講演題目: Photonic physics beyond the exceptional point: Defective Spectra in Non-Hermitian Photonics
講師: Henning Schomerus (Lancaster University, UK, Professor)
日時: 2026年7月9日(木) 16:30 – 18:00
場所: 北海道大学工学部 C325
要旨:
Over the past decade, non-Hermitian physics has developed into a powerful framework for understanding open photonic systems, where gain, loss, and coupling to the surrounding environment are treated as essential physical ingredients rather than as unwanted sources of dissipation. This perspective has led to a range of new phenomena and applications that are not accessible within conventional Hermitian descriptions.
One area that has attracted particular attention is sensing. A large body of work has shown that sensors based on resonance splitting can display fundamentally new behavior when operated in non-Hermitian regimes, where resonances are connected through complex couplings and decay channels. A key feature of such systems is the appearance of exceptional points (EPs), special spectral degeneracies at which not only the resonance frequencies but also the corresponding spatial mode profiles coalesce. EPs arise naturally in many open photonic platforms, including micro-ring resonators and coupled cavity systems, where coupling to the environment produces the non-orthogonality required for their formation. As a result, they modify the underlying structure of the system’s state space and lead to a variety of unusual physical effects.
Among the most prominent consequences of EPs are nontrivial topological properties in parameter space, asymmetric and chiral mode conversion, and an anomalously enhanced and nonanalytic response to external perturbations. These effects have motivated extensive theoretical and experimental activity. Concrete manifestations include modified resonance spectra and super-Lorentzian line shapes, which can appear, for example, in the quantum noise of radiation emitted from suitably designed optical cavities. More broadly, advances in the understanding of symmetry and topology in non-Hermitian systems have opened routes toward applications such as topological lasers, directed amplification, and robust control of light in open environments.
After providing an introduction to these concepts and a general overview of the underlying physics, I will focus on a central mathematical question that arises in the description of defective non-Hermitian systems. I will then show how the resulting framework can be used to uncover and design new physical phenomena associated with a generalized form of exceptional point.
Traditionally, EPs are described using generalized spectral decompositions based on the Jordan normal form. While mathematically correct, this description has important limitations. The Jordan normal form changes discontinuously when a system moves between different spectral configurations, making it difficult to compare and classify different degeneracy scenarios within a single framework. Furthermore, the most general Jordan normal form allows several Jordan blocks to be associated with the same eigenvalue. Such situations correspond to defective eigenvalues that support multiple independent eigenmodes and therefore extend beyond the conventional exceptional-point scenarios commonly studied in photonics.
To fully understand the physics of defective non-Hermitian systems, a description is needed that treats all of these possibilities on equal footing and connects them directly to experimentally observable behavior. I will present a unified and efficient framework that accomplishes this task. The approach provides a systematic way to classify, characterize, and design systems hosting both conventional exceptional points and a broader class of degeneracies that we refer to as fragmented exceptional points (FEPs). The method translates the physical signatures of these degeneracies into explicit algebraic conditions, allowing them to be identified and engineered in arbitrary finite-dimensional systems.
I will then demonstrate the power of this framework through several concrete examples. First, I will discuss topological model classes that support a rich collection of FEPs alongside conventional EPs and show how the different degeneracy structures can be understood within a common language. Next, I will show how the formalism can be used to design what may be called exceptionally deficient systems, in which every eigenvalue in the spectrum is an exceptional point. These systems display distinctive dynamical signatures, including broadband static amplification and non-Abelian adiabatic state amplification.
Finally, I will present a realistic interferometric platform in which FEPs are generated through non-Hermitian beam splitters. This setting provides a direct connection between the mathematical theory and experimentally accessible observables. In particular, it leads to nonanalytic dark-fringe operating conditions and reveals several distinct operational regimes that are governed by non-Hermitian braiding phenomena. Together, these examples illustrate how a unified understanding of defective spectra not only clarifies the mathematical structure of non-Hermitian systems but also enables the design of new photonic devices and functionalities.
Joint work with Subhajyoti Bid.
References
1. S. Bid and H. Schomerus, “Uniform response theory of non-Hermitian systems: Non-Hermitian physics beyond the exceptional point”, Phys. Rev. Res. 7, 023062 (2025).
2. S. Bid and H. Schomerus, “Fragmented exceptional points and their bulk and edge realizations in lattice models”, Phys. Rev. B 112, 195433 (2025).
3. S. Bid and H. Schomerus, “Exceptionally deficient topological square-root insulators”, Phys. Rev. Res. 8, L012031 (2026).
4. H. Schomerus, “Eigenvalue sensitivity from eigenstate geometry near and beyond arbitrary-order exceptional points”, Phys. Rev. Res 6, 013044 (2024)