Geometric scattering in the presence of line defects

Bui, Hai Viet; Mostafazadeh, Alí; Seymen, Sema

doi:10.1140/epjp/s13360-021-01108-5

Cited by 2 publications

(2 citation statements)

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“…This leads to an exact closed-form expression for the scattering amplitude of V 1 , [20]. Solving the scattering problem for the potential V 2 is much easier; one can reduce it to a one-dimensional problem and derive an exact formula for its scattering amplitude [21].…”

Section: Introductionmentioning

confidence: 99%

“…Refs. [20,21] consider the geometric scattering problem for the cases that the surface includes either point defects or a collection of parallel line defects. Following the approach of [20,21], we can determine the geometric scattering amplitude for a surface containing both point and parallel line defects by identifying the contribution of its geometry with a perturbation δV of the potential…”

Section: Introductionmentioning

confidence: 99%

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Scattering by a collection of $δ$-function point and parallel line defects in two dimensions

Bui,

Loran,

Mostafazadeh

2021

Preprint

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Interaction of waves with point and line defects are usually described by δ-function potentials supported on points or lines. In two dimensions, the scattering problem for a finite collection of point defects or parallel line defects is exactly solvable. This is not true when both point and parallel line defects are present. We offer a detailed treatment of the scattering problem for finite collections of point and parallel line defects in two dimensions. In particular, we perform the necessary renormalization of the coupling constants of the point defects, introduce an approximation scheme which allows for an analytic calculation of the scattering amplitude and Green's function for the corresponding singular potential, investigate the consequences of perturbing this potential, and comment on the application of our results in the study of the geometric scattering of a particle moving on a curved surface containing point and line defects. Our results provide a basic framework for the study of spectral singularities and the corresponding lasing and antilasing phenomena in two-dimensional optical systems involving lossy and/or active thin wires and parallel thin plates.

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Section: Introductionmentioning

confidence: 99%