Interferometric sorting of temporal Hermite-Gauss modes via temporal Gouy phase

We propose a device consisting of $m$ Mach-Zehnder interferometers and realizing sorting of the first ${2}^{m}$ temporal Hermite-Gauss modes of light passing through it by adjusting the accumulated temporal Gouy phase acquired by every mode. This mode-order-dependent phase shift is achieved by a fractional Fourier transform realized by a time lens in one of the interferometer's arms. We consider application of such a sorter with just two interferometers to sorting the Schmidt modes of a photon pair generated in spontaneous parametric downconversion and find the theoretical lower bound on the cross-talk probability of 5.5%.