Higher-order reciprocal copies in plasmonic-crystal finite-element spectra

Determine whether higher-order reciprocal-lattice copies of Bloch-wave solutions are computed or retained in the published second-order finite-element spectra for the complex-band formulation of the dispersive plasmonic crystal studied in the cited work.

Background

The paper discusses a finite-element periodic-factor formulation for complex bands in a dispersive plasmonic crystal reported in reference [8]. That earlier work identified duplicate out-of-first-Brillouin-zone eigensolutions whose real Bloch wavenumbers differ from a first-zone root by a reciprocal-lattice vector while their imaginary parts agree, suggesting that the computed solutions may represent reciprocal aliases.

The authors note that the published spectra resolve low-order reciprocal copies sufficiently well to be recognizable as aliases, but do not establish whether the same computation includes or preserves higher-order reciprocal copies. Consequently, the status of those higher-order solutions remains unresolved in the cited numerical results.