Metasurface Electromagnetics: The Cagniard-DeHoop time-domain approach

Description

The book is entirely dedicated to the exploration of time-domain electromagnetic fields in the presence of thin, high contrast sheets, with an emphasis on metasurfaces combining magnetic and dielectric properties. Since the number of problems that are amenable to exact solutions in terms of analytic functions is limited, the book's analysis is not restricted to analytical methods only, attention is paid to the development of computational and approximate techniques too. All the solution methodologies presented in the book heavily rely on the Cagniard-DeHoop technique. Regrettably, perhaps because of its origins in seismology, this powerful mathematical tool is still not fully appreciated in the electromagnetics and antenna community. It is hoped that this book will demonstrate the truly broad applicability of the Cagniard-DeHoop technique to achieving both analytical and numerical time-domain solutions. The book is for advanced researchers in computational electromagnetics and those looking for new approaches to modelling of metasurfaces. The book also includes a foreword from Professor Adrianus T. de Hoop, the originator of the Cagniard-DeHoop technique, who ingeniously simplified a joint transform initially put forward by the French geophysicist Cagniard. Cover Contents About the author Foreword Preface Acknowledgments List of acronyms List of symbols 1 Introduction 1.1 Synopsis 1.2 Prerequisites References 2 Cagniard–DeHoop technique 2.1 A concise survey of joint transform methods 2.1.1 Classical CdH technique 2.1.2 “Cartesian” CdH technique 2.1.3 Strick’s modification of Cagniard’s technique 2.2 EM radiation in a layered medium 2.2.1 Transformation to the space–time domain 2.2.1.1 Body-wave contribution 2.2.1.2 Head-wave contribution 2.2.2 Numerical implementation 2.2.2.1 Body-wave contribution 2.2.2.2 Head-wave contribution 2.3 Concluding remarks References 3 Thin-sheet high-contrast saltus-type conditions 3.1 Problem formulation 3.2 Transition conditions for a thin high-contrast layer with dielectric and conductive properties 3.3 Transition conditions for a thin high-contrast layer with combined magnetic and dielectric properties References 4 Pulsed EM-field response of an infinite metasurface 4.1 Pulsed EM plane-wave induced response of a metasurface 4.1.1 E-polarized waves 4.1.2 H-polarized waves 4.1.3 Illustrative example 4.2 Pulsed EM line-source induced response of a metasurface 4.2.1 Electric-line source 4.2.2 Magnetic-line source 4.2.3 Illustrative example 4.3 Dipole-excited pulsed EM signal transfers via a metasurface 4.3.1 Loop-to-loop pulsed EM signal transfer 4.3.2 Wire-to-wire pulsed EM signal transfer 4.3.3 Illustrative example 4.4 Concluding remarks 4.4.1 Transmission via a dielectric slab coated by metasurfaces 4.4.2 Reflection against a slab of finite thickness References 5 Pulsed EM-field surface phenomena on thin sheets 5.1 Pulsed EM line-source excited surface effects 5.1.1 Electric-line source induced surface effects 5.1.1.1 Layer with dielectric and conductive properties 5.1.1.2 Layer with magnetic properties 5.1.1.3 Plasmonic layer 5.1.2 Magnetic-line source induced surface effects 5.1.2.1 Layer with dielectric and conductive properties 5.1.2.2 Layer with magnetic properties 5.1.2.3 Plasmonic layer 5.2 Pulsed EM loop-excited surface effects above a layer with dielectric and conductive properties 5.2.1 Receiving horizontal magnetic dipole 5.2.1.1 The voltage in the absence of sheet 5.2.1.2 The correction voltage 5.2.2 Receiving horizontal electric dipole 5.3 Illustrative examples 5.3.1 Concluding remarks References 6 Pulsed