A new type of Green function approach is introduced for time‐domain scattering for a stratified dissipative slab. The new Green functions are defined as mappings from the transmitted field to the split fields (i.e., the right‐moving and left‐moving fields) at any point within the stratified slab. Unlike the usual Green functions, the present Green functions have compact support in the time variable. The new technique is illustrated for the case of normally incident electromagnetic waves on a stratified slab where the permittivity, permeability, and conductivity vary with the depth. The linear and homogeneous partial differential equations (PDEs) for these ‘‘compact Green functions’’ are derived. The PDEs together with the initial and boundary conditions are well suited for a numerical treatment. Numerical results for the compact Green functions are presented in the direct problem, while in the inverse problem the permittivity and conductivity (or the permeability and conductivity) are reconstructed simultaneously using the reflection and transmission data for the first round trip. The present method is useful and attractive for both the direct and inverse problems due to its simplicity, high speed, and high accuracy in numerical computations.
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October 1993
Research Article|
October 01 1993
A ‘‘compact Green function’’ approach to the time‐domain direct and inverse problems for a stratified dissipative slab
Sailing He
Sailing He
Department of Electromagnetic Theory, Royal Institute of Technology, S‐100 44 Stockholm, Sweden
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J. Math. Phys. 34, 4628–4645 (1993)
Article history
Received:
January 14 1993
Accepted:
June 07 1993
Citation
Sailing He; A ‘‘compact Green function’’ approach to the time‐domain direct and inverse problems for a stratified dissipative slab. J. Math. Phys. 1 October 1993; 34 (10): 4628–4645. https://doi.org/10.1063/1.530361
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