Microwave phase conjugation using nonlinearly loaded wire arrays

In this paper, we provide a mathematical description of the scattering properties of a two-dimensional double periodic array of wires that are loaded with nonlinear lumped elements. A combined electric field integral equation, Volterra series analysis is conducted and the respective integro-differential equations are solved numerically. The simulation results for the array when pumped by a spatially fed local oscillator signal show evidence of parametric amplification of the specular wave and also the production of a phase conjugated, retro-directed wave. The conventional condition under which the normal requirement for phase conjugate signal production in nonlinear artificial media, namely pumping at twice the frequency of the incident signal can be relaxed to fundamental pumping is discussed. In addition the conditions under which energy normally lost to specular reflection can be converted to energy in the phase conjugated signal, as well as the conditions for energy loss due to grating lobe formation under time harmonic pumping are discussed.