Highly efficient second-harmonic generation from a two-dimensional linear–nonlinear photonic crystal heterostructure

The theory of second-harmonic generation (SHG) in two-dimensional (2D) linear–nonlinear photonic crystal (PC) heterostructure has been developed by means of transmission matrices and a Green’s function approach based on lattice sums. Using this method, we can calculate the conversion efficiency of second-harmonic waves in various 2D PC heterostructures. Not only has great enhancement of SHG been observed when the frequencies of both fundamental frequency and second frequency waves are located at the photonic band edges, but some unique phenomena for the SHG based on resonant states in the heterostructure have also been found. The resonant SHG can appear at the corresponding frequency of the resonant state in the range of 160° of the incident angle around the normal direction, although the value of the SHG changes with the incident angle. The second-harmonic conversion efficiency appears to have a higher value in the heterostructure containing several nonlinear PC slabs because of the competition between phase matching and the decrease in transmittance. We believe that these findings are very beneficial for the design of SHG devices.