Gratings weave coherence carpets with non-diffracting coherence strands

When a spatially partially coherent optical field is transmitted by a grating, its two-point correlation function is found to show an intriguing behavior: it propagates along discrete diffraction orders and, with increasing coherence, gradually weaves a “coherence carpet” with an intricate fractional structure. Additionally, a low-coherence input field produces a “non-diffracting coherence needle”: a narrow (∼ λ ) longitudinal strand in which the correlation is a linear function of the lateral separation between two points. Such needles may be used as a testbed to explore spatial coherence effects at the wavelength scale. Because the paraxial wave equation has the same mathematical form as Schrödinger’s equation, similar correlation effects as reported here are expected to occur for matter waves as well.