A birefringent phase-matching method in multilayered hyperbolic metamaterials

Multilayered hyperbolic metamaterials (MHM) is proposed to create phase matching of fundamental-frequency (FF) and third-harmonic (TH) field components with a unique dispersion provided by the engineered MHM structure for third-harmonic generation in ultra-short pulse regime. In this work, we analytically study the ensuing possibilities and demonstrate that a birefringent phase-matching can be alternatively achieved with a wide range of involved material parameters and optimal engineering of MHM structure. When the phase-matched conditions is satisfied by birefringent phase-matching method, the growth rate of the TH intensity generating as a function of the nonlinear-optical interaction length to be obviously increased. This method opens new ways of improving the conversion efficiency of frequency tripling regardless of the coherence length in the bulk of a nonlinear material.