The Leontovich-Levin equation for optical scattering by an achiral carbon nanotube (CNT) of finite length is formulated, based on a quantum-mechanical microscopic model of the conductivity. Both approximate analytical and numerical solutions of the Leontovich-Levin equation yield a comparable surface current density distribution and scattering pattern. Applications over a wide frequency range from the terahertz to the ultraviolet are possible. The CNT polarizability in the low-frequency range and the scattering pattern in the range of optical interband transitions as well as in the vicinity of plasmon resonance are calculated. Geometric resonances of strongly retarded surface waves emerge and can be used for the qualitative interpretation of experimentally observed features in the optical response characteristics of CNT-based composite mediums. The potential of isolated CNTs as optical nanoantennas of both the receiving and transmitting types is established.

A model for the effective conductivity of a dilute and disordered composite material containing randomly single-wall carbon nanotube (SWCNT) inclusions was formulated. The modification of electron transport by the surface curvature of SWCNTs and an axial depolarization effect due to the finite length of metallic SWCNTs are taken into account. Simultaneous consideration of both effects permits the correct interpretation of the dependences of the effective conductivity on the frequency and temperature, and explains an experimentally observed terahertz peak in the spectrum of the effective conductivity.

The propagation of azimuthally symmetric guided waves in multiwalled carbon nanotubes (MWCNTs) was analyzed theoretically in the midinfrared and the visible regimes. The MWCNTs were modeled as ensembles of concentric, cylindrical, conducting shells. The influence of intershell electron tunneling on the optical properties of MWCNTs was examined by focusing on a double-walled carbon nanotube (DWCNT). Longitudinal electrostatic waves exist in DWCNTs due to intershell tunneling. Conditions for weak influence of intershell tunneling in DWCNTs were identified, and an integral-equation approach for scattering by an MWCNT was formulated when those conditions prevail. Slightly attenuated guided waves and antenna resonances due to the edge effect exist for not-too-thick MWCNTs in the far-infrared and the midinfrared regimes. Interband transitions retard the propagation of guided waves and have a deleterious effect on the performance of a finite-length MWCNT as a nanoantenna. Propagation of surface-plasmon waves along an MWCNT with a gold core was also analyzed. In the near-infrared and the visible regimes, the shells behave effectively as lossy dielectrics to suppress surface-plasmon-wave propagation along the gold core.

Experimental proof of localized plasmon resonance was found in thin films containing either single-walled carbon nanotubes (SWNT) or SWNT bundles of different length. All samples were prepared by a simple technique that permitted the selection of different SWNT lengths in different samples without significant differences in electronic properties. Fourier-transform infrared spectroscopy showed that an optical-density peak, the same as a terahertz conductivity peak, shifts to higher frequencies as the SWNT lengths are reduced—in agreement with a similar tendency predicted for the localized plasmon resonance in finite-length SWNTs [Slepyan et al., Phys. Rev. B 81, 205423 (2010)].

An equivalent-multishell approach for the approximate calculation of the characteristics of electromagnetic waves propagating in almost circular (azimuthally symmetric), closely packed bundles of parallel, identical, and metallic carbon nanotubes (CNTs) yields results in reasonably good agreement with a many-body technique, for infinitely long bundles when the number of CNTs is moderately high. The slow-wave coefficients for azimuthally symmetric guided waves increase with the number of metallic CNTs in the bundle, tending for thick bundles to unity, which is characteristic of macroscopic metallic wires. The existence of an azimuthally nonsymmetric guided wave at low frequencies in a bundle of a large number of finite-length CNTs stands in contrast to the characteristics of guided-wave propagation in a single CNT. The equivalent-multishell approach yields the polarizability scalar and the antenna efficiency of a bundle of finite-length CNTs in the long-wavelength regime over a wide frequency range spanning the terahertz and the near-infrared regimes. Edge effects give rise to geometric resonances in such bundles. The antenna efficiency of a CNT bundle at the first resonance can exceed that of a single CNT by 4 orders of magnitude, which is promising for the design and development of CNT-bundle antennas and composite materials containing CNT bundles as inclusions.