  Integrated Jx photonic lattices, inspired by the quantum harmonic oscillator
and due to their equidistant eigenvalue spectrum, have been proven extremely
useful for various applications, such as perfect imaging and coherent transfer
of quantum states. However, to date their large-scale implementation remains
challenging. We apply concepts from supersymmetry to construct two-dimensional
(2D) systems with spectra identical to that of one-dimensional (1D) Jx
lattices. While exhibiting different dynamics, these 2D systems retain the key
imaging and state transfer properties of the 1D Jx lattice. Our method extends
to other systems with separable spectra, facilitates experimental fabrication,
and may increase robustness to fabrication imperfections in large-scale
photonic circuits.
