Integral equation technique for scatterers with mesoscopic insertions: Application to a carbon nanotube

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 Hallén-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.

Scattering of electromagnetic waves by two crossing metallic single-walled carbon nanotubes of finite length

“…Additionally, due to the intertube tunneling current, the imaginary part of the polarizability increases drastically (by a factor 10 or even 100) below 1 THz, whereas the real part of the polarizability increases by a factor of about 2.1. It should be noticed that two crossing tubes do not behave as a single longer tube, however their response is qualitatively similar to that of a CNT with a short low-conductive section 8 .…”

“…On the other hand, we demonstrate that the intertube coupling cannot be excluded from consideration in the frequency range below the LPR. This paper is a continuation of our research on the synthesis of the electrodynamics and the theory of electrical nano-circuits 8 .…”

“…Electromagnetic properties of both individual carbon nanotubes (CNTs) and CNT-networks have been actively studied during the past two decades [1][2][3][4][5][6][7][8] . The theory of electromagnetic (EM) wave scattering has been developed for individual single-walled CNT (SWCNT) [2][3][4] , SWCNT bundle 9 , multiwalled CNT 10 , curved CNT 11 , SWCNT with mesoscopic insertion 8 , and SWCNT with dielectric coating 12 .…”

“…Electromagnetic properties of both individual carbon nanotubes (CNTs) and CNT-networks have been actively studied during the past two decades [1][2][3][4][5][6][7][8] . The theory of electromagnetic (EM) wave scattering has been developed for individual single-walled CNT (SWCNT) [2][3][4] , SWCNT bundle 9 , multiwalled CNT 10 , curved CNT 11 , SWCNT with mesoscopic insertion 8 , and SWCNT with dielectric coating 12 . Many interesting electromagnetic phenomena have been predicted and discovered in CNTs including slowed-down surface waves 1 , antenna effect in finite-length CNTs [2][3][4] , screening effect due to the strong depolarizing field 12 , near-field enhancement 13 , Purcell effect 14 , and specific thermal radiation 15 .…”

Electromagnetic properties of a composite medium comprising chains of tunnel-coupled carbon nanotubes

“…∈ [ ] 0, . На основе работы [13] поверхностная плотность аксиального тока в цепочке УНТ может быть найдена из решения интегрального уравнения Халлена:…”