Complex Photonic Systems with Broken Symmetries: Synergetic Effects of Wave Chaos and Non-Hermiticity

In this presentation, I present a novel experimental setup designed to study the influence of reciprocity breaking on light scattering in multimode optical fibers with longitudinal controlled disorder. Scatterers are photo-inscribed into the fibers using a direct laser writing device, and reciprocity breaking is achieved by placing the sample in an external magnetic field to induce Faraday effect. In a near future, the samples will be characterized by measuring the complete transmission matrix, paving the way for coherent wave control in such systems.

Non-Hermitian systems display remarkable response effects that directly reflect a variety of distinct spectral scenarios, such as exceptional points where the eigensystem becomes defective. However, present frameworks treat the different scenarios as separate cases, following the singular mathematical change between different spectral decompositions from one case to another. This not only complicates the coherent description of the response near the spectral singularities where the response qualitatively changes, but also prevents application to practical systems, as the determination of these decompositions is manifestly ill-conditioned. Here we develop a general response theory of non-Hermitian systems that uniformly applies across all spectral scenarios. We unravel this response by formulating an expansion of the Green's function that exclusively involves directly calculable data from the Hamiltonian, smoothly varies with external parameters and energy as spectral singularities are approached and attained, and nevertheless directly captures the qualitative differences of the response in these scenarios. We use this framework to determine the precise conditions for spectral degeneracies of geometric multiplicity greater than unity, and demonstrate that these previously inaccessible scenarios result in unique variants of super-Lorentzian response. Our approach widens the scope of non-Hermitian response theory to capture all spectral scenarios on an equal and uniform footing, identifies the exact mechanisms that lead to the qualitative changes of physical signatures, and renders non-Hermitian response theory fully applicable to numerical descriptions of practical systems.

Exceptional points are spectral degeneracies in open systems where not only the eigenvalues but also the corresponding eigenvectors coalesce. The fundamental reason behind the research interest in exceptional points stems from the enhanced system's sensitivity to external perturbations. Specifically, when a system at an exceptional point of order N is perturbed, the involved eigenvalues diverge generically with a characteristic N-root topology. The resulting eigenvalue splitting depends on the specific kind of perturbation and on a quantity--the spectral response strength--which can be assigned independently of the perturbation to a particular exceptional point. The response strength is therefore a quantitative measure for the system's sensitivity to external perturbations and allows to compare different exceptional points of the same order. So far, the theory for the spectral response strength is restricted to non-Hermitian Hamiltonians on finite-dimensional Hilbert spaces which can occur naturally as an effective description, e.g. within coupled-mode theory. On the other hand, realistic systems described by a wave equation give rise to an underlying infinite-dimensional Hilbert space. In this work we present a scheme to calculate the spectral response strength directly from the numerical results of wave simulations. To do so, the relation between the spectral response strength and the Petermann factor of the eigenstates near the exceptional point is exploited. For a validation of our approach, we consider three different photonic systems: a microring dimer, waveguide-coupled microrings, and a weakly deformed microdisk. For all three cases our approach shows an excellent agreement to results provided by an effective Hamiltonian based on coupled-mode theory.

Previous studies have noted the lasing modes whose intensities are localized along stable periodic orbits by pumping selectively along the orbits. The resonant modes localized along unstable periodic orbits called scar modes are well-known in quantum chaos, however, the localization of them was weak. It is shown that the lasing modes pumped selectively along unstable periodic orbits are strongly localized along the orbits by self-organized optimization.

We explain the structure of chaotic resonance states with arbitrary decay rates in scattering systems in the semiclassical limit [1]. It is given by a multifractal measure from classical dynamics. Numerical results are presented for dielectric cavities and the three-disk scattering system. [1] R. Ketzmerick, F. Lorenz, J. R. Schmidt, Semiclassical Limit of Resonance States in Chaotic Scattering, Phys. Rev. Lett. 134, 020404 (2025).

