arXiv subjects

Adam Mock

Publications and source records attributed to Adam Mock.

4 recordsLinked to original sources

arXiv2026

Chiral-Mode Control around a Hermitian Diabolic Point in Discrete Non-Hermitian Coupled Resonators

Motivated by the prospect of chiral-mode control in compact photonic systems, we analyze discrete coupled single-mode resonators. Using the minimal three-resonator model, we show that an infinitesimal complex onsite perturbation near a Hermitian diabolic point (DP) induces chiral-mode selection, governed by what we term an asymptotic exceptional point (AEP). Here, an AEP denotes a Hermitian DP equipped with a non-Hermitian perturbation that induces an asymptotically defective effective Hamiltonian. The eigenvectors coalesce in the asymptotic limit toward the DP, although the Hamiltonian at the point itself remains diagonalizable. Operationally, this AEP response realizes chirality switching from an achiral state to a chiral state. The associated eigenvalue response exhibits the anomalous fractional-power scaling ${\Delta}{\lambda} \propto {\varepsilon}^{3/2}$, distinct from the square-root response of an ordinary exceptional point (EP). We further show that, in a broader two-parameter perturbation space, ordinary EPs lie on exceptional-line branches that meet at the AEP. A finitebias control sweep crosses these branches at an EP pair, enabling chirality reversal between opposite chiral states. The central message is therefore that the AEP organizes two related routes for chirality switching: direct switching from an achiral state to a chiral state via the AEP, and switching between opposite chiral states via an EP pair in the vicinity of the AEP. Within a finite-resolution averaging model, these two operating points exhibit different practical performance characteristics, and under sufficiently high control resolution, the AEP operating point can become more favorable than the EP-pair operating point, suggesting a route toward compact and low-energy chiral photonic devices.

physics.optics↗

arXiv2025

Higher-order exceptional points unveiled by nilpotence and mathematical induction

Non-Hermitian systems can have peculiar degeneracies of eigenstates called exceptional points (EPs). An EP of $n$ degenerate states is said to have order $n$, and higher-order EPs (HEPs) with $n \ge 3$ exhibit intrinsic order-scaling responses potentially applied to superior sensing and state control. However, traditional eigenvalue-based searches for HEPs are facing fundamental limitations in terms of complexity and implementation. Here, we propose a design paradigm for HEPs based on a simple property for matrices termed nilpotence and concise inductive procedure. The nilpotence guarantees a HEP with desired order and helps divide the problem. Our inductive scheme repeatedly extends a system and doubles its EP order, starting with a known design. Based on the nilpotence, we systematically design photonic cavity arrays operating at chiral, passive, and active HEPs with $n = 3, 6, 7$ and show their peculiar directional radiation, induced transparency, and enhanced transmittance and spontaneous emission, respectively. We inductively find lattice systems with diverging EP order originating from a well-known $2 \times 2$ parity-time-symmetric Hamiltonian. We also extend the active HEP system with $n = 7$ to another with $n = 14$ and have further magnified responses. Our work pushes the investigation and application of HEPs to previously unexplored regimes in various physical systems.

physics.optics↗

arXiv2017

Comprehensive understanding of parity-time transitions in $\mathcal{PT}$ symmetric photonic crystals with an antiunitary group theory

Electromagnetic materials possessing parity-time symmetry have received significant attention since it was discovered that the eigenmodes of these materials possess either real-frequency eigenvalues or the eigenfrequencies appear in complex-conjugate pairs. Interestingly, some eigenstates of these systems show thresholdless $\mathcal{PT}$ transitions to the complex-conjugate regime, some exhibit a transition as a function of the degree of non-Hermiticity and some show no $\mathcal{PT}$ transition at all. While previous work has provided some insight on the nature of $\mathcal{PT}$ transitions, this work lays out a general and rigorous mathematical framework that is able to predict, based on symmetry alone, whether an eigenmode will exhibit a thresholdless $\mathcal{PT}$ transition or no $\mathcal{PT}$ transition at all. Developed within the context of ferromagnetic solids, Heesh-Shubnikov group theory is an extension of classical group theory that is applicable to antiunitary operators. This work illustrates the Heesh-Shubnikov approach by categorizing the modes of a two-dimensionally periodic photonic lattice that possesses $\mathcal{PT}$ symmetry.

math-ph↗

arXiv2016

Characterization of Parity-Time Symmetry in Photonic Lattices Using Heesh-Shubnikov Group Theory

We investigate the properties of parity-time symmetric periodic photonic structures using Heesh-Shubnikov group theory. Classical group theory cannot be used to categorize the symmetry of the eigenmodes because the time-inversion operator is antiunitary. Fortunately, corepresentations of Heesh-Shubnikov groups have been developed to characterize the effect of antiunitary operators on eigenfunctions. Using the example structure of a one-dimensional photonic lattice, we identify the corepresentations of eigenmodes at both low and high symmetry points in the photonic band diagram. We find that thresholdless parity-time transitions are associated with particular classes of corepresentations. The approach is completely general and can be applied to parity-time symmetric photonic lattices of any dimension. The predictive power of this approach provides a powerful design tool for parity-time symmetric photonic device design.

physics.optics↗