  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.
