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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.

The expected solution for overcoming this bottleneck includes near-or in-memory computing, [2] which imposes memory functions on processing units or vice versa. A representative example is found in electronics: the memristor, which is the so-called missing fourth circuit element. [3,4] The nonvolatile analog memory functions incorporated with Ohm's law and Kirchhoff 's law in an electronic memristor enable in-memory signal processing for artificial neural networks. [5] On the other hand, the realization of an in-memory processing unit in integrated photonics is not yet successful, especially for all-optical devices, although some insightful memory-related applications have been demonstrated such as stopping light, [6] electro-optical quantum memristors, [7] flip-flop memory, [8] and all-optical integrators. [9] To realize a photonic in-memory processor, its unit element must satisfy the following design criteria: multiple error-robust optical memory states and efficient transitions between them. First, the unit element needs to support optical states that are robust to possible noise or defects in its operation to stably memorize the state of light. Second, similar to a one-transistor-one-memristor (1T1R) configuration in electronics, [5] the unit element should include a toolkit for bidirectional transitions between multiple memory states. Notably, these criteria should be satisfied with a platform that is integratable with all-optical signal processors, for example, allowing state-preserving readout of the memory states. However, these criteria-the robustness of optical states to possible defects and the energy-efficient tunability-are usually contradictory, as proven in topological [10] and disordered photonics [11] and sensing applications. [12] The design of a photonic memristor-analogous unit for in-memory processors is thus not a straightforward task.In this paper, we propose an all-optical building block for photonic in-memory processors by exploiting dynamical parity-time (PT)-symmetric systems. We classify PT-symmetric phases and analyze the Lyapunov stability [13] for a triatomic PT-symmetric system including saturable nonlinearities. The analysis shows the coexistence of topologically protected stable states, that is, oscillation quenching states. We also demonstrate that the building block allows incoherent switching between these oscillation quenching states through all-optical modulations. With the simultaneous achievement of topology-enabled error robustness and all-optical transition in a platform integratable with all-optical signal processors, our study will pave the way for realizing robust photonic in-memory processors.The in-memory processor has played an essential role in overcoming the von Neumann bottleneck, which arises from the partition of memory and a processing unit. Although photonic technologies have recently attracted attention for ultrafast and power-efficient in-memory computing, the realization of an alloptical in-memory processor remains a challenge. This difficulty originates...

Recently, there has been increasing interest in the temporal degree of freedom in photonics due to its analogy with spatial axes, causality and open-system characteristics. In particular, the temporal analogues of photonic crystals have allowed the design of momentum gaps and their extension to topological and non-Hermitian photonics. Although recent studies have also revealed the effect of broken discrete time-translational symmetry in view of the temporal analogy of spatial Anderson localization, the broad intermediate regime between time order and time uncorrelated disorder has not been examined. Here we theoretically investigate the inverse design of photonic time disorder to achieve optical functionalities in spatially homogeneous platforms. By developing the structure factor and order metric using causal Green’s functions for disorder in the time domain, we propose an engineered time scatterer, which provides unidirectional scattering with controlled scattering amplitudes. We also show that the order-to-disorder transition in the time domain allows the manipulation of scattering bandwidths, which makes resonance-free temporal colour filtering possible. Our work could advance optical functionalities without spatial patterning.

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.