Effects of statistical variations on propagation of electromagnetic waves in disordered periodic structures

Abstract

Localization theory is employed to investigate the impact of statistical variations in material parameters and lumped-element values on the transmission properties of transmission-line based metamaterial structures. The theory yields closed-form expressions for the calculation of the propagation constant of the disordered structure that are shown to provide an accurate alternative to the more expensive Monte Carlo approach. Application of the theory to the investigation of transmission properties of a negative refractive index structure demonstrates its use for expedient assessment of the impact of statistical variations in unit cell length and the values of the lumped inductive and capacitive elements used in the definition of the structure. These results are then employed to develop a tool to analyze the effects of disorder on Veselago lenses performance. Finally, the localization theory is extended to the study of the electromagnetic properties of structures that do not lend themselves to modeling in terms of lumped circuit elements.