Mode-coexistent phase match condition for second harmonic generation in photonic crystal slabs consisting of centrosymmetric materials

Aimed at second harmonic generation (SHG) in photonic crystal slabs (PCS) consisting of centrosymmetric materials, we proposed a method based on eigenmodes in PCS, without resorting to birefringence or quasi phase matching, to realize a phase matching condition (PMC). The experimental and theoretical analysis shows that PMC can be achieved when two conditions coincide. One is that both the fundamental mode and the second harmonic mode are the eigenmodes of the PCS. The other is that they are excited simultaneously. Combined with PMC, PCS consisting of centrosymmetric materials provide a way to obtain SHG from nanoscale structures.