Optical Response of Ultrathin Periodically Aligned Single-Wall Carbon Nanotube Films

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.

Jonscher indices for dielectric materials

Two parameters are proposed as Jonscher indices, named after A. K. Jonscher for his pioneering contribution to the universal dielectric relaxation law. Time domain universal dielectric relaxation law is then obtained from the asymptotic behavior of dielectric response function and relaxation function by replacing parameters in Mittag–Leffler functions with Jonscher indices. Relaxation types can be easily determined from experimental data of discharge current in barium stannate titanate after their Jonscher indices are determined.