Concave and convex photonic barriers in gradient optics

Propagation and tunneling of light through photonic barriers formed by thin dielectric films with continuous curvilinear distributions of dielectric susceptibility across the film, are considered. Giant heterogeneity-induced dispersion of these films, both convex and concave, and its influence on their reflectivity and transmittivity are visualized by means of exact analytical solutions of Maxwell equations. Depending on the cut-off frequency of the film, governed by the spatial profile of its refractive index, propagation or tunneling of light through such barriers are examined. Subject to the shape of refractive index profile the group velocities of EM waves in these films are shown to be either increased or deccreased as compared with the homogeneous layers; however, these velocities for both propagation and tunneling regimes remain subluminal. The decisive influence of gradient and curvature of photonic barriers on the efficiency of tunneling is examined by means of generalized Fresnel formulae. Saturation of the phase of the wave tunneling through a stack of such films (Hartman effect), is demonstrated. The evanescent modes in lossy barriers and violation of Hartman effect in this case is discussed.