Finite-sized photonic crystal slabs have an effective refractive index that differs from that
calculated for infinite structures. We investigate the imaging characteristics of such slabs with nonideal
effective refractive index neff, namely |neff|<1 and |neff|>1 at the 2nd band of hexagonal lattice,
and observe an approximately linear object-image relation and saturated imaging. We focus on the slab
aperture effect on imaging and analyze the mechanisms of image formation. For the finite-sized
photonic crystal slab with fixed object distance, due to beam leakage, there is a limiting aperture size
beyond which the image resolution and image distance remain almost unchanged. A larger aperture
does not necessarily lead to higher image resolution. In order to be focused by the slab with negative
refraction, the physical source or the object must contain sufficient transversal wavevectors or higher
transversal spatial frequencies. The analyses are for the cases where propagating waves dominate imaging formation.
Photonic crystals (PhCs) exhibiting negative refraction have attracted much attention in recent years, with a vast majority of this research focusing on subwavelength imaging. Although the possibility of an open cavity using such a PhC is mentioned in Notomi's pioneering work, fewer researchers have addressed this issue except one study of an open cavity using three 60-degree PhC wedges of the hexagonal lattice. This paper reports our study of several different open cavity configurations in hexagonal and square lattices. To form an open cavity using PhC with negative refraction, there are many parameters to optimize, such as the lattice type, lattice period, the diameter of the hole or rod, materials, and the geometrical configurations. We first propose several configurations for open cavities in general, including two square slabs, two or more prism slabs, and one slab with two reflectors; Then we demonstrate some results obtained from photonic crystals with square and hexagonal lattices, simulated by the use of the finite-difference time-domain (FDTD) method. It is shown that resonance can occur at the first band and higher bands. The Q-factor obtained is about 280 to 400, which can be improved by optimizing the surface terminations of the photonic crystal prisms.
This paper reports a new super-resolution, "saturated" imaging method using a flat slab of photonic
crystal with negative refraction. The photonic crystal has hexagonal lattice with holes in dielectric material
with an index of 3.6. When the operating normalized frequency is around 0.30, the effective refractive
index is -1. Such a flat slab lens can tolerate disk deformation of approximately one-wavelength or more
while maintaining the same super-resolution as the near-field imaging of the photonic crystal slab. The
object distance can be as large as twice the slab thickness, and the resolution is about 0.43λ.