Uniqueness in a frequency-domain inverse problem of a stratified uniaxial bianisotropic medium

Sheen, Dongwoo; Shepelsky, Dmitry

doi:10.1016/s0165-2125(99)00033-5

Cited by 4 publications

(6 citation statements)

References 26 publications

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“…Let us finally point out that some pioneering works on the theory of inverse scattering for initial-value problems for equations with 3 × 3 Lax pairs are [1,10,20]. Other examples of the use of piecewise analytic solutions in studying the inverse problems for n × n systems (particularly for n = 4) can be found in [3,4,29].…”

Section: Introductionmentioning

confidence: 99%

Initial-boundary value problems for integrable evolution equations with 3×3 Lax pairs

Lenells

2012

Physica D: Nonlinear Phenomena

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We present an approach for analyzing initial-boundary value problems for integrable equations whose Lax pairs involve 3 × 3 matrices. Whereas initial value problems for integrable equations can be analyzed by means of the classical Inverse Scattering Transform (IST), the presence of a boundary presents new challenges. Over the last fifteen years, an extension of the IST formalism developed by Fokas and his collaborators has been successful in analyzing boundary value problems for several of the most important integrable equations with 2 × 2 Lax pairs, such as the Korteweg-de Vries, the nonlinear Schrödinger, and the sine-Gordon equations. In this paper, we extend these ideas to the case of equations with Lax pairs involving 3 × 3 matrices.

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Section: Introductionmentioning

confidence: 99%

Initial-boundary value problems for integrable evolution equations with 3×3 Lax pairs

Lenells

2012

Physica D: Nonlinear Phenomena

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“…Thus, it becomes clear that in a proposed subwavelength resonator with electric-dipole oscillations, the curl magnetic field arising from the Ampere-Maxwell law is unphysical. [69] Nevertheless, the problem of the "electromagnetic democracy" in ES resonances can be solved if we assume that electric-dipole dynamics in a dielectric sample are accompanied with the induced magnetization characterized by temporal-dispersion permeability (10). So, the fact of neglect of the magnetic displacement current does not contradict the presence of the curl magnetic field if the magnetization is induced.…”

Section: Es Resonances In Subwavelength Samplesmentioning

confidence: 99%

“…[2][3][4][5][6][7][8] In the analysis of ME interactions in bianisotropic metamaterials, simple models with dipolar terms are used. The known inverse-scatteringproblem solutions [9,10] and retrieval via measurements of the scattering-matrix characteristics, [11,12] used for the parameter reconstruction of bianisotropic samples, are far-field techniques. However, it is not possible to find 3D subwavelength details of a ME scatterer retrieved from far-field data.…”

Section: Introductionmentioning

confidence: 99%

Magnetoelectric‐Field Electrodynamics: Search for Magnetoelectric Point Scatterers

Kamenetskii

2022

Annalen der Physik

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Resonant scattering of electromagnetic (EM) waves by small particles is considered as one of the basic problems in metamaterial science. At present, special subwavelength resonators are considered as structural elements in chiral and bianisotropic metamaterials. There is a general consensus that these small scatterers behave like "artificial atoms" with strong electrical and magnetic responses and an interconnection between these responses. However, the observed effect of magnetoelectric (ME) coupling in these meta-atoms is not associated with the near-field manipulation properties caused by intrinsic magnetoelectricity. This arises the question whether ME point scatterers of EM radiation really exist. In this paper, we show that there are mesoscopic structures with electric and magnetic dipole-carrying excitations that behave like point scatterers with their inherent magnetoelectricity. In such subwavelength resonators, coherent oscillations of the electric polarization and magnetization can be considered as quasistatic oscillations described by electrostatic (ES) and magnetostatic (MS) scalar wave functions. The ME resonance effect arises from the coupling of two, ES and MS, oscillations. The near fields of these resonators, called the ME near fields, are characterized by simultaneous violation of time reversal and inversion symmetry. In study of ME fields and EM problems associated with these fields, we put forward the concept of ME-field electrodynamics.

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“…Due to the regularity of the spectrum of a compactsupported (square-integrable) function, in some cases there is a theoretical possibility to prolong this spectrum outside the limited region directly related to the data (Slepian and Pollack, 1961) (apart from ill-posedness problems, not explicit-ly considered here). This rationale has given rise to various uniqueness theorems for the solution of several inverse problems (Colton and Paivarinta, 1992;Sheen and Shepelsky, 2000). However, uniqueness theorems always require a continuous set of data to be available and often assume some regularity of the object function, which is not achieved in many practical cases (Ramm, 1990;Colton and Paivarinta, 1992).…”

Section: Introductionmentioning

confidence: 99%

«Paralipomena» on uniqueness in inverse scattering from a finite number of data

Persico

2009

Annals of Geophysics

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This paper shows new proof of non-uniqueness of the solution for the retrieving of a compact-supported function starting from a finite number of samples of its spectrum. As will be shown, this is relevant for linear inverse scattering problems, that in many cases can be recast as the reconstruction of a compact supported function from a finite set of samples of its spectrum. Since this reconstruction is not unique, from a practical point of view, any linear inverse scattering algorithm that can be recast in terms of a Fourier relationship between unknowns and data necessarily «trusts» on the absence of invisible objects in the particular situation at hand.

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Uniqueness in a frequency-domain inverse problem of a stratified uniaxial bianisotropic medium

Cited by 4 publications

References 26 publications

Initial-boundary value problems for integrable evolution equations with 3×3 Lax pairs

Initial-boundary value problems for integrable evolution equations with 3×3 Lax pairs

Magnetoelectric‐Field Electrodynamics: Search for Magnetoelectric Point Scatterers

«Paralipomena» on uniqueness in inverse scattering from a finite number of data

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