks on 2D Lattices 444 14.6.3 Applications: Wavepacket Dynamics and Detection of Topological Phases 446 14.7 Outlook 450 References 450 Index 457