Electromagnetic Metasurfaces (eBook)

KARIM ACHOURI, PhD, is a Postdoctoral Fellow in the Laboratory of Nanophotonics and Metrology at École Polytechnique de Montréal. He obtained his PhD from the same institution in electrical engineering in 2017. His research focus is on metamaterials, metasurfaces, photonics and optical systems. CHRISTOPHE CALOZ, PhD, is Full Professor at École Polytechnique de Montréal, the holder of a Canada Research Chair Tier-I and Head of the Electromagnetics Research Group. He has authored or co-authored over 700 technical conference, letter, and journal papers, as well as 13 books and book chapters.

Preface ix

1 Introduction 1

1.1 Metamaterials 1

1.2 Emergence of Metasurfaces 4

2 Electromagnetic Properties of Materials 9

2.1 Bianisotropic Constitutive Relations 10

2.2 Temporal Dispersion 14

2.2.1 Causality and Kramers-Kronig Relations 15

2.2.2 Lorentz Oscillator Model 17

2.3 Spatial Dispersion 23

2.4 Lorentz Reciprocity Theorem 27

2.5 Poynting Theorem 32

2.6 Energy Conservation in Lossless-Gainless Systems 38

2.7 Classi_cation of Bianisotropic Media 41

3 Metasurface Modeling 43

3.1 E_ective Homogeneity 44

3.1.1 The Homogeneity Paradox 44

3.1.2 Theory of Periodic Structures 44

3.1.3 Scattering from Gratings 46

3.1.4 Homogenization 47

3.2 E_ective Zero Thickness 50

3.3 Sheet Boundary Conditions 53

3.3.1 Impedance Modeling 54

3.3.2 Polarizability Modeling 57

3.3.3 Susceptibility Modeling 60

3.3.4 Comparisons between the Models 66

4 Susceptibility Synthesis 69

4.1 Linear Time-Invariant Metasurfaces 69

4.1.1 Basic Assumptions 69

4.1.2 Birefringent Metasurfaces 76

4.1.3 Multiple-Transformation Metasurfaces 78

4.1.4 Relations between Susceptibilities and Scattering Parameters 81

4.1.5 Surface-Wave Eigenvalue Problem 92

4.1.5.1 Formulation of the Problem 92

4.1.5.2 Dispersion in a Symmetric Environments 96

4.1.6 Metasurfaces with Normal Polarizations 100

4.1.7 Illustrative Examples 104

4.1.7.1 Polarization Rotation 104

4.1.7.2 Multiple Nonreciprocal Transformations 109

4.1.7.3 Angle-Dependent Transformations 112

4.2 Time-Varying Metasurfaces 117

4.2.1 Formulation of the Problem 117

4.2.2 Harmonic-Generation Time-Varying Metasurface 120

4.3 Nonlinear Metasurfaces 121

4.3.1 Second-Order Nonlinearity 122

4.3.1.1 Frequency-Domain Approach 123

4.3.1.2 Time-Domain Approach 128

5 Scattered Field Computation 133

5.1 Fourier-Based Propagation Method 134

5.2 Finite-Di_erence Frequency-Domain Method 141

5.3 Finite-Di_erence Time-Domain Method 147

5.3.1 Time-Varying Dispersionless Metasurfaces 150

5.3.2 Time-Varying Dispersive Metasurfaces 156

5.4 Spectral-Domain Integral Equation Method 164

6 Practical Implementation 173

6.1 General Implementation Procedure 174

6.2 Basic Strategies for Full-Phase Coverage 178

6.2.1 Linear Polarization 179

6.2.1.1 Metallic Scattering Particles 179

6.2.1.2 Dielectric Scattering Particles 188

6.2.2 Circular Polarization 194

6.3 Full-Phase Coverage with Perfect Matching 198

6.4 Effects of Symmetry Breaking 207

6.4.1 Angular Scattering 208

6.4.2 Polarization Conversion 215

7 Applications 223

7.1 Angle-Independent Transformation 224

7.2 Perfect Matching 229

7.3 Generalized Refraction 234

7.3.1 Limitations of Conventional Synthesis Methods 234

7.3.2 Perfect Refraction using Bianisotropy 239

8 Conclusions 245

9 Appendix 249

9.1 Approximation of Average Fields at an Interface 249

9.2 Fields Radiated by a Sheet of Dipole Moments 252

9.3 Relations between Susceptibilities and Polarizabilities 255

Bibliography 260