The coupling between the two different polarizations (TE and TM) is a feature in realistic three-dimensional (3D) optical cavities, that is not present in two-dimensional systems. We find the interaction of polarized modes to be governed by a network of exceptional points that reflects the openness, or non-Hermiticity, of the system. The mode coupling is analyzed using an extended 3D Husimi formalism, which maps the wave function on the cavity surface into phase space [1]. To this end we expand the Husimi function method by applying the formalism to 3D systems. We find it to be a comprehensive and useful way to represent the mode structure of 3D microcavities and confirm characteristic features such as exceptional points [2]. [1] Hentschel et al., Europhys. Lett. 62 636 (2003) [2] Rodemund et al., arXiv:2503.12570

The distribution of resonance poles of chaotic scattering systems is investigated in the semiclassical limit at unprecedented small wavelengths. For the paradigmatic three-disk scattering system, we study the spectral gap towards the real axis, the fractal Weyl law, which counts the number of resonance poles, and the distribution of decay rates. These properties are compared to previous analytical results, e.g. from random matrix theory. In contrast to this system with full escape, systems with partial escape have significantly different properties. For the example of a dielectric cavity, we show that results from random matrix theory cannot explain the distribution of decay rates.

Billiard systems are a widely used and common tool for studying nonlinear dynamics. Over the past decades, theoretical studies have been enriched by experimental realizations, such as optical microcavities and ballistic quantum dots. However, these systems are typically isotropic, and chaotic behavior arises only from deviations of the cavity geometry from the perfect circular symmetry. However, an anisotropy, and thus a symmetry breaking in momentum space (as for light in birefringent optical materials or for electrons in bilayer graphene), can induce chaotic dynamics even in circular cavities [1]. We developed a ray-tracing algorithm to model billiard dynamics in anisotropic media and analyze how anisotropy influences the system’s phase space structure [2]. In addition, we investigate the impact of an additional symmetry breaking in real space on the stability of trajectories and quantify the fraction of stable trajectories by calculating Lyapunov exponents [3]. [1] L. Seemann, A. Knothe, M. Hentschel, Phys. Rev. B 107, 205404, 2023 [2] L. Seemann, A. Knothe, M. Hentschel, New J. Phys. 26 103045, 2024 [3] L. Seemann, J. Lukin, M. Häßler, S. Gemming, M. Hentschel, Symmetry 2025, 17(2), 202

We study theoretical models of three coupled wave guides with a PT-symmetric distribution of gain and loss. A realistic matrix model is developed in terms of a three-mode expansion. By comparing with a previously postulated matrix model it is shown how parameter ranges with good prospects of finding a third-order exceptional point (EP3) in an experimentally feasible arrangement of semiconductors can be determined. In addition it is demonstrated that continuous distributions of exceptional points, which render the discovery of the EP3 difficult, are not only a feature of extended wave guides but appear also in an idealised model of infinitely thin guides shaped by delta functions.

Scale-free localization in non-Hermitian systems is a distinctive form of localization where the localization length of certain eigenstates, called scale-free localized (SFL) states, scales proportionally with the system size. Unlike skin states, which have size-independent localization lengths, SFL states preserve their spatial profile across different system sizes. We consider a model consisting of a single non-Hermitian impurity embedded in an otherwise Hermitian one-dimensional lattice. The introduction of disorder transforms these SFL states into Anderson-localized states. In contrast to the Hatano-Nelson model, where disorder localizes skin states with a size-independent transition, the presence of SFL states leads to a size-dependent Anderson transition in our model. Extending this theme, we also examine the competition between Non-Hermitian Skin Effect (NHSE), Anderson Localization (AL), and Nonlinearity (NL) in a nonlinear Schrödinger-type lattice. Time-domain simulations reveal distinct transport behaviors under varying disorder and nonlinearity strengths, offering a complementary dynamical perspective to the static transition studied in the scale-free model.