Focusing Analysis and Negative Refraction without Negative Effective Index in a Three-Dimensional Photonic Crystal Structure

Since two-dimensional (2D) photonic crystal (PC) problems have been largely explored in the literature, the natural step is a three-dimensional (3D) formulation of these structures. In this paper, negative refraction effect that does not employ negative effective index of refraction which involves (3D) photonic crystal, is formulated using the finitedifference time-domain (FDTD) method in conjunction with perfectly matched layers (PMLs). To illustrate focusing phenomenon, a flat (PC) base lens is designed and simulated. The results demonstrate numerically the focusing of the field emitted from an omni-directional line source placed in front of the crystal. Both the source and the focus pattern are away from the slab interfaces at two sides of the slab to have a real, perfect image. Dimensions of the simulation domain are set to have both source and image in the resulted plots. The focus pattern shows the ability of photonic crystal structure to make a true flat lens.

Keywords:

Negative Refraction , Photonic Crystal Flat Lens , 3D FDTD Method , Perfectly Matched Layers