The independent tailoring of wave quantities lays the foundation for controlling wave phenomena and designing wave devices. The concept of isospectrality, which suggests the existence of systems that provide identical spectra, has inspired a novel route to the spectrum-preserved engineering of wave–matter interactions in photonics, acoustics, and quantum mechanics. Recently, in photonics, constructing isospectral optical structures has become an emerging research topic to handle the intricate spectral responses of the systems composed of many-particles or inhomogeneous materials. The cornerstones in this field have stimulated the realization of non-Hermitian systems with real eigenspectra, one-dimensional structures exhibiting higher-dimensional physics, and novel engineering methodologies for broadband devices such as phase-matched multiplexers and multimodal lasing platforms. Here we review recent achievements based on isospectrality in photonics. We outline milestones in two different subfields of supersymmetric photonics and interdimensional isospectrality. We illustrate that isospectrality has paved the way for the independent control of wave quantities, showing great potential for the analytical and platform-transparent design of photonic systems with complex structures and materials.

Resolving spatial and temporal complexities in wave–matter interactions is essential for controlling the light behavior inside disordered and nonstationary systems and therefore achieving high capacity devices. Although these complexities have usually been studied separately, a few examples exploiting both degrees of freedom have derived intriguing phenomena such as hyper‐transport in evolving disorder and topological phenomena in synthetic dimensions. Here, engineering active disorder—disordered structures with external modulation—is proposed by employing deep neural networks. A functional regressor and a material evaluator are developed to enable inverse design of active disorder with target wave responses and evaluation of disordered structures according to the wave response controllability, respectively. By machine engineering deep‐subwavelength disorder including a phase change material, functional disorder for light is revealed, which leads to angle‐selective or broadband digital switching. A generative configuration of the neural network utilizing a single wave metric is also developed to realize a family of disordered structures with independent engineering of multiple wave properties, in contrast to the traditional engineering of disorder with a specific order metric. This approach establishes realization of reconfigurable devices by exploiting the spatiotemporal complexity in wave mechanics.

No abstract