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We analyse, using integral equations and a previously developed in-house numerical algorithm, the scattering and absorption of theH -polarized plane wave by a metasurface consisting of a double-layer grating of flat graphene strips placed into a lossless dielectric slab. The algorithm is meshless and its convergence is guaranteed mathematically. It is a version of the method of analytical preconditioning; namely, it uses the set of weighted Chebyshev polynomials as expansion functions in the discretization of a hypersingular electric field integral equation for the on-strip current. Then the computational error is controlled by the matrix size and can be reduced to machine precision. Using this advanced tool, we plot the frequency dependences, in a huge range from 1 GHz to 10 THz, of the transmittance, reflectance and absorbance of such a metasurface. This accurate analysis reveals resonances on several types of natural modes, best understood via visualization of in-resonance near-fields. In addition to plasmon-mode resonances, special attention is paid to the ultra-high-Q resonances on the lattice modes, which are absent on the free-standing graphene strip gratings.

Terahertz range resonances of metasurface formed by double-layer grating of microsize graphene strips inside dielectric slab