Optical spatial mode sorter of azimuthal and radial components

Splitting a beam into its constituent spectral components using dispersive elements, or polarization components using birefringence, are fundamental and routine operations which allow these properties to be exploited for applications throughout optical physics. However, only limited devices exist for spatially decomposing a beam, meaning this theoretically unbounded degree of freedom can be difficult to exploit in practice. Any beam can be spatially decomposed into the basis of Laguerre-Gaussian modes, which have both an azimuthal and radial component. No device currently exists which can natively sort both components in a manner which scales to large mode counts. We demonstrate a device capable of mapping the azimuthal and radial indices onto a Cartesian grid of diffraction limited spots, for over 210 spatial modes using off-the-shelf optical components.