Improved superlensing in two-dimensional photonic crystals with a basis

We study propagation of light in square and hexagonal two-dimensional photonic crystals. We show, that slabs of these crystals focus light with subwavelength resolution. We propose a systematic way to increase this resolution, at an essentially fixed frequency, by employing a hierarchy of crystals of the same structure, and the same lattice constant, but with an increasingly complex basis.