| 41. |
- Fridén, Jonas, et al.
(författare)
-
Transient electromagnetic wave propagation in anisotropic dispersive media
- 1993
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Ingår i: Journal of the Optical Society of America A: Optics and Image Science, and Vision. - 1084-7529. ; 10:12, s. 2618-2627
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Tidskriftsartikel (refereegranskat)abstract
- Transient electromagnetic wave propagation in a stratified, anisotropic, dispersive medium is considered. Specifically, the direct scattering problem is addressed. The dispersive, anisotropic medium is modeled by constitutive relations (a 3 3 matrix-valued susceptibility operator) containing time convolution integrals. In the general case, nine different susceptibility kernels characterize the medium. An incident plane wave impinges obliquely upon a finite slab consisting of a stratified anisotropic medium. The scattered fields are obtained as time convolutions of the incident field with the scattering kernels. The scattering (reflection and transmission) kernels are uniquely determined by the slab and are independent of the incident field. The scattering problem is solved by a wave-splitting technique. Two different methods for determining the scattering kernels are presented: an embedding and a Green's function approach. Explicit analytic expressions of the wave front are given for a special class of media. Some numerical examples illustrate the analysis.
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| 42. |
- Fridén, Jonas, et al.
(författare)
-
Transient Electromagnetic Wave Propagation in Anisotropic Dispersive Media
- 1992
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper transient electromagnetic wave propagation in a stratified, anisotropic, dispersive medium is considered. Specifically, the direct scattering problem is addressed. The dispersive, anisotropic medium is modeled by constitutive relations (a 3 × 3 matrix-valued susceptibility operator)con taining time convolution integrals. In the general case, nine different susceptibility kernels characterize the medium. An incident plane wave impinges obliquely on a finite slab consisting of a stratified anisotropic medium. The scattered fields are obtained as time convolutions of the incident field with the scattering kernels. The scattering (reflection and transmission)k ernels are uniquely determined by the slab and are independent of the incident field. The scattering problem is solved by a wave splitting technique. Two different methods to determine the scattering kernels are presented; an imbedding and a Green functions approach. Explicit analytic expressions of the wave front are given for a special class of media. Some numerical examples illustrate the analysis.
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| 43. |
- Fridén, Jonas, et al.
(författare)
-
Transient external 3D excitation of a dispersive and anisotropic slab
- 1997
-
Ingår i: Inverse Problems. - : IOP Publishing. - 0266-5611 .- 1361-6420. ; 13:3, s. 691-709
-
Tidskriftsartikel (refereegranskat)abstract
- Propagation of a transient electromagnetic field in a stratified, dispersive and anisotropic slab, and related direct and inverse problems, are investigated. The field is generated by a transient external three-dimensional (3D) source. The analysis relies on the wave splitting concept and a two-dimensional Fourier transformation in the transverse spatial coordinates. An investigation of the physical properties of the split fields is made. To solve the direct and inverse scattering problems, wave propagators are used. This method is a generalization and a unification of the previously used imbedding and Green functions methods. The wave propagator approach provides an exact solution of the transmission operator. From this solution it is possible to extract the first precursor (the Sommerfeld forerunner). These results also hold for a bi-anisotropic slab. An inverse problem is outlined using reflection and transmission data corresponding to four, two-dimensional Fourier parameters. Due to the stratification of the medium, the inverse Fourier transformation is not needed in the inverse problem.
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| 44. |
- Friden, Jonas, et al.
(författare)
-
Transient External 3D Excitation of a Dispersive and Antisotropic Slab
- 1995
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Propagation of a transient electromagnetic field in a stratified, dispersive and anisotropic slab and related direct and inverse problems are investigated. The field is generated by a transient external 3D source. The analysis relies on the wave splitting concept and a two-dimensional Fourier transformation in the transverse spatial coordinates. An investigation of the physical properties of the split fields is made. To solve the direct and inverse scattering problems, wave propagators are used. This method is a generalization and a unification of the previously used imbedding and Green functions methods. The wave propagator approach provides an exact solution of the transmission operator. From this solution it is possible to extract the first precursor (the Sommerfeld forerunner). These results also hold for a bi-anisotropic slab. An inverse problem is outlined using reflection and transmission data corresponding to four, two-dimensional Fourier parameters. Due to the stratification of the medium, the inverse Fourier transformation is not needed in the inverse problem.
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| 45. |
- Fuks, Peter, et al.
