We analyse, using integral equations and a previously developed in-house numerical algorithm, the scattering and absorption of the
H
-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.
Abstract-An efficient numerical solution is been developed to compute the impedances of rectangular transmission lines. Method of moments is applied to integral equations for the current density, where the cross section is discretized, to improve the convergence, by a nonuniform grid that obeys the skin effect. Powerfulness of this approach up to rather high frequencies is verified by comparing with asymptotic formulas and other references. Detailed discussion is given for the current density distribution and its effect to the impedance, especially for a high frequency range.
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