Abstract
Abstract 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.
Highlights
A light wave is characterized by multiple physical quantities defined in spatial and temporal domains, their reciprocal spaces, and the other intrinsic spaces of photons such as polarization [1]
Starting from the comprehensible description of isospectrality, we focus on two subfields: supersymmetric photonics and interdimensional isospectrality, covering analytical methods such as Darboux, Householder, and Lanczos transformations, extraordinary phenomena in phase matching, non-Hermitian potentials, and higher-dimensional physics, and device applications such as multimodal filtering and broadband switching
In the context of independent handling of wave quantities, we have reviewed cornerstones in the field of designing isospectral photonic systems, focusing on the engineering of photonic structures based on analytical methods
Summary
A light wave is characterized by multiple physical quantities defined in spatial and temporal domains, their reciprocal spaces, and the other intrinsic spaces of photons such as polarization [1]. Information processing through light waves requires handling such physical quantities in the desired manner, especially independent control of the target physical quantities. Such independent handling of optical quantities is usually a challenging issue due to their mutual connections, which are generally described with nonlinear functions of a large number of system parameters even in a straightforward environment. Consider the eigenfrequencies of a whispering-gallery-mode resonator These physical quantities are determined by multiple parameters, such as the structural boundaries [4] and material compositions [5]. As an example of the independent control of wave quantities, in this review, we introduce the emerging field in photonics, which originates from the concept of isospectrality. We briefly discuss the related field of hyperuniformity and machine learning, which corresponds to the realization of quasi-isospectrality with statistical or numerical tools
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