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.
Author(s): Martin Štumpf
Series: The ACES Series on Computational and Numerical Modelling in Electrical Engineering
Publisher: The Institution of Engineering and Technology
Year: 2022
Language: English
Pages: 441
City: London
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
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