image: Figure 1 | Graphical abstract of Lifshitz-like states phenomenology in Hyperuniform Disordered Photonic Networks. A schematic of the two-dimensional hyperuniform disordered photonic network investigated in this work is shown, highlighting the underlying correlated disorder and two four-sided topological defects that support Lifshitz-like localized modes, here represented in a hybridized bonding configuration. A representative electromagnetic field distribution of the resulting photonic molecule is overlaid, illustrating light confinement around the defects and their spatial overlap. Hyperspectral maps were experimentally acquired with sub-diffraction resolution using an aperture SNOM tip in illumination/collection geometry, sketched on the left. On the right, the localization length is plotted for optical modes near the lower photonic bandgap edge for different degrees of structural order (blue to red, with red indicating the highest order considered). Three spectral regions can be distinguished. Region I corresponds to Lifshitz-like states, region II to conventional Anderson-localized modes, and region III to extended Anderson-like modes. In region II, localization length decreases as disorder increases, whereas region I shows the opposite trend, reflecting the different physical origin of the two localization mechanisms. Between regions I and II, the localization-length curves cross within a narrow spectral interval, marking the crossover between the two localization regimes. Region III is dominated by extended modes exhibiting spectral level repulsion.
Credit: Nicoletta Granchi et al.
Disorder, long regarded as a limitation in photonics, is increasingly being harnessed as a resource for controlling light. Recent advances in nanophotonics are redefining its role, turning structural correlated disorder into a design principle rather than a fabrication imperfection. In this context, hyperuniform disordered (HuD) photonic networks, structures positioned between order and randomness, have emerged as a distinctive platform for controlling light localization and transport. In a new paper published in Light: Science & Applications, Nicoletta Granchi (University of Florence, Department of Physics and Astronomy, Italy) and colleagues reveal that a single HuD architecture can host an unexpectedly rich landscape of optical modes.
The work, carried out by the team led by Professor Francesca Intonti (University of Florence, Italy), in collaboration with Professor Marian Florescu (University of Southampton, UK) and co-workers, provides direct experimental evidence of multiple light-transport regimes that are usually studied separately. A central challenge in disordered photonics is distinguishing localized from delocalized modes and identifying their physical origin. By combining large-scale numerical simulations with hyperspectral near-field optical microscopy, the authors show that delocalized modes in HuD structures exhibit spectral correlations governed by level repulsion, a hallmark of interacting states known from quantum chaos and complex systems. This places delocalized HuD modes within the same universality class as chaotic quantum systems and provides a stringent benchmark for identifying true delocalization. At the same time, it shows that these modes are not randomly distributed in frequency, but instead form a correlated and stable spectrum, in sharp contrast to Anderson-localized states, which can cluster irregularly and unpredictably.
The most intriguing results, however, emerge where light becomes localized. The team shows that not all localized modes share the same origin. Alongside conventional Anderson localization, driven by multiple scattering, they identify a distinct class of tightly confined states promoted inside the photonic bandgap of the HuD architecture. Rooted in four-sided topological defects, these Lifshitz-like states emerge not as rare statistical anomalies, but as localized modes whose spatial and spectral positions can be anticipated at the design stage. “We argue that the modes associated with four-sided cells, which form a miniband within the photonic band gap, can be interpreted as the photonic analogue of Lifshitz states known from electronic systems. In a HuD geometry, their topological origin implies a degree of predictability in their spatial location,” the authors explain. Because the study further shows that these states can hybridize into coupled “photonic molecules”, it marks the first step toward chains of interacting localized modes, so-called necklace states, with important consequences for light transport in disordered media.
Together, these results establish HuD photonic networks as a uniquely versatile platform in which spectral correlations, localization, and mode coupling can coexist and be deliberately controlled within a single architecture. By bringing together regimes that are usually treated separately, the work opens a new route toward disorder-enabled photonic functionalities based on correlated spectra and interacting localized states rather than isolated resonances. This shift enables unprecedented control over light transport and confinement, with direct implications for robust random lasing, reconfigurable optical filtering, and multiplexing schemes that exploit spectral correlations. More broadly, the ability to design and couple localized modes in a controlled disordered environment lays the foundation for scalable implementations of complex photonic functionalities, including neuromorphic processing and quantum photonic architectures where controlled interactions between modes are essential.
Journal
Light: Science & Applications
Article Title
Spectral level repulsion and Lifshitz-like states in hyperuniform disordered photonic networks