Stochastic Modeling of Wave Propagation in Waveguides With Rough Surface Walls

Waveguide components at terahertz (THz) frequencies suffer from increased conductor losses. These losses are further exacerbated by surface roughness. In this article, we introduce an expedient approach for modeling surface roughness, which is suitable for microwave to THz applications. Our model combines the high accuracy of a full-wave method with the computational efficiency of the polynomial chaos expansion (PCE). Wave propagation inside the waveguide is simulated with the finite-difference time-domain (FDTD) method, capturing both the excess attenuation and diffuse scattering phenomena due to roughness. Then, a small number of FDTD simulations (considerably smaller than what is needed in the standard Monte Carlo procedure) is used to determine the coefficients for the PCE representation of the guided waves as random variable functions. This allows us to determine the probability density function of all electromagnetic field components in a rough surface waveguide. Extraction of mean value and standard deviation of fields, as well as of other quantities of interest such as the attenuation constant, is just a matter of rapid postprocessing of these results over the entire simulated bandwidth.