EM-field diffraction by semi-infinite sheets 6.1 Pulsed EM diffraction by a semi-infinite PEC sheet 6.1.1 TD solution 6.1.2 Illustrative example 6.2 Pulsed EM diffraction by a semi-infinite sheet with conductive and dielectric properties 6.2.1 TD solution 6.2.1.1 Screen with conductive properties 6.2.1.2 Screen with conductive and dielectric properties 6.2.2 Alternative factorization 6.2.3 Illustrative examples 6.3 Pulsed EM diffraction by the junction of two coplanar semi-infinite sheets with conductive and dielectric properties 6.3.1 TD solution 6.3.2 Illustrative examples 6.4 Pulsed EM diffraction by a semi-infinite metasurface 6.4.1 TD solution 6.4.2 Illustrative examples 6.5 Pulsed EM diffraction by the junction of two coplanar semi-infinite metasurfaces 6.5.1 TD solution 6.5.2 Illustrative examples 6.6 Kirchhoff diffraction by semi-infinite sheets 6.6.1 PEC sheets 6.6.2 EM penetrable sheets 6.6.3 Illustrative examples References 7 Pulsed EM-field scattering by narrow metastrips 7.1 Pulsed EM scattering by a narrow PEC strip 7.1.1 Alternative expressions for the external impedance 7.1.2 TD solution 7.2 Pulsed EM scattering by a narrow strip with conductive and dielectric properties 7.2.1 TD solution 7.2.1.1 Strip with conductive properties 7.2.1.2 Strip with conductive and dielectric properties 7.2.1.3 Strip with plasmonic properties 7.3 Pulsed EM scattering by a narrow metastrip 7.3.1 TD solution 7.4 Concluding remarks References 8 Pulsed EM-field scattering by bounded metasurfaces in a homogeneous embedding 8.1 Pulsed EM scattering by a bounded PEC screen 8.1.1 Problem formulation 8.1.2 Problem solution 8.1.3 Illustrative examples 8.2 Pulsed EM scattering by a bounded screen with conductive and dielectric properties 8.2.1 Screen with conductive properties 8.2.2 Screen with conductive and dielectric properties 8.2.3 Screen with plasmonic properties 8.2.4 Illustrative examples 8.3 Pulsed EM scattering by a bounded metasurface 8.3.1 Problem solution 8.3.2 Illustrative examples 8.3.3 Concluding remarks References 9 Pulsed EM-field scattering by bounded and narrow screens in a layered embedding 9.1 Pulsed EM scattering by a bounded screen above the PEC ground 9.1.1 Problem formulation 9.1.2 Problem solution 9.1.3 Narrow-screen approximation 9.1.4 Illustrative examples 9.2 Pulsed EM scattering by a bounded screen on a dielectric half-space 9.2.1 Problem formulation 9.2.2 Problem solution 9.2.3 Narrow-screen approximation 9.2.4 Illustrative examples 9.3 Pulsed EM scattering by a bounded screen on a grounded dielectric slab 9.3.1 Problem formulation 9.3.2 Problem solution 9.3.3 Narrow-screen approximation 9.3.4 Illustrative examples 9.4 Concluding remarks References 10 Pulsed EM-field coupling between bounded and narrow conductive screens 10.1 Problem formulation 10.2 Problem solution 10.2.1 EM coupling between screens in a homogeneous embedding 10.2.1.1 Narrow-screen approximation 10.2.1.2 Numerical examples 10.2.2 EM coupling between screens on a dielectric half-space 10.2.2.1 Narrow-screen approximation 10.2.2.2 Numerical examples 10.2.3 EM coupling between screens on a grounded dielectric slab 10.2.3.1 Narrow-screen approximation 10.2.3.2 Numerical examples References 11 Pulsed EM-field coupling between bounded and narrow metasurfaces 11.1 Problem formulation 11.2 Problem solution 11.2.1 Entries of ˆZ and ˆR 11.2.2 Entries of ˆY and ˆG 11.2.3 Entries of ˆF and ˆQ 11.2.4 Entries of the excitation array 11.2.5 Solving the TD system of equations 11.3 Narrow-screen approximation 11.4 Illustrative examples References 12 Pulsed EM-field scattering by 3-D bounded metasurfaces 12.1 Pulsed EM scattering by a bounded 3-D screen with