Diffraction of an electromagnetic wave on the finite lattice of carbon nanotubes-vibrators located at dielectric interfaces

A solution of the boundary problem on electromagnetic wave diffraction on a lattice of carbon nanotubes-vibrators is reduced to the solution of a set of integrodifferential equations, whose kernels are represented as a Fourier integral. Such representation of kernels makes it possible to easily overcome solution problems related to their singularities and reduce the computation time by one order of magnitude. Integrodifferential equations are solved using the Galerkin method with a Chebyshev basis. The effect of a substrate on amplitude-frequency characteristics and the scattering pattern of carbon nanotube antennas is studied. Both the resonance frequency and the amplitude of a scattered field are shown to increase in the case of approaching nanovibrators. The amplitude dependence on the number of vibrators is nonlinear.