Contributors xix Foreword xxi Preface xxv Acknowledgments xxvii Acronyms xxxi Introduction xxxv 1 Foundations of Electromagnetic Theory 1 1.1 Maxwell Equations 2 1.1.1 Time-domain Maxwell Equations in differential form 2 1.1.2 Frequency domain Maxwell Equations in differential form 4 1.1.3 Frequency-domain Maxwell Equations in lossy medium 6 1.

2 Curl-curl equations for the electric and magnetic fields 7 1.3 Boundary conditions 8 1.4 Poynting Theorem 13 1.4.1 Time-domain Poynting theorem and instanteneous balance of power 13 1.4.2 Frequency-domain Poynting theorem and average balance of energy 15 1.5 Vector and scalar potentials 18 1.

5.1 Magnetic vector potential Ae and electric scalar potential e 18 1.5.2 Electric vector potential Am and magnetic scalar potential m 20 1.6 Quasi-electrostatics Scalar potential Capacitance 23 1.7 Quasi-magnetostatics 25 1.7.1 Governing equations for potentials and fields in time domain 25 1.

7.2 Governing equations for potentials and fields in frequency (spectral) domain 26 1.7.3 Energy definition of self-inductance, mutual inductance, and resistance 29 1.7.4 Field-based definition of self-inductance and mutual inductance 33 1.8 Theory of DC and AC circuits as a limiting form of Maxwell equations 35 1.9 Conclusions 40 2 Green''s Functions in Free Space 43 2.

1 1D Green''s function 43 2.2 3D Green''s function expansion in Cartesian coordinates 48 2.3 3D Green''s function in cylindrical coordinates 50 2.4 Physical Interpretation of Conical Waves Forming Sommerfeld Identity 53 2.5 Integral field representation using Green''s function 57 2.6 Field Decomposition into TE- and TM-waves in Cartesian coordinates 58 2.7 Free-space dyadic Green''s functions of electric and magnetic field 61 2.8 Conclusions 65 3 Equivalence Principle and Integral Equations in Layered Media 67 3.

1 Quasi-Electrostatics Reciprocity Relations in Layered Media 68 3.2 Equivalence Principle for the External Electrostatic Field in Layered Media 69 3.3 Integral Equation of Electrostatics for Metal Object in Layered Media 75 3.4 Integral Equation of Electrostatics for Disjoint Metal and Dielectric Objects in Layered Media 75 3.5 Integral Equation of Electrostatics for Metal and Dielectric Objects Sharing a Common Boundary and Situated in Layered Media 81 3.6 Integral Equation of Electrostatics for Dielectric Objects Sharing a Common Boundary and Situated in Layered Media 84 3.7 Integral Equations of Quasi-Magnetostatics for Wires in Layered Media 88 3.7.

1 Matrix form of the MoM discretized SVS-EFIE 91 3.8 Full-Wave Reciprocity Relations in Layered Media 92 3.9 Integral representations of electromagnetic fields via equivalence principle 99 3.9.1 Equivalence Principle for the external electric field 99 3.9.2 Equivalence Principle for the external magnetic field 107 3.9.

3 Equivalence Principle for the internal fields 110 3.10 Electric Field Integral Equation (EFIE) for PEC object in layered medium 113 3.11 Magnetic Field Integral Equation (MFIE) for PEC object 115 3.12 Coupled EFIEs for penetrable object 118 3.13 Coupled MFIEs for penetrable object 120 3.14 Muller, PMCHWT, and CFIE Formulations for Penetrable Object 121 3.15 Volume Integral Equation 124 3.16 Single Source Integral Field Representations and Integral Equations 126 3.

17 Conclusions 129 4 Canonical Problems of Vertical and Horizontal Dipoles Radiation in Layered Media 131 4.1 The Electromagnetics of Dipole Currents in Open Planar Multi-Layered Media 131 4.2 Vertical electric dipole above half-space 132 4.3 Vertical Magnetic Dipole in layered media 136 4.3.1 VMD above half-space 136 4.3.1.

1 Asymptotic behavior of electric vector potential at k! 1 137 4.4 Vertical magnetic dipole (VMD) in 3-layer medium 138 4.4.1 Ray Tracing Solution 139 4.4.2 The Fields of a Vertical Electric and Magnetic Dipoles: Spectral 1D BVP in General Layered Media 142 4.5 Horizontal Electric Dipole in Layered Media 144 4.5.

1 HED above PEC ground 144 4.5.2 Spatial boundary value problem for HED: Non-uniqueness of vector potential 145 4.5.3 HED spectral domain solution: 2-layer medium 150 4.5.4 HED spectral domain solution: 4-layer medium 155 4.5.

5 The Fields of a Horizontal Electric and Magnetic Dipoles: Spectral 1D BVP in General Layered Media 159 4.6 Integration Paths of Complex Plane k 162 4.6.1 Multi-Valued Sommerfeld Integrands 162 4.6.2 Integration Along Sommerfeld Integration Path and Its Modifications 167 4.6.2.

