Engineering isospectrality in multidimensional photonic systems

Abstract Selective manipulation of energy levels plays an essential role in realizing multichannel wave devices. One the representative examples is to utilize concept quasi-isospectrality: a family systems with almost identical spectrum except for part levels. Most approaches toward quasi-isospectrality have employed analytical methods based on symmetry or tridiagonalization, such as supersymmetry, Householder, Lanczos transformations. Although provide deterministic and stable designs operator factorizations, mathematical strictness at same time, hinders isospectral engineering given multidimension. Here we develop semi-analytical method isospectrality multidimensional photonic systems. The provides systematic perturbation target level shifts by decomposing allowed form system changes into basis. We demonstrate lower-, higher-, random-order states while imposing designed other states. stability analysis shows that accuracy determined ranges state numbers strength. systematic, free-form, natures proposed show great potential platform-transparent design