Microwave modeling of single multi-wall carbon nanotubes

A novel estimation of the permittivity and permeability of an individual carbon nanotube is presented using optimization techniques. The complex effective permittivity and effective permeability of a vertically aligned carbon nanotube array are extracted by waveguide measurements. The extracted parameters are verified by full wave simulations (CST-Microwave Studio) and very good agreement has been obtained. Assuming that the S-parameter results are accurate enough, the quasi-Newton optimization technique has been applied to a unit cell of a periodic structure, consisting of solid isotropic cylinders with unknown complex permittivity. As a result, the relative permittivity of an individual carbon nanotube is calculated for each frequency point.