Analytical Foundations of Loop Antennas and Nano-Scaled Rings (eBook)

Dr. McKinley received his PhD in Engineering from the Australian National University, where he worked in the Centre for Sustainable Energy Systems. Dr. McKinley also holds two Master's degrees from Stanford University in Electrical Engineering and in Engineering Economic Systems. His interests focus on the use of these rings for solar cells, for meta-materials, and for terahertz (THz) communications. Dr. McKinley recently accepted a post asa Teaching Fellow in the Electrical Engineering Department at University College London,where he plans to develop courses in Renewable Energy Systems and to continue his research into the theory and application of loop antennas and nano-scaled rings.

Preface 7
Acknowledgements 9
Contents 11
List of Figures 15
Part I Preliminaries 23
1 General Introduction 24
1.1 A Motivation for the Study of Loops and Rings as Radiating Structures 24
1.2 The Experimental History of Loops 25
1.3 The Analytical History of Loops 30
1.4 The Recent History of Nano-Scaled Rings 32
References 35
2 Foundations 38
2.1 The Geometry of the Closed Toroidal Ring 38
2.1.1 Measurements in Different Coordinate Systems 38
2.1.2 Coordinate Systems In Detail 44
2.1.3 A Measure of Thickness of the Toroidal Ring: ? 46
2.1.4 A Measure of Frequency and Wavelength Related to Loop Geometry: kb 47
2.1.5 The Distance Between Points Within and on the Toroid 47
2.2 Useful Expressions of Maxwell's Equations for Toroidal Rings 50
2.2.1 Materials Linear in Maxwell's Equations 51
2.2.2 Linear Wave Equations 53
2.3 Propagation Parameters 54
2.3.1 Material Impedance and Absorption 56
2.3.2 Frequency Dependence of Material Parameters 57
2.3.3 Characteristics of Metals and Dielectrics From RF to Optical Wavelengths 63
2.4 Vector and Scalar Potentials 66
2.5 The Governing Equation of the Loop Antenna and Nano-Scaled Ring 71
2.5.1 The General Equation 71
2.5.2 The Governing Equation for Perfectly Conducting (PEC) Metals 72
2.5.3 The Governing Equation for Thin-Wire, PEC Loops and Rings 73
2.5.4 The Governing Equation for Thick-Wire, PEC Loops and Rings 75
2.6 Coupling a Driving Source to the Loop or Ring 76
2.6.1 Direct Coupling 76
2.6.2 Inductive Coupling 78
2.6.3 Illuminated Coupling 79
References 87
Part II Standalone Loop Antennas and Rings 88
3 Thin-Wire Perfectly Conducting Loops and Rings 89
3.1 The Early History 89
3.2 The Governing Equation and Solutions 91
3.3 Determining the Coefficients, an and Kn 94
3.3.1 Storer's Recursive Solution 94
3.3.2 Storer's Non-recursive Solution 96
3.3.3 Wu's Solution 97
3.4 An Elliptical Solution 102
3.5 Determining Non-solvability and Convergence 104
3.6 Summary of Solutions to the Thin-Wire PEC Loop 109
3.6.1 The Symmetry of the Closed Loop Coefficients, In, Around Mode n=0 110
References 111
4 The Driving Point Impedance and Admittance of Thin, PEC Loops and Rings 112
4.1 Formation of the Input Impedance 112
4.2 The Circuit Element Representation of the Loop 114
4.2.1 The Closed Loop as an R, L and C Circuit at Any kb 118
4.2.2 Difficulties with the Series Resonant Model of the Loop 121
4.3 The Subwavelength Anti-resonance 123
References 124
5 Current Distribution and Radiation Characteristics of Thin, PEC Loops and Rings 125
5.1 Current Characteristics 125
5.2 Characterizing Radiation of the PEC Loop 125
5.2.1 Radiating "0245E Field Patterns, Near and Far 127
5.2.2 Radiated Power, Radiation Intensity, Directivity and Gain 130
5.3 Characterising the Large Closed Loop 132
5.4 Characterising the Small Closed Loop 134
References 137
6 Lossy Thin Loops and Rings 138
6.1 The Effect of Surface Impedance on Loop Characteristics 138
6.1.1 The Functional Dependencies of the Surface Impedance 139
6.1.2 Modelling the Index of Refraction 140
6.2 The Driving Point Impedance and Admittance 142
6.3 The RLC Model for Lossy Metals 143
6.3.1 The Total R, L and C of the Lossy Metal Loop at Any kb 146
6.4 Resonance Saturation of Rings in the Optical Region 147
6.5 Radiation and Radiation Losses in the Thin-Wire Loop 148
References 149
7 Lossy Thin Loops and Rings with Multiple Impedance Loads 151
7.1 The Usefulness of Loop Antennas with Multiple Loads 151
7.2 Current in Multiply Loaded Loops 152
7.2.1 A Simplification 155
7.2.2 Current Coefficients 156
7.2.3 Asymmetries Due to Loads 157
7.3 The Input Impedance and Circuit Representation of Multiply Loaded Loops 158
7.4 Radiation from Multiply Loaded Loops 158
7.5 The Single Capacitor Loop 159
7.5.1 Constant Value Capacitor 159
7.5.2 Tuning by Varying the Capacitance Value, l? 165
7.6 The Effects of Multiple Capacitors 167
References 172
8 Thick PEC Rings 173
8.1 Thick Rings in Use in the Short-Wavelength Regions 173
8.2 The Governing Equations 174
8.2.1 Perfectly Conducting, Thick Ring Equations Applicable at Low Frequency to 150 GHz 174
8.2.2 Solutions to the Perfectly Conducting, Thick Ring Equations Applicable to 150 GHz 189
References 192
Part III Coupled Rings in One, Two and Three Dimensions 193
9 Meta-atoms & Rings as Large-Scale Atoms
9.1 Introduction 194
9.2 Plane Wave Illumination of Meta-atom Rings 195
9.3 Gap Capacitance 200
9.3.1 Standard Models 202
9.3.2 Testing the Models 205
References 209
10 Coupled Loops and Rings 210
10.1 Coupled Rings as Meta-atoms 210
10.2 Near-Field Coupling of Thin Rings 211
10.3 Optimization Procedure for the Design of Coupled Nano-Loop Antennas 214
References 215
A Bessel Functions 216
A.1 Bessel of the First Kind 216
A.2 Modified Bessel of the First and Second Kind 217
A.3 Lommel-Weber Function 217
A.4 Combinations 218
References 218