Induced group and phase velocity changes by a cascaded quadratic nonlinear interaction within a one-dimensional photonic crystal

Abstract

We study the cascaded quadratic nonlinear interaction between a weak fundamental and an intense second-harmonic beam within a finite one-dimensional photonic crystal with a defect. We show that, in the neighborhood of the defect resonance, this quadratic interaction induces changes in the value of the effective index of refraction and in the effective group velocity of the fundamental wave as well. We show that the effective group velocity can actively be controlled by means of this cascaded interaction. In fact, the strongly reduced effective group velocity found at the resonance of the linear periodic structure is shown to be restored to a value close to its value in the homogeneous material. These effective group and phase velocity active changes were studied in two cascading cases. Both effects are present when the nonlinear interaction modifies the defect resonance.