Single plane spatial mode sorter

A mode sorter separates a set of <i>M</i> orthogonal spatial modes in a shared input channel into <i>M</i> different output channels. Here we present an analytic derivation and experimental validation of a single plane device for sorting spatial modes from a diverse variety of mode families, including Hermite-Gaussian (HG), Laguerre-Gaussian (LG), and Bessel-Gaussian (BG), with almost no cross-talk. This sorting capability is required for a wide range of applications that employ classical or quantum light. We also show that applying this design in order to sort a set of Orbital Angular Momentum (OAM) modes with zero radial index reproduces the well-known Fork grating configuration. Furthermore, by taking the limit of <i>M</i> → ∞, we present an analytical expression for sorting all the modes of a given family. By operating this device in reverse, it can be used to generate arbitrary modes by illuminating it with a Gaussian beam. The power transmission coefficient for this sorter goes as <i>O</i>(<i>M</i>^-1), and we provide a mathematical proof that this is optimal for any typical arrangement of the detector positions. We further study the sorter's sensitivity to wavelength and random phase noise.