1 Integration over the real axis of k 167 4.6.2.2 Integration on parametric path avoiding singularities and landing on real axis of k 168 4.7 Conclusions 170 5 Computation of Fields Via Integration Along Branch Cuts 171 5.1 Transformation of SIP to Integrals Along Banks of Branch Cuts 171 5.2 Parametrization of the Path Along Branch Cut Banks under 2p -Convention 177 5.3 Parametrization of the Path Along Branch Cut Banks under =2 p Convention 182 5.

4 Surface Waves 184 5.4.1 Surface (Zenneck) Waves For VED about Half-Space (Sommerfeld Problem) 184 5.4.2 Analysis of Zenneck''s pole location under 2p branch cut convention 186 5.4.3 Analysis of Zenneck''s pole location under =2 p branch cut convention 190 5.4.

4 On Sommerfeld Problem and Existence of Zenneck''s Wave 192 5.4.5 Guided and Leaky Surface Waves 197 6 Computation of Fields Via Integration Along Steepest Descent Path 203 6.1 Definition of Integrand and Spherical Wave SDP S1 206 6.2 Saddle Point on Plane kand SDP in Its Vicinity 208 6.3 Parametrization of Spherical Wave SDP S1 210 6.4 Crossing Point k= k1 sin on the SDP S1 214 6.5 Case 1: SDP S1 Switches Riemann Sheets after Crossing Branch Cut 215 6.

5.1 Integral Circumventing Branch Point as Conical Wave SDP S2 218 6.5.2 Parametrization of Path S2 Around Branch Point 219 6.5.3 Analysis of Field Dependence on Radial Coordinate In SDP Integration Approach 222 6.6 Case 2: SDP S1 Remains on Same Riemann Sheet after Crossing Branch Cut 226 6.7 Final Remark on Numerical Integration Along SDP 227 6.

8 Reflected Far Field from Saddle Point: Spherical Wave 227 6.9 Reflected Far Field from Branch Point: Lateral (Conical) Wave 229 6.9.1 Physical interpretation of lateral wave 235 7 Computation of Fields Via Angular Spectral Representation 237 7.1 Transformation of SIP to a path on complex plane of angles 237 7.2 Reflected field as integral on complex plane of angles 240 7.3 Modification of integration path on angles plane to the SDP 244 7.4 Accounting For Branch Cut and Surface Wave Poles in Integration Along SDP on Plane 248 7.

4.1 Case 1: SDP S1 Switches to Different Riemann Sheet after Crossing Branch Cut 251 7.4.2 Case 2: SDP S1 Remains on Same Riemann Sheet after Crossing Branch Cut 254 7.5 Asymptotic Evaluation of SDP Integrals For k1R 1 255 7.5.1 Reflected Far Field: Spherical Wave 255 7.5.

2 Transmitted Field: VED above Half-Space 258 8 Fields in Spherical Layered Media 265 8.1 Scalar Green''s Function in Spherical Coordinates 265 8.2 Electromagnetic Field in terms of Debye potentials 268 8.3 Radial Electric Dipole (RED) in Spherical Layered Media 271 8.4 Tangential Electric Dipole (TED) in Spherical Layered Media 277 8.5 Conclusions 285 9 Mixed Potential Integral Equation 287 9.1 Mixed Potential Integral Equations in Free Space 287 9.2 MPIE Formulation in Layered Medium 292 9.

3 Reduction of 3D vector Maxwell''s equations to 1D scalar Telegraphers equations 305 9.4 Telegraphers equations for transmission line voltages and currents and their 1D Green''s functions 318 9.5 Relations of 3D Dyadic Green''s Functions to 1D Transmission Line Green''s Functions 319 9.6 Transmission line formulation of mixed-potential Green''s function components in formulation C 323 9.7 Closed-form expressions for voltages and currents in general layered medium 334 9.7.1 Generalized voltage reflection coefficients 335 9.7.

2 Transmission line Green''s function V ejh i , when z is within the source section (the case of p = p0 ) 339 9.7.3 Transmission line Green''s function Iejh i , when z is within the source section (the case of p = p0 ) 346 9.7.4 Transmission line Green''s function V ejh v and Iejh v , when z is within the source section (the case of p = p0 ) 347 9.7.5 Transmission line Green''s function V ejh and Iejh when z is outside the source section and z > z0 349 9.7.

6 Transmission line Green''s function V ejh and Iejh when z is outside the source section and z < z0 352 9.8 Conclusions 355 10 Discretization of the MPIE with Shape Functions Based RWG MoM 357 10.1 MPIE with augmented vector potential dyadic Green''s function 357 10.2 Current expansion over RWG- and half-RWG (ramp) basis functions 358 10.3 Representation of MoM matrix elements in terms of shape function interactions 370 10.4 Delta-gap port model and pertinent discretization 377 10.5 Conclusions 387 11 Computation of Incident Field from Electric Dipole Situated in the Far Zone 389 11.1 Reciprocity theorem application 389 11.

2 The method of stationary phase and Green''s f.