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