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TM scattering by an impedance-loaded rectangular groove: an enhanced computational mode-matching formulation
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DOI：10.1016/j.optlastec.2026.116129.png)
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Abstract
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We develop an enhanced mode-matching formulation for two-dimensional transverse-magnetic electromagnetic scattering by a rectangular groove recessed in a perfectly conducting plane and lined internally with impedance side walls and an impedance bottom. The impedance loading renders the transverse cavity spectrum non-Hermitian and allows for the coalescence of two cavity states at a second-order exceptional point (EP2), where the ordinary modal expansion loses completeness and fails to reconstruct the aperture matching conditions. The missing generalized direction is restored through an associated EP2 mode and a non-singular enhanced projected system, and every scattering result is validated through direct reconstruction of the imposed interface continuity and the upper-half-space power balance. The convergence of the ordinary and enhanced schemes is compared, and the family of exceptional-point configurations set by the bottom impedance is examined. The enhanced formulation recovers accurate matching and a conservation-consistent power partition where the ordinary formulation fails, and identifies the EP2 as a loading condition that redistributes the extracted power between reradiation and cavity coupling in impedance-loaded electromagnetic resonators.
Keywords:
Exceptional point
Mode-matching
TM groove scattering
Non-Hermitian eigenvalue problem
Bilinear orthogonality
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