Approximate boundary conditions for the problem of evaluating the optical coefficients of ultrathin metallic films in microwave and THz frequency range

Approximate boundary conditions for a problem of calculating the optical coefficients of a system composed of inhomogeneous ultrathin metallic film with an arbitrary thickness dependence of conductivity deposited on dielectric substrate are obtained. The derivation of the boundary conditions is based on the Picard method of successive approximations. Analytical expressions for the errors in calculating the optical coefficients with use of the proposed approximate boundary conditions are presented. It is shown that the error increases with the frequency and the film thickness increasing. The maximum error for films of 10 nm-thickness does not exceed 10.7% at 1 THz. As an example, the complex optical coefficients of a system similar to Fabry–Perot etalon and a metal film without a substrate with model thickness dependence of conductivity are calculated. The coincidence between the results of numerical simulation and calculations performed with approximate boundary conditions is shown. The possibility of direct calculating the average conductivity of a film from experimentally measured reflection and transmission coefficients is demonstrated.