Figure 1. Schematic of a SUSY-inspired non-Hermitian mode-selection system (the structures are assumed to be invariant in the y and z directions).

Starting from a -symmetric waveguide in the unbroken phase (i.e., real eigenspectrum, with three propagating modes in this example), a SUSY-partner waveguide is constructed, whose modes are perfectly phase-matched with the original ones with the exception of one modal order (n = 2 of the original waveguide, in this example) that is removed [cf. Eqs. (12) and (13)]. By placing in close proximity the two waveguides, the phase-matched modes couple periodically between the two waveguides, and can be filtered out via a slight loss unbalance in the SUSY-partner waveguide. As a result, the original waveguide supports only the n = 2 mode.