Characteristics of second harmonic generation with a short-pulse laser in nonlinear photonic crystals

Based on a calculation of the dispersion relation and a numerical simulation of the nonlinear wave equations, this paper theoretically analyzes the characteristics of second harmonic generation (SHG) with short pulse laser in one-dimensional photonic crystals (PCs). We propose and demonstrate a simple means for compensating for the group velocity mismatch (GVM), which is accomplished by using PCs in a tilted version. Unlike in the case of conventional bulk crystals, the strong group velocity dispersion (GVD) induced by the periodic structures in PCs plays a big role in nonlinear SHG processes. Similar to the effects of GVM, the effects of GVD in PCs broaden the harmonic pulse and/or decrease the conversion efficiency. For the present structure used in PCs, we show that because of the influences of GVD and the limited bandwidth of PCs, the shortest pulse appropriate for SHG will be around picosecond.