E-polarized plane-wave scattering from a PEC strip grating on a dielectric substrate: analytical regularization and lattice-mode resonances

Electromagnetic characterization of tuneable graphene‐strips‐on‐substrate metasurface over entire THz range: Analytical regularization and natural‐mode resonance interplay

“…In addition to the dielectric-slab and graphene-strip modes, our metasurface possesses specific 'collective' modes that appear because of periodicity; these are the lattice modes (also called grating modes [28], L mn . These mode resonances have been analysed for the PEC-strip-on-substrate grating in [23,24] and the graphene-strip gratings inside a slab in [14,21]. Here, the index m corresponds to the 'parent' RA (35) because their complex frequencies tend to the latter if the slab thickness shrinks to zero.…”

“…Inspection of ( 23), (24), and (27) shows that both Δ n and A m n contain the terms proportional to the normalized frequency, κ ¼ p=λ, and the terms proportional to e −jnj2πh=p . This means that the regularization, which is the semi-inversion of DSE, is performed via the analytical inversion of the static limit of the part corresponding to the strip grating on the interface between two media, air and dielectric.…”

“…First, we would like to adapt the MAR version, which is based on the analytical solution of the Riemann-Hilbert problem (RHP) in complex calculus, to the analysis of wave scattering and absorption by an infinite grating of flat graphene strips lying on a flat dielectric-slab substrate. This MAR-RHP technique was developed earlier to analyze scattering from zero-thickness perfectly electrically conducting (PEC) on-substrate strip grating [22][23][24]. Its modification for graphene strips has not been done so far and is expected to outperform other techniques, including existing MAR-based techniques.…”