Cerenkov second harmonic generation revisited: existence of phase matching

We show that in Cerenkov second harmonic generation the phase-matching condition is not automatically satisfied. The new concept of a Cerenkov phase-matching surface is introduced and the expression of the Cerenkov phase-matching condition is derived. We also show that the Cerenkov scheme includes second harmonic generation at distributed couplers. For example, use of grating couplers leads to grating-assisted Cerenkov second harmonic generation. These are important results which modify the understanding of the physics underlying Cerenkov frequency doubling.