Expedient electromagnetic analysis of the impact of statistical disorder in periodic waveguides

A methodology is presented for the fast electromagnetic analysis of the impact of statistical disorder on the transmission properties of periodic waveguides. The proposed methodology makes use of ideas from the Anderson localization theory to derive closed-form expressions for the calculation of an effective exponential decay ratio that quantifies the impact of periodicity disorder on the transmission properties of the waveguide. With regard to the quantification of the statistics of periodicity disorder from data obtained from a limited number of manufactured devices, a nonparametric probability density estimation process is examined and found to be satisfactory for our purposes. The computational efficiency of the proposed method over brute-force Monte-Carlo-based alternatives is demonstrated through specific examples involving a periodically loaded parallel-plate waveguide. Furthermore, this numerical study is used to examine the accuracy of calculating the overall change in the propagation constant of the structure due to several sources of disorder as the sum of the changes calculated with each one of the sources of disorder considered individually.