Lower bound of group velocity imposed by non-linearities induced by external sources in photonic and phononic crystals with losses

Abstract

In the present work, it has been studied how the group velocity, in waves propagating trough photonic and phonic crystals with losses, is affected by non-linearities induced by external sources. The work takes as starting point the mathematical approach exposed in the article called ‘Effect of loss on the dispersion relation of photonic and phononic crystals’ of V Laude et al, where it is considered, as a plausible hypothesis, that the non-linearities are only induced by external mechanisms and not by the modes propagating through the structure. The research has been focused on some points of the band structure that are of great interest: frozen modes and in the middle of bandgap. A strong dependency of the lower bound of group velocity has been found as a function of points considered. As a main result, it has been observed that the non-linear effects induced and material losses considered can have opposite effects on the group velocity, observing cases where the lower bound of group velocity is reduced below the limits established by the work of V Laude et al.On the other hand, it has been found that the non-linearities limit the group velocity in the middle of bandgap, disappearing the classical Hartman effect.