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| 2. |
- Fridén, Jonas, et al.
(författare)
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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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| 3. |
- Karlsson, Anders, et al.
(författare)
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Constitutive relations, dissipation and reciprocity for the Maxwell equations in the time domain
- 1992
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Ingår i: Journal Electromagnetic Waves and Applications. - 1569-3937. ; 6:5-6, s. 537-551
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Tidskriftsartikel (refereegranskat)abstract
- The main goal of this paper is to establish general constitutive relations for the electromagnetic fields EBAR, DBAR, BBAR, and HBAR in a time domain setting. The four basic assumptions of the medium are linearity, invariance to time translations, causality, and continuity. These four assumptions imply that the constitutive relations are convolutions of the Riemann-Stieltjes type. A review of the classification of media in bianisotropic, biisotropic, anisotropic, and isotropic media, respectively, is made. Dissipation and reciprocity are defined and the constraints these concepts make on the constitutive relations are analyzed. Furthermore, an appropriate form of time reversal and functions of positive type are introduced and some consequences of these concepts are showed.
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| 4. |
- Karlsson, Anders, et al.
(författare)
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Wave splitting in the time domain for a radially symmetric geometry
- 1990
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Ingår i: Wave Motion. - : Elsevier BV. - 0165-2125. ; 12:3, s. 197-211
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Tidskriftsartikel (refereegranskat)abstract
- A decomposition of the field of the wave equation in three dimensions is suggested. This wave splitting decomposes the field into two components such that in free space simple propagation properties are obtained. The inhomogeneous region is assumed to have a phase velocity variation that varies only in the radial coordinate r from the origin. The suggested wave splitting is a generalization of the wave splitting concept in one spatial dimension. Specifically, the propagation properties in free space in the three-dimensional wave splitting are very analogous to the corresponding propagation properties in free space in one dimension. The three-dimensional decomposition is illustrated in an example of scattering by a sound-soft sphere of radius a.
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| 5. |
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| 6. |
- Kristensson, Gerhard, et al.
(författare)
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Scattering of transient electromagnetic waves in reciprocal bi-isotropic media
- 1992
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Ingår i: Journal Electromagnetic Waves and Applications. - 1569-3937. ; 6:11, s. 1517-1535
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Tidskriftsartikel (refereegranskat)abstract
- In this paper propagation of transient electromagnetic waves in a reciprocal bi-isotropic medium is presented. The constitutive relations are convolution integrals with two susceptibility kernels that model the medium. The propagation problem is solved by the introduction of a wave-splitting technique. This wave-splitting is used to solve the propagation problem using either an imbedding approach or a Green's function technique. In particular, the scattering problem of an electromagnetic wave that impinges normally on a slab of finite or infinite extent is solved. The slab is assumed to be inhomogeneous with respect to depth. The scattering problem consists of finding the reflected and the transmitted fields and the generic quantities are the reflection and the transmission kernels of the medium. Explicit expressions for the rotation and the attenuation of the wave front is presented for the inhomogeneous slab. In the special case of a homogeneous infinite slab it is proved that the reflection kernel satisfies a nonlinear Volterra equation of the second kind, very suitable for numerical calculations. It is also proved that no cross polarization contribution appears for the homogeneous slab. Several numerical computations illustrate the analysis.
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| 7. |
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| 8. |
- Kristensson, Gerhard, et al.
(författare)
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Transient wave propagation in reciprocal bi-isotropic media at oblique incidence
- 1993
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Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 34:4, s. 1339-1359
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Tidskriftsartikel (refereegranskat)abstract
- In this paper a new wave splitting is suggested that simplifies the analysis of wave propagation in reciprocal bi-isotropic media. Two different methods to solve the scattering problem are analyzed: the invariant imbedding and the Green function approach. The medium is modeled by constitutive relations in the time domain (time convolutions) and the slab is assumed to be inhomogeneous with respect to the depth. It is shown that the cross-polarized contribution to the reflected field at normal incidence is zero for the general reciprocal inhomogeneous slab. Moreover, the rotation and the attenuation of the wave front are calculated explicitly in the general inhomogeneous slab case. Special attention is paid to normal incidence and to the homogeneous semi-infinite medium.
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| 9. |
- Olsson, Peter, et al.
(författare)
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Wave splitting of the Timoshenko beam equation in the time domain
- 1994
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Ingår i: Zeitschrift für Angewandte Mathematik und Physik. - 1420-9039. ; 45:6, s. 866-881
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Tidskriftsartikel (refereegranskat)abstract
- In recent years, wave splitting in conjunction with invariant imbedding and Green's function techniques has been applied with great success to a number of interesting inverse and direct scattering problems. The aim of the present paper is to derive a wave splitting for the Timoshenko equation, a fourth order PDE of importance in beam theory. An analysis of the hyperbolicity of the Timoshenko equation and its, in a sense, less physical relatives - the Euler-Bernoulli and the Rayleigh equations - is also provided.
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