Superluminal and negative delay times in isotropic-anisotropic one-dimensional photonic crystal

Abstract

In this work, we investigate the possibility of superluminal and negative delay times for electromagnetic wave propagation in a linear and passive periodic structure consisting of alternating isotropic and anisotropic media. This phenomenon is due to the birefringence of the anisotropic layers of the structure. By adjusting the orientations of these layers, the delay times of transmitted waves can be controlled from subluminality to superluminality and vice versa. Numerical results indicate that the apparent superluminal propagation of light occurs inside the photonic band-gaps when the principal axes of the anisotropic layers are parallel or perpendicular to the fixed axes. For other orientations of these layers, tunneling and superluminal regimes appear inside the photonic bandgaps and in the allowed bands for frequencies close to the transmission minima. The effect of the number of unit cells of the photonic crystal structure on the propagation of light with superluminal and negative delay times is also investigated. We show that the structure exhibits the Hartman effect in which the tunneling delay time of the electromagnetic wave through the photonic band-gap of the structure converges asymptotically to a finite value with increasing the number of layers. The Green's function approach has been used to derive the transmission and reflection coefficients, the density of states, and the delay times of electromagnetic waves propagating through the structure. The control of the magnitude and the sign of the delay time of light propagation represent a key point in slow and fast light technologies. The proposed structure in this study represents a new system for controlling the delay times of wave propagation without a need of active or non-linear media as well as lossy or asymmetric periodic structures.