Nonlinear, Tunable and Active Metamaterials (eBook)

Ilya V. Shadrivov received his B.Sc. and M.Sc. in Radiophysics from the Nizhny Novgorod University, Nizhny Novgorod, Russia. He received the Ph.D. degree in Physics from the Australian National University, Canberra, Australia, in 2005. He is currently a Queen Elizabeth Fellow at the Nonlinear Physics Centre in the Research School of Physical Sciences and a Panel Member of the Optical Society of America ‘Spotlight in Optics.Mikhail Lapine received a Diploma (M.Sc., with honours) in biophysics from Moscow State University in 1997, and a PhD (summa cum laude) in physics from Osnabrück University in 2004. Upon working for a few years in biophysics and biochemistry at Moscow State University, Russia (1996-1999) and Osnabrück University, Germany (1999-2001), he turned to theoretical electrodynamics with a specific interest to effective medium treatment of metamaterials as well as development of nonlinear, tunable and reconfigurable metamaterials and worked on these topics at Osnabrück University (2001-2004; 2008), Helsinki University of Technology (2005-2007) and the University of Seville (2008-2010). He was also a visiting researcher at the Australian National University (2009; 2010-2011) and St.Petersburg National Research University ITMO (2011) and joined the University of Sydney in 2012. In 2007, Dr. Mikhail Lapine initiated an international journal Metamaterials (Elsevier) and since then acts as the Editor for this journal. He also serves as a reviewer for a number of journals in physics.Yuri S. Kivshar received his Ph.D. degree in 1984 from the USSR Academy of Science and was at the Institute for Low Temperature Physics and Engineering, Kharkov, Ukraine. From 1988 to 1993, he worked at different research centres in USA, France, Spain and Germany. In 1993, he accepted an appointment at the Research School of Physical Sciences and Engineering of the Australian National University where presently he is Professor and Head of the Nonlinear Physics Center. Professor Yuri Kivshar was a recipient of Medal and Award of the Ukrainian Academy of Science, 1989, International Pnevmatikos Prize in Nonlinear Physics, 1995, Pawsey Medal and Lylde Medal, 2007, of the Australian Academy of Science, 1998 and Boas Medal of the Australian Institute of Physics, 2005. He is Fellow of Optical Society of America, American Physical Society and elected Fellow of the Australian Academy of Sciences. In 1999–2004, he served as an Associate Editor of the Physical Review E (second non-American in the APS history). Yuri Kivshar published more than 800 research papers and his interests include nonlinear guided waves, solitons, nonlinear atom optics, photonic crystals and nonlinear waves.

Foreword 6
Preface 8
Contents 11
Contributors 18
1 A Constitutive Description of Nonlinear Metamaterials Through Electric, Magnetic, and Magnetoelectric Nonlinearities 22
1.1 Introduction 22
1.2 Effective Nonlinear Susceptibilities: Coupled Mode Theory 24
1.3 Effective Nonlinear Susceptibilities: Transfer Matrix Method 27
1.4 Symmetries and Spatial Dispersion 31
1.5 Application to Varactor-Loaded Split-Ring Resonators 35
1.5.1 Linear Properties 36
1.5.2 Nonlinear Properties 36
1.6 Conclusion 39
References 39
2 Active and Applied Functional RF Metamaterials 41
2.1 Introduction 41
2.2 Powered Active RF Metamaterials 43
2.2.1 Zero Loss Active Metamaterials 44
2.2.2 Nonreciprocal Active Metamaterials 46
2.3 Applied Functional Metamaterials 46
2.3.1 Individually Addressable and Nonvolatile Tunable Metamaterials 48
2.3.2 A Metamaterial Limiter 50
2.4 Summary 52
References 53
3 Parametric Amplification of Magneto-Inductive Waves 54
3.1 Introduction 54
3.2 Magneto-Inductive Waves and Ring Resonators 57
3.3 Parametric Amplification 60
3.4 Amplification of Magneto-Inductive Waves 63
3.5 Experimental Verification 66
3.6 Conclusions 74
References 75
4 Coupled Electromagnetic and Elastic Dynamics in Metamaterials 78
4.1 Introduction 78
4.2 Magneto-Elastic Metamaterials 80
4.2.1 Theory 82
4.2.2 Experimental Demonstration 84
4.3 Torsional System 85
4.3.1 Theoretical Treatment 87
4.3.2 Numerical Results 89
4.3.3 Experimental Verification 91
4.4 Dynamic Response 94
4.4.1 Model of the System 94
4.4.2 Self-Oscillations 96
4.4.3 Stability Analysis 97
4.5 Nonlinear Chirality of Helical Resonators 101
4.6 Conclusion and Outlook 104
References 105
5 Nonlinear and Tunable Left-Handed Transmission Lines 107
5.1 Introduction 107
5.2 Comparison of Conventional Right-Handed and Left-Handed Nonlinear Transmission Lines 108
5.3 Parametric Generation and Amplification 110
5.3.1 Theory 110
5.3.2 Experiment 111
5.3.3 Motivation for Considering Parametric Generation and Amplification 113
5.4 Higher Harmonic Generation 114
5.5 Envelope Solitons in LH NLTLs 115
5.6 Pulse Formation in LH NLTL Media 117
5.7 Conclusion 119
References 119
