Optical properties of carbon nanotubes with non-local conductivity

In this talk, we present a new framework for analyzing the optical properties of carbon nanotubes (CNTs) with spatially dispersive conductivity. Spatial dispersion is modeled through a non-local operator that couples the surface current density to the electric field on the CNT surface. The nonlocal conductivity is derived using the Kubo formalism applied to the Dirac equation for pseudospins.

The central methodology is the imposition of effective physical boundary conditions. We introduce a smooth, homogeneous cylinder of the same radius as the real CNT and enforce electromagnetic (EM) boundary conditions on its surface such that the external EM field reproduces the field of the actual CNT beyond a short distance from the atomic lattice. This construction allows a rigorous treatment of nonlocal effects.

Using this approach, we obtain and analyze the dispersion relation for the CNT eigenmodes. Spatial dispersion leads to the emergence of new eigenmodes absent in the local-conductivity model. To capture these effects, we formulate additional boundary conditions that explicitly incorporate nonlocality, based on exact solutions obtained with the Wiener–Hopf technique for a semi-infinite CNT.

The scattering of electromagnetic waves by a finite-length CNT is then studied by solving a Fredholm integral equation of the second kind for the surface current density. Both numerical and approximate analytical solutions are developed, enabling calculation of the current distribution and far-field scattering pattern over a wide frequency range for realistic CNT parameters.