Two-Photon X-Ray Diffraction.

The interference pattern of a circular photon source has long been used to define the optical diffraction limit. Here we show the breakdown of conventional x-ray diffraction theory for the fundamental case of a "source," consisting of a back-illuminated thin film in a circular aperture. When the conventional spontaneous x-ray scattering by atoms in the film is replaced at high incident intensity by stimulated resonant scattering, the film becomes the source of cloned photon twins and the diffraction pattern becomes self-focussed beyond the diffraction limit. The case of cloned x-ray biphotons is compared to and distinguished from the much studied case of entangled optical biphotons.