Laguerre-Gaussian mode sorters of high spatial mode count

We discuss the extension of Laguerre-Gaussian (LG) mode sorters to higher spatial mode counts. LG mode sorters based on multi-plane light conversion were recently demonstrated. The device consist of a cascade of phase planes separated by free-space propagation which performs a spatial decomposition in the Laguerre-Gaussian basis. Whereby an incoming beam, described by a basis of N LG modes is mapped onto a Cartesian array of N Gaussian spots in the output plane. Each spot in the array contains a particular LG spatial component of the original beam. Previously, LG mode sorters have been demonstrated supporting as many as 325 modes using 7 planes. In this paper we present a design for a device that supports 1035 modes corresponding with the first 45 degenerate mode groups using 14 planes. At the centre wavelength, the device has a theoretical insertion loss of 2.10dB. The lowest loss LG mode is -1.65dB and the highest loss LG mode is -3.22dB. The average crosstalk over all modes is 12.75dB. The worst-case mode has a crosstalk of 9.20dB.