Manipulation of Surface Waves through Metasurfaces (eBook)

Supervisor’s Foreword 7
Parts of this thesis have been published in the following articles and chapters 10
Journal Paper 10
Book Chapter 10
Conference Proceedings 11
Acknowledgements 13
Contents 15
1 Introduction 18
1.1 Background on Electromagnetic Metasurfaces 18
1.2 Motivation 19
1.3 Thesis Outline 21
References 22
2 Surface Wave Dispersion for Anisotropic Metasurfaces Constituted by Elliptical Patches 24
2.1 Analytic Basis Functions 25
2.1.1 Problem Geometry 25
2.1.2 Circular Patches 26
2.1.3 Elliptical Patches 29
2.2 Spectral Analysis 31
2.2.1 MoM Matrix Entries 31
2.2.2 Anisotropic MTS Impedance 34
2.2.3 Homogenized MTS-Impedance Approximation 35
2.2.4 Dispersion Equation of the Dominant SW Mode 36
2.3 Numerical Results 37
2.4 Chapter Summary 42
References 42
3 Closed-Form Representation of Metasurface Reactance and Isofrequency Dispersion Curve 43
3.1 Dispersion Equation 45
3.1.1 Equivalent Capacitance 45
3.1.2 Closed Form Formulas for Quasi-static Capacitance 46
3.1.3 Frequency (Phasings) Regions 48
3.2 Low Frequency and Transition Regions 49
3.2.1 Low Frequency Approximation 50
3.2.2 Cardano's Transition Function 50
3.2.3 Simple Non-uniform Approximation 53
3.2.4 Identification of the Limits of the Frequency Regions 54
3.3 FB Region Correction 55
3.4 TE Dispersion Close to Its Cut-Off Frequency 58
3.5 Comparison with Full-Wave Analysis 58
3.6 Extension to Anisotropic MTS 59
3.6.1 Approximation of the IDCs 62
3.6.2 Phase and Group Velocities 63
3.7 Numerical Results 64
3.8 Chapter Summary 69
References 69
4 Flat Optics for Surface Waves 71
4.1 Flat Optics for Isotropic MTSs 72
4.1.1 Eikonal Equation 73
4.1.2 Ray Tracing and Phase Velocity 75
4.1.3 Poynting Vector 75
4.1.4 Transport of Energy Equation 76
4.2 Flat Optics for Anisotropic MTSs 77
4.2.1 Eikonal Equation 78
4.2.2 Poynting Vector 81
4.2.3 Ray Tracing and Ray Velocity 82
4.2.4 Transport of Energy Equation 83
4.3 Flat Transformation Optics 84
4.3.1 Rays and Wavefronts 86
4.3.2 Conformal and Quasi-conformal Mappings 86
4.4 Comparison with Full-Wave Analysis 87
4.5 Synthesis of Modulated IBC 92
4.5.1 Luneburg and Maxwell's Fish-Eye Lens 92
4.5.2 Modified Luneburg Lens 93
4.5.3 Beam Bender 94
4.5.4 Beam Splitter 95
4.6 Chapter Summary 97
References 97
5 Basic Properties of Checkerboard Metasurfaces 99
5.1 Connected Patch Transmission Lines 100
5.2 Experimental Results 103
5.2.1 CBMS Transmission Lines 103
5.2.2 CBMS Patch Antennas 103
5.2.3 Preliminary Results for Optically Tunable CBMS 104
5.3 Chapter Summary 107
References 107
6 Conclusion 108
6.1 Summary of Contributions 108
6.2 Future Directions 109
References 110
Author Biography 112
Asymptotic Evaluation of Grounded Slab Green's Function 113
Derivation of the Validity Conditions for Homogenization of the MTS-Impedance 114
Solution of Third-Degree Algebraic Equation Relevant to Impenetrable Impedance of Isotropic MTS 116
MFE and LL Differential Geometry 118