  We propose to use a continuous supersymmetric (SUSY) transformation of a
dielectric permittivity profile in order to design a photonic mode sorter. The
iso-spectrality of the SUSY transformation ensures that modes of the waveguide
preserve their propagation constants while being spatially separated. This
global matching of the propagation constants, in conjunction with the adiabatic
modification of the refractive index landscape along the propagation direction
results in the negligible modal cross-talk and low scattering losses in the
sorter. We show that a properly optimized SUSY mode sorter outperforms a
standard asymmetric Y-splitter by reducing the cross-talk by at least two
orders of magnitude. Moreover, the SUSY sorter is capable of sorting either
transverse-electric or transverse-magnetic polarized modes and operates in a
broad range of wavelengths. The design proposed here paves the way toward
efficient signal manipulation in integrated photonic devices.
