Spontaneous parametric downconversion in linearly uncoupled resonators

We study degenerate spontaneous parametric downconversion in a structure composed of two linearly uncoupled resonators, in which the linear properties of the fundamental and second-harmonic field can be engineered independently. As an example, we show that in this system it is simple to generate photon pairs that are nearly uncorrelated in energy. These results extend the use of linearly uncoupled resonators to the case of second-order nonlinear interactions.