Emission of photon pairs at discontinuities of nonlinearity in spontaneous parametric down-conversion

In order to fulfill the continuity requirements for electric- and magnetic-field amplitudes at discontinuities of χ⁽²⁾ nonlinearity, additional photon pairs have to be emitted in the area of discontinuity. Generalized two-photon spectral amplitudes can be used to describe properties of photon pairs generated in this process that we call surface spontaneous parametric down-conversion. The spectral structure of such photon pairs is similar to that derived for photon pairs generated in the volume. Surface and volume contributions to spontaneous down-conversion can be comparable as an example of nonlinear layered structures shows.