Dielectric Constant Estimation of a Carbon Nanotube Layer on the Dielectric Rod Waveguide at Millimeter Wavelengths

A method has been developed to estimate dielectric properties of a layer containing carbon nanotubes (CNTs) randomly arranged in plane, deposited on a dielectric rod waveguide (DRW). In the framework of this method, a theoretical model of a layered DRW with extended narrow walls and perfect electric conductor walls was used to fit the experimental results. The experimental results were obtained by measuring the wave propagation characteristics ( S11 and S21) of a DRW unloaded and loaded with different CNT layers at 75-110 GHz. The developed model allows derivation of the dispersion equation of the wave excited in the loaded DRW in an analytical form. The propagation constant is then found numerically through the fitting process with measurement results. Additionally, the complex permittivity of the CNT layer can be estimated using the surface conductivity model of the CNT and mixing formulas. Both methods give reasonable and comparable results. The obtained results (ε = 1- j5×10
³
) allow full-wave simulation (e.g., HFSS) of DRW structures loaded with CNT layers with a thickness of 60 nm or more. Simulation and measurement results agree rather well.