M.V. Davidovich – Dr.Sc. (Phys.-Math.), Professor, Department of Radiotechnique and Electrodynamics, Saratov State University named after N.G. Chernyshevsky

E-mail: davidovichmv@info.sgu.ru

The paper deals with the immitance (impedance and admittance) integral and integro-differential equations on conducting twodimensional films described by surface conductivity. The main types of such equations are presented, as well as surface-volume equations for dielectric particles with a conducting two-dimensional shell. The methods of transformation of the integral equations allowing reduce the singularities of kernels are considered. A number of equations are obtained by mode matching technique. The equations are applied for surface plasmon-polaritons along graphene structures and for localized plasmons in fullerenes. The resonant frequencies of free oscillations of fullerenes, scattering and absorption cross sections, as well as the dispersion equations of various surface modes on two-dimensional electron gas structures inside dielectric substrates are obtained. We used еру surface conductivity based on the Cubo-Greenwood model, as well as plasma approximation for sigma and pi carbon electrons distributed over a thin layer of fullerene. For graphene conductivity, we also used dynamic tensor conductivity based on the Bhatnagar-Gross-Crook approximation, taking into account spatial dispersion. The results are in good agreements with photoionization of C60 and C20 fullerenes, presented in the literature on the basis of the density functional theory method.

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