Second harmonic generation by matching the phase distributions of topological corner and edge states

Second harmonic generation (SHG) in topological photonic crystals is chiefly concerned with frequency conversion between the same topological states. However, little attention has been paid to the effect of coupling between different topological states on the SHG. In this study, we propose a method for achieving optimal SHG in a topological cavity by matching the phase distributions of the electric fields of the topological corner state (TCS) and topological edge state (TES). Our results show that the intrinsic efficiency can be improved when the phase distributions of the fundamental wave within the TCS and the second harmonic wave within the TES have the same symmetry. Otherwise, conversion efficiency will be greatly inhibited. With this method, we achieved an optimal intrinsic efficiency of 0.165%. Such a platform may enable the development of integrated nanoscale light sources and on-chip frequency converters.