Analysis of a microwave lens formed using a pair of frequency selective surfaces comprised of back-to-back doubleperiodic wire arrays interconnected through phase-conjugating microwave circuitry is given in this paper. It is shown that such a structure when illuminated with a plane wave generates a phase-conjugated forward-transmitted plane wave which experiences negative refraction. Negative refraction makes it possible to produce focusing of wave packets incident on such structures both in the far- and near-field regions. We provide analytical formulation of the problem and develop a rigorous calculation of the EM field transmitted through the structure: i) when excited by a plane wave; and ii) due to an electric line source suspended above it. Numerical simulations illustrate the focusing properties of the proposed lens. These properties are shown to include half wavelength compression of the focused line source image in the transverse direction in the far-field zone. A physical explanation of why