Negative refraction and focusing analysis in a left-handed material slab and realization with a 3D photonic crystal structure

The increasing interest in metamaterials and structures with negative refraction index requires a formulation capable of a full analysis of wave propagation in such materials and structures. Since two-dimensional (2D) problems have been largely explored in the literature, the natural step is a three-dimensional (3D) formulation of these structures. In this paper, (3D) formulation and simulation of a left-handed metamaterial slab using the finite-difference time domain (FDTD) method in conjunction with perfectly matched layers (PMLs) is presented, and also a (3D) photonic crystal (PC) based structure is presented as a candidate for replacing the left-handed medium slab to realize the negative index of refraction on natural dielectric substrates. The results of these simulations are compared with each other, and the resulting outputs of the developed model are in good agreement. The results demonstrate numerically the focusing of the field emitted from an omnidirectional line source placed in front of the slab and crystal. Both the source and the focus pattern are away from the slab interfaces at two sides of the slab to have a real, negative perfect image. The dimensions of the simulation domain are set to have both source and image in the resulted plots. The focus pattern shows the ability of a photonic crystal structure in making a true flat lens.