Potentials with Identical Scattering Properties Below a Critical Energy

Abstract

A pair of scattering potentials are called $\alpha$-equivalent if they have identical scattering properties for incident plane waves with wavenumber $k\le \alpha$ (energy $k^2\le {\alpha }^2$.) We use a recently developed multidimensional transfer-matrix formulation of scattering theory to obtain a simple criterion for $\alpha$-equivalence of complex potentials in two and three dimensions.

arXiv comment9 pages

References in corpus (11)

• Spectral Singularities of Complex Scattering Potentials and Infinite Reflection and Transmission Coefficients at real Energies
• The transfer matrix: a geometrical perspective
• Wave reflection in dielectric media obeying spatial Kramers-Kronig relations
• Transfer Matrices as Non-Unitary S-Matrices, Multimode Unidirectional Invisibility, and Perturbative Inverse Scattering
• Half-spectral unidirectional invisibility in non-Hermitian periodic optical structures
• Transfer Matrix Formulation of Scattering Theory in Two and Three Dimensions
• Bidirectional invisibility in Kramers-Kronig optical media
• Perfect Broadband Invisibility in Isotropic Media with Gain and Loss
• Unidirectional Invisibility and Nonreciprocal Transmission in Two and Three Dimensions
• A Class of Exactly Solvable Scattering Potentials in Two Dimensions, Entangled State Pair Generation, and a Grazing Angle Resonance Effect
• Exact Solution of the Two-Dimensional Scattering Problem for a Class of $\delta$-Function Potentials Supported on Subsets of a Line

Cited by in corpus (2)

• Transfer-matrix formulation of the scattering of electromagnetic waves and broadband invisibility in three dimensions
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