Second harmonic generation in disordered media: Random resonators

We theoretically study the effect of random resonators on the conversion efficiency of fundamental mode propagating through disordered nonlinear dielectric film. Only resonators with double-resonant properties, i.e., which can trap both the fundamental and second harmonic modes, contribute to local generation of the second harmonic light of high intensity. We calculate the density of such resonators. The parameters of the random media under which all the random resonators with the given quality factors have the double-resonant properties are found.