  Improving axial resolution is crucial for three-dimensional optical imaging
systems. Here we present a scheme of axial superresolution for two incoherent
point sources based on spatial mode demultiplexing. A radial mode sorter is
used to losslessly decompose the optical fields into a radial mode basis set to
extract the phase information associated with the axial positions of the point
sources. We show theoretically and experimentally that, in the limit of a zero
axial separation, our scheme allows for reaching the quantum Cram\'er-Rao lower
bound and thus can be considered as one of the optimal measurement methods.
Unlike other superresolution schemes, this scheme does not require neither
activation of fluorophores nor sophisticated stabilization control. Moreover,
it is applicable to the localization of a single point source in the axial
direction. Our demonstration can be useful to a variety of applications such as
far-field fluorescence microscopy.
