Do corners always scatter?
Eemeli Bl{\aa}sten, Lassi P\"aiv\"arinta, John Sylvester
TL;DR
This paper investigates wave scattering by penetrable objects with rectangular corners, demonstrating they always scatter incident waves nontrivially despite having interior transmission eigenvalues.
Contribution
It shows that certain penetrable scatterers with corners always scatter waves and that the scattering operator remains invertible at all real wavenumbers.
Findings
Rectangular corners ensure nontrivial scattering.
Interior transmission eigenvalues do not prevent scattering.
Scattering operator has trivial kernel and cokernel at all real wavenumbers.
Abstract
We study time harmonic scattering for the Helmholtz equation in Rn. We show that certain penetrable scatterers with rectangular corners scatter every incident wave nontrivially. Even though these scatterers have interior transmission eigenvalues, the relative scattering (a.k.a. far field) operator has a trivial kernel and cokernel at every real wavenumber.
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