dielectric and conductive properties 12.1.1 Problem formulation 12.1.2 Problem solution 12.2 Pulsed EM scattering by a bounded 3-D metasurface 12.2.1 Problem solution 12.3 Pulsed EM scattering by a small rectangular screen 12.3.1 A small rectangular screen with dielectric and conductive properties 12.3.2 A small rectangular metasurface 12.4 Illustrative examples 12.5 Concluding remarks 12.5.1 EM scattering by a metasurface 12.5.2 EM scattering by a small rectangular sheet References 13 Pulsed EM-field scattering by apertures 13.1 Pulsed EM scattering by a bounded slot 13.1.1 Problem formulation 13.1.2 Problem solution 13.2 Pulsed EM scattering by narrow slots 13.2.1 Slot on a dielectric half-space 13.2.2 Filled rectangular groove 13.2.3 Slot with a homogeneous filling 13.2.3.1 Conductive and dielectric filling 13.2.3.2 Metasurface filling 13.2.4 Two slots in a PEC screen 13.2.5 Two filled rectangular grooves 13.3 Pulsed EM scattering by a bounded aperture 13.3.1 Problem formulation 13.3.2 Problem solution 13.4 Pulsed EM scattering by a small rectangular aperture 13.5 Illustrative examples 13.6 Concluding remarks 13.6.1 EM scattering by a slot 13.6.2 EM scattering by a small rectangular aperture References 14 Pulsed EM plane-wave scattering by time-varying metasurfaces 14.1 Pulsed EM plane-wave induced response of a time-varying PEC/PMC metasurface 14.2 Pulsed EM plane-wave induced response of a time-varying conductive sheet 14.2.1 Illustrative examples 14.3 Concluding remarks References 15 Pulsed EM response of transmission lines over a metasurface 15.1 Transmission line above a PEC plane 15.1.1 Problem formulation 15.1.2 Problem solution 15.1.2.1 Delta-gap excitation 15.1.2.2 Plane-wave excitation 15.1.3 Incorporating termination loads 15.2 Transmission line above a layer with dielectric and conductive properties 15.3 Transmission line above a metasurface 15.3.1 Illustrative examples 15.4 Concluding remarks 15.4.1 Multiconductor transmission line 15.4.2 Transmission line above a lossy ground 15.4.3 Extending the applicability of the numerical solution References 16 Miscellaneous applications 16.1 Loop-to-loop pulsed EM close-range signal transfer via a conductive sheet 16.1.1 Problem formulation 16.1.2 Problem solution 16.1.3 Illustrative examples 16.2 Loop-to-loop pulsed EM signal transfer via a plasmonic sheet 16.3 A Kirchhoff-approximation-based analysis of a slot-excited resonator antenna 16.3.1 Problem formulation 16.3.2 Problem solution 16.3.3 Illustrative examples References Appendix A: Diffracted-wave amplitude References Appendix B: Impeditivity array of a PEC screen B.1 Generic integral ˆΥA B.2 Generic integral ˆΥB References Appendix C: Plane-wave excitation array C.1 Generic integral Θ Reference Appendix D: Impeditivity array of a screen with conductive and dielectric properties D.1 Generic integral D.2 Generic integral Reference Appendix E: Admittivity array of a PMC screen E.1 Generic integral Appendix F: Modified impeditivity array F.1 Generic integral F.2 Generic integral Reference Appendix G: Interface impeditivity array G.1 Generic integral G.2 Generic integral Reference Appendix H: Slab impeditivity array H.1 Generic integral H.2 Generic integral References Appendix I: Modified admittivity array I.1 Generic integral Appendix J: Coupling array of noncoplanar metasurfaces J.1 Generic integral J.2 Generic integral Appendix K: Impedance array of a 3-D screen with dielectric and conductive properties K.1 Generic integral K.2 Generic integral K.3 Generic integral References Appendix L: Recursive convolution technique L.1 Representation of the convolution-type integral L.2 Illustrative example References Index Back Cover