Resonance-forbidden second-harmonic generation in nonlinear photonic crystals

Second-harmonic generation is widely used in optoelectronics including both the classical and quantum regimes. In planar nanophotonics structures, people would expect that second harmonic waves along the vertical direction can always be generated if appropriate quadratic nonlinearities and pumping beams are present since the phase-matching condition is automatically satisfied due to the ultra-thin thickness. 

Here we present an abnormal phenomenon we call “resonance-forbidden second-harmonic generation” in a nonlinear photonic crystal slab. We show that the second harmonic fields of certain modes supported by the structure can be completely non-radiative. As a result, no pumping energy is transferred into the second harmonic frequency and the second harmonic generation is completely suppressed. We identify two mechanisms that can achieve this phenomenon: symmetry protection and parameter tuning through numerical simulation.