Abstract
We present the electromagnetic scattering theory for a finite-length nanowire with an embedded mesoscopic object. The theory is based on a synthesis of the integral equation technique of classical electrodynamics and the quantum transport formalism. We formulate Hall\'en-type integral equations, where the canonical integral operators from wire antenna theory are combined with special terms responsible for the mesoscopic structure. The theory is applied to calculate the polarizability of a finite-length single-walled carbon nanotube (CNT) with a short low-conductive section (LCS) in the microwave and subterahertz ranges. The LCS is modeled as a multichannel two-electrode mesoscopic system. The effective resistive sheet impedance boundary conditions for the scattered field are applied on the CNT surface. It is shown that the imaginary part of the polarizability spectrum has three peaks. Two of them are in the terahertz range, while the third is in the gigahertz range. The polarizability spectrum of the CNT with many LCSs has only one gigahertz peak, which shifts to low frequencies as the number of LCSs increases. The physical nature of these peaks is explained, and potential applications of nanoantennas are proposed.
Highlights
Over the past two decades, the methods of electrical engineering have been evolving toward a self-consistent description of mesoscopic structures with a feature size larger than the atomic distance but smaller than the characteristic length at which quantum correlations already appear [1]
We have developed the integral equation technique for the problem of electromagnetic scattering by a finite-length nanowire with a number of embedded mesoscopic objects
The theory is based on combining the integral equations of the classical antenna theory (Hallén-type equations) with the quantum transport formalism [47,49]
Summary
Over the past two decades, the methods of electrical engineering have been evolving toward a self-consistent description of mesoscopic structures with a feature size larger than the atomic distance but smaller than the characteristic length at which quantum correlations already appear [1]. This equation is valid for an arbitrary type of coherent conductors and quantum wires, whose physical origin manifests itself only in the values of the electron transmission coefficient and conductance, respectively. Such parameters appear in the integral equations as a priori given, and they should be found separately via numerical modeling or experiment. Our approach will be illustrated by analyzing the problem of the scattering of an EM wave by a finite-length carbon nanotube (CNT) with a short low-conductive section (LCS) in the microwave and terahertz ranges.
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