Imaging properties of dielectric photonic crystal slabs for large object distances

We extend the understanding of the imaging properties of dielectric photonic crystal slabs to object distances that are larger than the slab thickness. We specifically consider hexagonal crystal lattices in the second band. For object distances smaller than the slab thickness, the image distance is a negative linear function of the object distance as expected for negative refractive index materials. The effective refractive index extracted from this linear object-image relation is close to the negative unity value calculated for infinite photonic crystal using the plane wave expansion method. In contrast to previous predictions, we find that a real image can still be formed for object distances up to twice the slab thickness. In this regime the image distance changes little as the object distance increases, and can thus be described as the saturated image regime. Sub-wavelength resolution performance can be approximately maintained even for these larger object distances. The full-width half-maximum spot size at the image is approximately (0.43-0.55)lambda up to object distances 1.5 times the slab thickness. By evaluating the image angular frequency spectrum we show that this sub-wavelength resolution imaging at larger object distances is due to evanescent waves that arise within the slab, rather than being directly transferred from the object. The eventual loss of image resolution is due to interference side lobes which enter the image plane.