Radial diffraction of light in the radial momentum state space

While linear or angular position and momentum can be linked by a continuous or discrete Fourier transform, there are some subtle problems in the analogous Fourier relationship between radial position and radial momentum in history. Here we exploit radial position and newly introduced radial momentum variables to report a radial version of light's diffraction. The mask with single or multiple radial slits confines the light to a radial transmission function. As a result, in the radial momentum state space, we can observe the diffraction sidebands generated on the transmitted light due to a transverse restriction of the radial range. Our experimental results clearly reveal the intriguing diffraction behaviors between radial position and radial momentum variables at the single-photon level, making them another candidate for fundamental tests of quantum mechanics and for a variety of quantum information applications.