Dual localizations for second-harmonic generations using left-handed materials

Abstract

We show that dual localized modes can be achieved in defective one-dimensional photonic crystals containing left-handed materials. By inserting a nonlinear defect into a photonic crystal formed by stacked alternating left-handed materials and air layers, defective modes for fundamental wave and second-harmonic signal inside the zero-n¯ gap and a Bragg gap are formed, respectively. We present a theory in designing the whole structure, and show that a giant enhancement of second-harmonic generation is achieved. The merits and character of such a scheme comparing with that in ordinary photonic crystals are discussed.