Time Domain Wave-Splittings and Inverse Problems,9780198565499

Time Domain Wave-Splittings and Inverse Problems

by ; ;
ISBN13: 9780198565499
ISBN10: 0198565496
Format: Hardcover
Pub. Date: 1998-12-10
Publisher(s): Oxford University Press
List Price: $144.06

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Summary

This is an introduction to recent developments in the application of wave-splitting methods to direct and inverse scattering of wave fields. Here wave-splitting refers to the decomposition of the total field into two components which propagate in opposite directions. Although the text emphasizes time domain methods, it includes some applications to frequency domain problems.

Author Biography

Sailing He is Docent, Senior Lecturer of Electromagnetic Theory, Royal Institute of Technology, Stockholm.

Table of Contents

1 Introduction to the time domain wave-splitting and imbedding approach in one space dimension
1(37)
1.1 Wave-splitting in the time domain: an introductory example
1(4)
1.2 The dynamic equations for the split fields
5(1)
1.3 The scattering kernels
6(1)
1.4 The Redheffer star product
7(4)
1.5 The imbedding equations for the scattering operators
11(3)
1.6 The imbedding equations for the scattering kernels
14(10)
1.7 The `extension of data' property
24(2)
1.8 Travel time coordinates
26(3)
1.9 The direct scattering problem
29(3)
1.10 The inverse scattering problem
32(2)
1.11 Extensions
34(1)
Exercises for Chapter 1
35(3)
2 Time domain wave-splitting Green's function approaches
38(46)
2.1 Time domain Green's functions
39(21)
2.1.1 Structure of the fundamental solution
39(3)
2.1.2 Equations for time-shifted Green's functions
42(4)
2.1.3 Numerical implementation of a direct problem
46(2)
2.1.4 Numerical implementation of an inverse problem
48(3)
2.1.5 An example of an exact and explicit solution
51(4)
2.1.6 The case with an impedance mismatch at the front surface
55(2)
2.1.7 Two-sided excitation and connections with the imbedding kernels
57(3)
2.2 Mathematical analysis of the Green's function approach
60(4)
2.3 The compact Green's function approach
64(7)
2.4 The propagator approach
71(2)
2.5 Measurements in a coaxial cable and the reconstruction of the permittivity
73(10)
2.5.1 Experimental set-up
74(2)
2.5.2 Deconvolution
76(4)
2.5.3 Reconstruction results
80(3)
Exercises for Chapter 2
83(1)
3 Extensions of the one-dimensional wave-splitting approaches
84(54)
3.1 Non-uniform LCRG transmission lines
84(22)
3.1.1 Reconstruction of the electrical parameters
85(6)
3.1.2 Signal restoration after transmission through a non-uniform LCRG line
91(4)
3.1.3 Reconstruction of a transient source on a transmission line
95(11)
3.2 Propagation and scattering of obliquely incident electromagnetic plane waves
106(9)
3.2.1 Wave-splitting in a homogeneous lossless half-space
106(2)
3.2.2 Parameter reconstruction for a stratified half-space
108(2)
3.2.3 Wave-splitting in a finitely conducting medium
110(2)
3.2.4 Calculation of the transient reflection from a conducting half-space
112(3)
3.3 Electromagnetically dispersive media
115(20)
3.3.1 Time domain models for dispersive media
117(2)
3.3.2 Wave-splitting in dispersive media
119(2)
3.3.3 The propagator kernel
121(4)
3.3.4 The first precursor
125(1)
3.3.5 Transient reflection from a dispersive half-space
126(1)
3.3.6 Reconstruction of the temporal behaviour for a stratified dispersive slab
127(4)
3.3.7 Reconstruction of the electric susceptibility kernel for a homogeneous dispersive medium
131(4)
Exercises for Chapter 3
135(3)
4 Inverse problems related to fields from localized sources over a stratified half-space
138(47)
4.1 Parameter reconstruction using moments of the fields
139(17)
4.1.1 Equations for the split moments
139(5)
4.1.2 Imbedding equations and parameter reconstruction
144(6)
4.1.3 Reconstruction of the permittivity tensor
150(6)
4.2 Linearization of the imbedding equations
156(1)
