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The transverse structure of light is recognized as a resource that can beused to encode information onto photons and has been shown to be useful toenhance communication capacity as well as resolve point sources insuperresolution imaging. The Laguerre-Gaussian (LG) modes form a complete andorthonormal basis set and are described by a radial index p and an orbitalangular momentum (OAM) index l. Earlier works have shown how to build a sorterfor the radial index p or/and the OAM index l of LG modes, but a scalable anddedicated LG mode sorter which simultaneous determinate p and l is immature.Here we propose and experimentally demonstrate a scheme to accomplish completeLG mode sorting, which consists of a novel, robust radial mode sorter that canbe used to couple radial modes to polarizations, an l-dependent phase shifterand an OAM mode sorter. Our scheme is in principle efficient, scalable, andcrosstalk-free, and therefore has potential for applications in opticalcommunications, quantum information technology, superresolution imaging, andfiber optics.

Realization of a scalable Laguerre-Gaussian mode sorter based on a robust radial mode sorter