Supersymmetric Compactification and Higher-Dimensional Rearrangement of Photonic Lattices

The evolution dynamics of wave-mechanical systems are governed by the full set of their modes and their respective eigenvalues. The key task of transferring arbitrary excitation patterns between two specific planes can therefore be accomplished by an appropriate structure of the eigenvalue spectrum. Along these lines, self-imaging is particularly effective if the spectrum is equidistantly spaced, similar to that of the harmonic oscillator. In finite-size discrete systems, the so-called $J_{\mathrm{x}}$ lattice fulfils this condition and has been employed for the perfect coherent transfer of quantum and classical states alike [1]–[3]. Yet, implementing large-scale $J_{\mathrm{x}}$ arrays remains experimentally challenging, as this class of systems relies on a precise realization of a large number of different yet finely tuned nearest-neighbor interaction strengths spanning a substantial dynamic range. To overcome these limitations, we leverage the concept of supersymmetric (SUSY) photonics [4], [5] and present a method to design families of compact two-dimensional equivalent systems that inherit the spectral and key dynamic features of one-dimensional $J_{\mathrm{x}}$ arrays while requiring dramatically fewer distinct coupling values [6].