Optical Response of Ultrathin Periodically Aligned Single-Wall Carbon Nanotube Films
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MRS Advances © 2020 Materials Research Society DOI: 10.1557/adv.2020.234
Optical Response of Ultrathin Periodically Aligned Single-Wall Carbon Nanotube Films Chandra M. Adhikari and Igor V. Bondarev Department of Mathematics & Physics, North Carolina Central University, Durham, NC 27707, U.S.A.
ABSTRACT
We present a semi-analytical expression for the dielectric response function of quasi-2D ultrathin films of periodically aligned single-walled carbon nanotubes. We derive the response function in terms of the individual nanotube conductivity, plasma frequency, and the volume fraction of carbon nanotubes in the film. The real part of the dielectric response function is negative for a sufficiently wide range of the incident photon energy, indicating that the film behaves as a hyperbolic metamaterial. Inhomogeneous broadening increases the effect.
INTRODUCTION The study of the response functions of parallel aligned carbon nanotube (CNT) films is of great interest. Finite-thickness films of aligned single-wall CNTs (SWCNT) were recently shown experimentally to exhibit extraordinary optoplasmonic properties such as a tuneable negative dielectric response [1], which makes them a promising candidate for the development of a new family of highly anisotropic hyperbolic metamaterials (HMMs) [2]. To explain and help with the interpretation of these observations, we hereby present our theoretical study of the response functions for planar periodic quasi-2D arrays of identical SWCNTs. We consider a homogeneous quasi-2D array of parallel aligned, identical SWCNTs immersed in a finite-thickness dielectric medium of static relative dielectric permittivity ϵ sandwiched between a substrate and a superstrate of relative permittivities ϵ1 and ϵ2 as shown in the inset of Fig.1 (a) below. The CNTs are aligned along the y-axis 1
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with the intertube center-to-center distance ∆ . The electron charge density is distributed uniformly all over the periodic cylindrical nanotube surfaces, whereby the pairwise electron Coulomb interaction in the system of CNTs embedded in a dielectric layer of thickness d, can be approximated by that of two uniformly charged rings of radius R of the respective n-th and l-th tubules [3]. An interesting thing occurs when ϵ1 + ϵ2
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