4.3 Parameter reconstruction using the Hankel transform of a point source field
157(19)
4.3.1 Explicit form of the splitting
159(2)
4.3.2 Equations for the Green's functions
161(1)
4.3.3 Parameter reconstruction
162(7)
4.3.4 A dissipative half-space with a velocity mismatch at the surface
169(7)
4.4 Applications of the explicit form of the wave-splitting to some electromagnetic wave propagation problems
176(7)
4.4.1 Wave propagation in a homogeneous plasma
176(2)
4.4.2 First precursor in Lorentz dispersive media
178(1)
4.4.3 Wave propagation in cylindrical waveguides
179(4)
Exercises for Chapter 4
183(2)
5 Wave-splittings combined with optimization techniques
185(44)
5.1 Explicit expressions for gradients and parameter reconstruction
185(32)
5.1.1 Reconstruction of source distributions on a line
186(9)
5.1.2 Reconstruction of line parameters
195(6)
5.1.3 Reconstruction of the temporal behaviour of a bi-isotropic slab
201(8)
5.1.4 Reconstruction of density and/or sound speed in two or three dimensions
209(8)
5.2 Newton-Kantorovich approach for a quasi-linear wave equation
217(7)
5.3 Reconstruction of the susceptibility kernel of 1-buthanol from experimental data
224(4)
Exercises for Chapter 5
228(1)
6 Time-harmonic wave-splitting approaches
229(61)
6.1 Time-harmonic wave scattering and propagation in chiral media
230(17)
6.1.1 Right-and left-moving modes in a homogeneous chiral medium
232(2)
6.1.2 Reflection from a vacuum-chiral interface and Brewster angles
234(3)
6.1.3 Reflection and transmission from a homogeneous chiral slab
237(1)
6.1.4 Invariant imbedding approach for a stratified chiral slab
238(4)
6.1.5 The Green's function approach and the internal fields
242(3)
6.1.6 The transmission Green's function approach
245(2)
6.2 Vacuum-splitting and scattering from stratified composite structures
247(13)
6.2.1 Vacuum-splitting in bi-anisotropic media
247(2)
6.2.2 Reflection, transmission and internal fields
249(4)
6.2.3 Discussion and comparison with other approaches
253(2)
6.2.4 Fractional linear transformations for the Riccati equation
255(5)
6.3 Reconstruction of transmission line parameters with band-limited scattering data
260(9)
6.3.1 The direct solver
260(2)
6.3.2 Explicit expression for the gradient
262(2)
6.3.3 Numerical reconstruction
264(5)
6.4 Trace formalism and explicit gradients
269(10)
6.4.1 Riccati equation, trace formalism and explicit gradients
269(6)
6.4.2 Reconstruction/design using both reflection and transmission data
275(2)
6.4.3 Reconstruction/design using the transmission Green's function approach
277(2)
6.5 Scattering from a laterally periodic inhomogeneous structure
279(6)
Exercises for Chapter 6
285(5)
7 Three-dimensional wave-splitting for the scalar wave and telegraph equations
290(43)
7.1 Planar wave-splitting in IR(3) and the associated operators
290(13)
7.2 The dynamical equations for the split components for the wave and telegraph equations
303(4)
7.3 Inverse problem: the Green's function approach
307(10)
7.4 Inverse problem: the continuation method
317(9)
7.5 Non-planar wave-splitting for the wave equation
326(4)
7.6 Present and future research
330(1)
Exercises for Chapter 7
331(2)
8 Wave-splitting of Maxwell's equations in IR(3) and applications
333(34)
8.1 Positive-and negative-going wave conditions in an isotropic medium with transverse dependence
334(6)
8.2 Exact splitting in a medium where Epsilon = Epsilon(x(1), x(2), Alpha), Mu = Mu(x(1), x(2), Alpha)
340(3)
8.3 Splitting in a medium where Epsilon = Epsilon(x(1), x(2), x(3)), Mu = Mu(x(1), x(2), x(3)
343(2)
8.4 Wave-splitting in a medium with dispersion
345(1)
8.5 Determination of the permittivity and conductivity in IR(3) using the wave-splitting
346(7)
8.6 Non-planar wave-splitting and absorbing boundary conditions
353(9)
Appendix: Asymptotic behaviour of E(-)(T)
362(4)
Exercises for Chapter 8
366(1)
References 367(12)
Bibliography 379(6)
Index 385

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