6 Optimization Strategies for Second-Order Nonlinear Metamaterials 122
6.1 Introduction 123
6.2 Samples and Techniques 123
6.3 Tailoring Nonlinear Optical Response 124
6.3.1 Sample Quality 125
6.3.2 Particle Ordering 126
6.3.3 Passive Elements 127
6.4 Towards Optimized Response 129
6.5 Conclusions 130
References 131
7 Nonlinear Optical Interactions in ?-Near-Zero Materials: Second and Third Harmonic Generation 134
7.1 Introduction 134
7.2 Nonlinear Processes in ?-Near-Zero Materials 135
7.2.1 Second and Third Harmonic Generation Arising from Bulk Nonlinearities 138
7.2.2 Harmonic Generation from Surface and Volume Sources 139
7.2.3 Phase-Locked Second Harmonic Generation in ?-Near-Zero Media 143
7.3 Conclusions 146
References 146
8 Nonlinear Optical Effects in Positive-Negative Refractive Index Materials 149
8.1 Introduction 149
8.2 Parametric Interaction of the Backward and Forward Waves 150
8.2.1 Second Harmonic Generation 151
8.2.2 Third Harmonic Generation 159
8.3 Oppositely Directional Nonlinear Coupler 161
8.3.1 Nonlinear Waveguide Array 161
8.3.2 Two Tunnel Coupled Waveguides 163
8.3.3 Interaction of the Gap Solitons in Oppositely Directional Coupler 166
8.3.4 Influence of Dissipation on Threshold of Gap Soliton Formation 167
8.3.5 A Selection of Nonlinear Phenomena in Oppositely Directional Coupler 168
8.4 Extremely Short Steady State Pulses 170
8.4.1 The Model Formulation 170
8.4.2 Extremely Short Solitary Waves 171
8.4.3 Interaction of the Steady State Solitary Waves 172
8.5 Conclusion 173
References 174
9 From `Trapped Rainbow' Slow Light to Spatial Solitons 177
9.1 Introduction 177
9.2 The ``Trapped-Rainbow'' Principle: Light Stopping in Metamaterial and Plasmonic Waveguides 180
9.2.1 Light Stopping in the Presence of Disorder and Plasmonic Losses 182
9.2.2 From Loss-Compensation to Amplification by Cladding Gain 184
9.3 Spatial Solitons in Controlled Metamaterials 187
9.3.1 The Schrödinger Equation Description of Propagating Beams 187
9.3.2 Introduction of a Magnetooptic Environment 194
9.3.3 Controlling the Beam Diffraction 196
9.3.4 Simulation Outcomes 201
9.4 Conclusions 205
References 206
10 Nonlinear Optics with Backward Waves 208
10.1 Introduction 208
10.2 Huge Enhancement of Nonlinear Optical Energy Conversion, Reflectivity and Amplification Through Three-Wave Mixing of Ordinary and Backward Electromagnetic Waves 210
10.2.1 ``Geometrical'' Resonances 210
10.2.2 Three Alternative Coupling Schemes: Three Sensing Options 214
10.3 Coherent Nonlinear Optical Coupling of Ordinary and Backward Electromagnetic Waves in Spatially Dispersive Metamaterials 215
10.3.1 Carbon ``Nanoforest'' and Phase Matching of Ordinary Fundamental and Backward Second Harmonic Electromagnetic Waves 216
10.3.2 Coherent Energy Exchange Between Short Counter-Propagating Pulses of Fundamental Radiation and Its Second Harmonic 217
10.4 Mimicking Nonlinear Optics of Backward-Waves in Fully Dielectric Materials: Enhancing Coherent Energy Transfer Between Electromagnetic Waves in Ordinary Crystals by Coupling with Optical Phonons with Negative Phase Velocity 220
10.5 Conclusions 227
References 228
11 Tailoring Nonlinear Interactions in Metamaterials 231
11.1 Introduction 231
11.2 Nonlinear Wave-Mixing and Pulse Propagation 236
11.3 Magnetic and Reconfigurable Metamaterials 240
11.4 Optical Solitons, Bistability and Modulation Instability 242
References 246
12 Metamaterials Tunable with Liquid Crystals 250
12.1 Introduction 250
12.2 Liquid-Crystal Tunability of Metamaterials 252
12.3 Tunable Microwave and THz Metamaterials 255
12.4 Tunable Optical Metamaterials 260
References 265
13 Superconducting Quantum Metamaterials 267
13.1 Introduction 267
13.2 Superconducting Quantum Circuits 269
13.3 1D Quantum Metamaterials 274
13.3.1 Flux Qubit Quantum Metamaterial 274
13.3.2 Charge Qubit Quantum Metamaterial 276
13.3.3 Tuneable, Quantum Birefringent and Ambidextrous Quantum Metamaterials 278
13.3.4 Initializing a Quantum Photonic Crystal 280
13.4 Initial Data: Single Superconducting Artificial Atom in a Transmission Line 282
13.5 Further Perspectives 285
References 290
14 Nonlinear Localization in Metamaterials 292
14.1 Introduction 293
14.2 Metalic SRR-Based Metamaterial 295
14.3 rf SQUID Metamaterial 298
14.3.1 Dynamic Equations and Dissipative Breathers 298
14.3.2 Recent Experimental Results on SQUID Metamaterials 302
14.4 mathscrPT-Symmetric Metamaterial 304
14.5 Summary 309
References 310
15 Field Enhancement with Classical Electromagnetically Induced Transparency 313
15.1 Introduction 313
15.2 Design of EIT Metamaterials 316
15.3 A Simple Model for EIT Metamaterials 320
15.3.1 The Two-Oscillator Model 320
15.3.2 The Radiating Two-Oscillator Model 322
15.4 Electromagnetically Induced Absorption 324
15.5 EIT Metamaterials for Nonlinear and Tunable Operation 326
15.5.1 At Microwave Frequencies 326
15.5.2 At Terahertz Frequencies 326
References 328
Index 330