Bloch harmonics and focusing properties in the photonic crystal planoconcave lens structure

Abstract

Focusing properties of a plane wave by the photonic crystal (PC) concave lens placed in the air environment are studied through the finite-difference time-domain technique. The PC concave lens works in the frequency window located in the second transversal electric (TE)-polarized photonic band. A good-quality focus of a plane wave can form out of the planoconcave lens, while a plane wave is also formed for a point source placed at the focus point consistent with the analysis of the band structure and the equifrequency contours. Besides the plane-wave expansion method, we also analyze the Bloch harmonics inside the region of planoconcave lens with the Fourier analysis method. It is shown that the Bloch mode, which consists of more than one spatial frequency, contributes to the focus. The results show that the spatial frequencies in the second Brillouin zone are mainly generated due to the periodic potential arising from the PC or the existence of the interfaces.