Full-wave analysis of imaging by the Pendry-Ramakrishna stackable lens

We perform a full-wave analysis of a stackable lens proposed in a recent paper [Ramakrishna , J. Mod. Optics 50, 1419 (2003)]. This lens was suggested for improving subwavelength imaging and can be obtained by splitting a single-layer lens into a set of thinner layers. Our analysis shows that (i) such a lens, which forms a one-dimensional photonic crystal (PC), is a resonator cavity for traveling Bloch waves that cannot leave this PC resonator due to total internal reflection; (ii) imaging is possible outside the band gaps only and no imaging can be achieved in the vicinity of the eigenstates of the PC resonator as well as near the state associated with the excitation of the volume plasmon; (iii) the expected advantage is due to thinning the layers, which results in shifting of both the band edge and the eigenstates toward higher values of the wave number; and (iv) a single-layer lens has the broadest working range compared to a stackable lens with the same elementary layer thickness.