(författare)
-
Permittivity profile reconstructions using transient electromagnetic reflection data
- 1997
-
Ingår i: Progress in Electromagnetics Research PIER. - 1070-4698. ; 17, s. 265-303
-
Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- This paper is concerned with the permittivity reconstruction of inhomogeneous dielectric media. The method applies to profiles that vary with depth only, i.e. it provides a one-dimensional profile reconstruction. The data are collected and analyzed in the time domain. In the first part of the paper the theory of the method is reviewed. It is showed that a finite time trace of reflection data suffices to uniquely reconstruct the permittivity profile of the medium. The latter part of the paper presents the experimental set-up and contains also a thorough discussion of the errors that affect the measurements. The inverse scattering algorithm that is used is either based upon an imbedding procedure or on a Green functions approach. The input to either of these algorithms is the reflection kernel or the impulse response of the medium, i.e. the delta function response of the medium. Therefore, a deconvolution of the the measured reflected field and the incident field must be performed. This deconvolution problem is also addressed briefly in this paper.
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| 46. |
- Fuks, Peter, et al.
(författare)
-
Permittivity profile reconstructions using transient electromagnetic reflection data
- 1990
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This paper is concerned with the permittivity reconstruction of inhomogeneous dielectric media. The method applies to profiles that vary with depth only, i.e. it provides a one-dimensional profile reconstruction. The data are collected and analyzed in the time domain. In the first part of the paper the theory of the method is reviewed. It is showed that a finite time trace of reflection data suffices to uniquely reconstruct the permittivity profile of the medium. The latter part of the paper presents the experimental set-up and contains also a thorough discussion of the errors that affect the measurements. The inverse scattering algorithm that is used is either based upon an imbedding procedure or on a Green functions approach. The input to either of these algorithms is the reflection kernel or the impulse response of the medium, i.e. the delta function response of the medium. Therefore, a deconvolution of the the measured reflected field and the incident field must be performed. This deconvolution problem is also addressed briefly in this paper.
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| 47. |
- Gower, Artur, et al.
(författare)
-
A simple model to validate effective waves in random particulate media: radial symmetry
- 2023
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Ingår i: Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences. - 1364-5021. ; 479:2279
-
Tidskriftsartikel (refereegranskat)abstract
- There has not been a satisfying numerical validation of the theory of effective waves in random particulate materials. Validation has been challenging because the theoretical methods for effective waves have been limited to random particulate media in infinite slabs or half-spaces, which require a very large number of particles to perform accurate numerical simulations. This paper offers a solution by providing, from first principles, a method to calculate effective waves for a sphere filled with particles for a spherically symmetric incident wave. We show that this case can excite exactly the same effective wavenumbers, which are the most important feature to validate for effective waves. To check correctness, we also deduce an integral equation method which does not assume the effective wave solution. Our methods are, in principal, valid for any frequency, particle volume fraction and disordered pair-correlation. With the methods we provide, it is now possible to validate, with a heavier Monte Carlo simulation, the predictions from effective wave theory.
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| 48. |
- Gower, Artur, et al.
(författare)
-
Effective Waves for Random Three-dimensional Particulate Materials
- 2020
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- How do you take a reliable measurement of a material whose microstructure is random? When using wave scattering, the answer is often to take an ensemble average (average over time or space). By ensemble averaging we can calculate the average scattered wave and the effective wavenumber. To date, the literature has focused on calculating the effective wavenumber for a plate filled with particles. One clear unanswered question was how to extend this approach to a material of any geometry and for any source. For example, does the effective wavenumber depend on only the microstructure, or also on the material geometry? In this work, we demonstrate that the effective wavenumbers depend on only microstructure and not the geometry, though beyond the long wavelength limit there are multiple effective wavenumbers. We show how to calculate the average wave scattered from a random particulate material of any shape, and for broad frequency ranges. As an example, we show how to calculate the average wave scattered from a sphere filled with particles.
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| 49. |
- Gower, Artur, et al.
(författare)
-
Effective waves for random three-dimensional particulate materials
- 2021
-
Ingår i: New Journal of Physics. - : IOP Publishing. - 1367-2630. ; 23:6
-
Tidskriftsartikel (refereegranskat)abstract
- How do you take a reliable measurement of a material whose microstructure is random? When using wave scattering, the answer is often to take an ensemble average (average over time or space). By ensemble averaging we can calculate the average scattered wave and the effective wavenumber. To date, the literature has focused on calculating the effective wavenumber for a plate filled with particles. One clear unanswered question was how to extend this approach to a material of any geometry and for any source. For example, does the effective wavenumber depend on only the microstructure, or also on the material geometry? In this work, we demonstrate that the effective wavenumbers depend on only microstructure, though beyond the long wavelength limit there are multiple effective wavenumbers for one fixed incident frequency. We show how to calculate the average wave scattered from a random particulate material of any shape, and for broad frequency ranges. As an example, we show how to calculate the average wave scattered from a sphere filled with particles.
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| 50. |
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