Exceptional points appear in non-Hermitian systems as degeneracies, where not only eigenvalues but also eigenvectors coalesce. They are of great theoretical and experimental interest due to their exotic topological properties and enhanced sensitivity to perturbations. Experimental realizations of higher-order exceptional points, where more than two eigenvectors coalesce, rely on highly fine-tuned setups. Recently, stimulated Brillouin scattering has been employed to generate second-order exceptional points in a fabrication-free setup by leveraging off-resonant scattering. In this work we generalize this approach, and we develop an off-resonant, multimode theory for stimulated Brillouin scattering as an avenue towards realizing symmetry-induced exceptional points of any order. We present the experimental implementation of our program in an accompanying paper. Our multimode theory could also be employed in applications in optoacoustic sensing, synthetic neuromorphic computing, microwave photonic filters, and optoacoustic quantum signal processing.

Exceptional points (EPs) are degeneracies in the spectrum of non-Hermitian systems, where both the eigenvalues and eigenvectors coalesce. In the vicinity of an n-th order EP, the eigenvalues generally show n-th-root dependence on the system parameters, making EPs potentially promising candidates for ultra-sensitive measurements. Usually EPs are implemented in precisely fabricated nano- and microstructures. In this work, we instead show the experimental implementation of a third-order EP (EP3) using the synthetic dimension in a single-mode optical fiber, leveraging multi-frequency Brillouin scattering. We perform a multi-dimensional scan of the parameter space revealing not only an EP3 but also additional topological structures connected to it. Our work paves the way toward fabrication-free realizations of exceptional points of arbitrary order.

Acute spectral sensitivity to boundary conditions and the formation of a generalized Brillouin zone associated with complex quasimomenta are features frequently attributed to systems with non-trivial non-Hermitian topology, showcasing the non-Hermitian skin effect. We show that, away from the thermodynamic limit, these features themselves are not uniquely tied to this phenomenon; they can similarly arise as parity-induced even-odd effects in non-Hermitian systems without skin effect. Despite an underlying generalized Brillouin zone description, wavefunctions remain delocalized. In addition, the effect can arise in skin-effect models as entirely separate distinguishable feature.

We study atom-photon bound states seeded by two-level emitters coupled to self-similar photonic lattices. By expressing the photonic Green's function through the heat kernel, we show that the far-field localization length obeys xi ~ Delta^(-1/dw), with the detuning Delta from the lower spectral edge and the walk dimension dw of the underlying fractal. This scaling is controlled by anomalous diffusion and does not rely on translational invariance or a band-edge effective-mass approximation. Exact diagonalization on Sierpiński gaskets, pyramids, Vicsek graphs, and Sierpiński carpets confirms the far-field prediction once the bath Hamiltonian is rendered Laplacian-like by compensating the local inhomogeneity in the connectivities with on-site potentials. In the near field, the bound-state amplitude exhibits an additional algebraic variation. For nested finitely ramified fractals, the corresponding exponent agrees with the classical resistance/first-passage scaling, whereas Sierpiński carpets display clear deviations from this simple law. Our results extend structured-bath waveguide QED to self-similar non-periodic geometries and connect bound-state profiles to transport exponents of the underlying fractal lattice.

Integrated photonics has enabled a wide class of chip-scale light sources and quantum technologies. Within this field, microresonator-based degenerate optical parametric oscillators (DOPOs) have gained prominence. Above a critical power threshold, these systems undergo spontaneous symmetry breaking to settle into one of two stable, π-phase-shifted states -- a mechanism successfully used for quantum random number generation and photonic Ising machines. Here, we show that DOPOs based on the Kerr nonlinearity host a significantly broader range of nonlinear dynamics than previously explored. Using a silicon nitride microring resonator, we experimentally identify Hopf bifurcations that trigger a transition from stationary operation to self-sustained oscillations at MHz frequencies. By adjusting pump detunings and powers, we achieve turnkey control over these oscillatory regimes, navigating the system between stable binary states and periodic limit cycles. Furthermore, we report the experimental observation of period-doubling bifurcations, which numerical simulations reveal as the precursor to a cascading instability culminating in chaos at elevated pump powers. Our results establish a framework for controlling nonlinear instabilities in chip-scale parametric oscillators, with applications in programmable photonic hardware and dynamical optical computing.

Surface plasmon polaritons propagating along curved metal-dielectric interfaces experience geometry-induced modifications absent on flat surfaces. In this work, we derive a covariant, effective two-dimensional wave equation for the transverse magnetic surface plasmon mode on weakly curved smooth interfaces. By perturbatively expanding Maxwell's equations with curvature-adapted boundary conditions, we find a Helmholtz equation with two geometric potential terms that enter at first order in the extrinsic curvature: an isotropic contribution proportional to the extrinsic curvature, and an anisotropic operator arising from the traceless part of the second fundamental form. These linear-in-curvature potentials distinguish convex from concave interfaces, in contrast to the quadratic potentials known from symmetrically confined systems such as dielectric waveguides. We show that our equation reproduces established results for spherical and cylindrical interfaces. We furthermore predict that the anisotropic contribution vanishes when the ratio of the material permittivities equals the square of the golden ratio. As an application, we demonstrate sign-dependent cooperative frequency shifts as well as a curvature-driven redistribution of superradiant and subradiant decay rates for a ring of quantum emitters on a curved metallic spheroid interacting through the surface plasmons.

Spontaneous symmetry breaking leads to diverse phenomena across the natural sciences, from the Higgs mechanism in particle physics to superconductors and collective animal behavior. In photonic systems, the symmetry of light states can be broken when two optical fields interact through the Kerr nonlinearity, as shown in early demonstrations with counterpropagating and cross-polarized modes. Here, we report the first observation of color symmetry breaking in an integrated silicon nitride microring, where spontaneous power imbalance arises between optical mode at different wavelengths, mediated by the Kerr effect. The threshold power for this effect is as low as 19 mW. By examining the system's homogeneous states, we further demonstrate a Kerr-based nonlinear activation-function generator that produces sigmoid-, quadratic-, and leaky-ReLU-like responses. These findings reveal previously unexplored nonlinear dynamics in dual-pumped Kerr resonators and establish new pathways towards compact, all-optical neuromorphic circuits.