On spurious solutions encountered in Helmholtz scattering resonance computations in R^d with applications to nano-photonics and acoustics
This work provides a practical tool for filtering spurious solutions in resonance computations, benefiting researchers in nano-photonics and acoustics.
The paper introduces a sorting scheme based on a Lippmann-Schwinger volume integral equation to identify spurious scattering resonance pairs in electromagnetic and acoustic problems, demonstrating its effectiveness on Drude-Lorentz resonators and graded materials at low computational cost.
In this paper, we consider a sorting scheme for potentially spurious scattering resonant pairs in one- and two-dimensional electromagnetic problems and in three-dimensional acoustic problems. The novel sorting scheme is based on a Lippmann-Schwinger type of volume integral equation and can, therefore, be applied to structures with graded materials as well as to configurations including piece-wise constant material properties. For TM/TE polarized electromagnetic waves and for acoustic waves, we compute first approximations of scattering resonances with finite elements. Then, we apply the novel sorting scheme to the computed eigenpairs and use it to mark potentially spurious solutions in electromagnetic and acoustic scattering resonances computations at a low computational cost. Several test cases with Drude-Lorentz dielectric resonators as well as with graded material properties are considered.