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| 2. |
- Kristensson, Gerhard, et al.
(författare)
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Direct and inverse scattering for transient electromagnetic waves in nonlinear media
- 1998
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Ingår i: Inverse Problems. - : IOP Publishing. - 0266-5611 .- 1361-6420. ; II, s. 587-589
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Tidskriftsartikel (refereegranskat)abstract
- Nonlinear propagation of electromagnetic waves is an important problem in optics. Often the properties of the nonlinear media are not fully understood. The solution of an inverse problem can provide an aid to that understanding. An inverse transmission problem is posed; it is one of reconstructing the medium parameters, by measurement of a wave that has been propagated through the nonlinear medium. The nonlinear medium is assumed to be homogeneous and isotropic. The methods have application to nonlinear optics, and the numerical results for both the direct and inverse problems presented are based on the nonlinear Kerr effect, which is observed in the optical wavelength band. However, the mathematical techniques that are developed are applicable to any set of nonlinear first-order equations. The method is therefore model independent.
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| 4. |
- Sjöberg, Daniel, et al.
(författare)
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A Floquet-Bloch decomposition of Maxwell's equations, applied to homogenization
- 2003
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Using Bloch waves to represent the full solution of Maxwell’s equations in periodic media, we study the limit where the material’s period becomes much smaller than the wavelength. It is seen that for steady-state fields, only a few of the Bloch waves contribute to the full solution. Effective material parameters can be explicitly represented in terms of dyadic products of the mean values of the non-vanishing Bloch waves, providing a new means of homogenization. The representation is valid for an arbitrary wave vector in the first Brillouin zone.
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| 7. |
- Åberg, Ingegerd, et al.
(författare)
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Propagation of transient electromagnetic waves in time-varying media-direct and inverse scattering problems
- 1995
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Ingår i: Inverse Problems. - : IOP Publishing. - 0266-5611 .- 1361-6420. ; 11:1, s. 29-49
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Tidskriftsartikel (refereegranskat)abstract
- Wave propagation of transient electromagnetic waves in time-varying media is considered. The medium, which is assumed to be inhomogeneous and dispersive, lacks invariance under time translations. The spatial variation of the medium is assumed to be in the depth coordinate, i.e. it is stratified. The constitutive relations of the medium are a time integral of a generalized susceptibility kernel and the field. The generalized susceptibility kernel depends on one spatial and two time coordinates. The concept of wave splitting is introduced. The direct and inverse scattering problems are solved by the use of an imbedding or a Green function approach. The direct and the inverse scattering problems are solved for a homogeneous semi-infinite medium. Explicit algorithms are developed. In this inverse scattering problem, a function depending on two time coordinates is reconstructed. Several numerical computations illustrate the performance of the algorithms.
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| 8. |
- Åberg, Ingegerd, et al.
(författare)
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Propagation of transient electromagnetic waves in time-varying media - Direct and inverse scattering problems
- 1994
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Wave propagation of transient electromagnetic waves in time-varying media is considered. The medium, which is assumed to be inhomogeneous and dispersive, lacks invariance under time translations. The spatial variation of the medium is assumed to be in the depth coordinate, i.e., it is stratified. The constitutive relations of the medium is a time integral of a generalized susceptibility kernel and the field. The generalized susceptibility kernel depends on one spatial and two time coordinates. The concept of wave splitting is introduced. The direct and inverse scattering problems are solved by the use of an imbedding or a Green functions approach. The direct and the inverse scattering problems are solved for a homogeneous semi-infinite medium. Explicit algorithms are developed. In this inverse scattering problem, a function depending on two time coordinates is reconstructed. Several numerical computations illustrate the performance of the algorithms.
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| 9. |
- Åberg, Ingegerd, et al.
(författare)
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Transient waves in nonstationary media
- 1996
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Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 37:5, s. 2229-2252
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Tidskriftsartikel (refereegranskat)abstract
- This paper treats propagation of transient waves in nonstationary media, which has many applications in, for example, electromagnetics and acoustics. The underlying hyperbolic equation is a general, homogeneous, linear, first-order 2×2 system of equations. The coefficients in this system depend on one spatial coordinate and time. Furthermore, memory effects are modeled by integral kernels, which, in addition to the spatial dependence, are functions of two different time coordinates. These integrals generalize the convolution integrals, frequently used as a model for memory effects in the medium. Specifically, the scattering problem for this system of equations is addressed. This problem is solved by a generalization of the wave splitting concept, originally developed for wave propagation in media which are invariant under time translations, and by an imbedding or a Green's functions technique. More explicitly, the imbedding equation for the reflection kernel and the Green's functions (propagator kernels) equations are derived. Special attention is paid to the problem of nonstationary characteristics. A few numerical examples illustrate this problem.
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