Phase recovery from phaseless scattering data for discrete Schrödinger operators

Novikov, Roman; Sharma, Basant Lal

doi:10.1088/1361-6420/ad03fe

Cited by 3 publications

(1 citation statement)

References 41 publications

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“…On the other hand, open problems belonging to the characterization of material defects, especially in the presence of surfaces exist, wherein the forward analysis, such the one contained in this article, plays a crucial role. In this context, some recent studies on inverse scattering and inverse source problems in lattices, but without surfaces, are worth a mention [35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Scattering of surface waves by inhomogeneities in crystalline structures

Sharma

2024

Proc. R. Soc. A.

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In current scientific and technological scenarios, studies of transmittance of surface waves across structured interfaces have gained some wind amidst applications to metasurfaces, electronic edge-waves, crystal grain boundaries, etc. The results presented in the present article shed a light on the influence of material inhomogeneities on propagation of surface waves. Within the framework of classical mechanics, an analogue of the Gurtin–Murdoch model is employed where elastic properties on surface are assumed to be distinct from bulk. Restricting to scalar waves on prototype square lattice half-plane, particles on considered structured surface have piecewise-constant mass and surface force-constants across an interfacial point. Particles in bulk lattice interact with nearest neighbours in a way that involves unequal force-constants parallel to surface versus normal to it. A surface wave band exists for such lattice structure wherein the waveform decays exponentially inside the half-plane. A formula for surface wave transmittance is given based on an exact solution on half-plane, and, thus, previous work (Sharma & Eremeyev 2019 Int. J. Eng. Sci. 143 , 33–38 ( doi:10.1016/j.ijengsci.2019.06.007 )) is extended. An explicit expression for fraction of energy influx leaked via bulk waves is a highlight. Included are graphical results for several illustrative values of surface structure parameters.

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Section: Introductionmentioning

confidence: 99%

Scattering of surface waves by inhomogeneities in crystalline structures

Sharma

2024

Proc. R. Soc. A.

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Interaction of in-plane waves with a structured penetrable line defect in an elastic lattice

Nieves,

Sharma

2024

International Journal of Engineering Science

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Inverse source problem for discrete Helmholtz equation

Novikov,

Lal Sharma

2024

Inverse Problems

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We consider multi-frequency inverse source problem for the discrete Helmholtz operator on the square lattice Z^d, d \ge 1. We consider this problem for the cases with and without phase information. We prove uniqueness results and present examples of non-uniqueness for this problem for the case of compactly supported source function, and a Lipshitz stability estimate for the phased case is established. Relations with inverse scattering problem for the discrete Schr"{o}dinger operators in the Born approximation are also provided.

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Phase recovery from phaseless scattering data for discrete Schrödinger operators

Abstract: We consider scattering for the discrete Schr ̈ödinger operator on the square lattice Z^d, d ≧ 1, with compactly supported potential. We give formulas for finding the phased scattering amplitude from phaseless near-field scattering data.

Cited by 3 publications

References 41 publications

Scattering of surface waves by inhomogeneities in crystalline structures

Scattering of surface waves by inhomogeneities in crystalline structures

Interaction of in-plane waves with a structured penetrable line defect in an elastic lattice

Inverse source problem for discrete Helmholtz equation

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