Abstract
Many novel properties of non-Hermitian systems are found at or near the exceptional points—branch points of complex energy surfaces at which eigenvalues and eigenvectors coalesce. In particular, higher-order exceptional points can result in optical structures that are ultrasensitive to external perturbations. Here we show that an arbitrary order exceptional point can be achieved in a simple system consisting of identical resonators placed near a waveguide. Unidirectional coupling between any two chiral dipolar states of the resonators mediated by the waveguide mode leads to the exceptional point, which is protected by the transverse spin–momentum locking of the guided wave and is independent of the positions of the resonators. Various analytic response functions of the resonators at the exceptional points are experimentally manifested in the microwave regime. The enhancement of sensitivity to external perturbations near the exceptional point is also numerically and analytically demonstrated.
Highlights
Many novel properties of non-Hermitian systems are found at or near the exceptional points— branch points of complex energy surfaces at which eigenvalues and eigenvectors coalesce
A higher-order exceptional point (EP) is a result of coalescence of multiple eigenvalues[22], which normally requires a delicate variation of parameters in a larger parameter space and is much more difficult to achieve[25,28]
For a physical system described by a Hamiltonian involving many physical parameters, it typically requires tedious tuning of multiple parameters to achieve a higher-order EP
Summary
Many novel properties of non-Hermitian systems are found at or near the exceptional points— branch points of complex energy surfaces at which eigenvalues and eigenvectors coalesce. Higher-order exceptional points can result in optical structures that are ultrasensitive to external perturbations. We show that an arbitrary order exceptional point can be achieved in a simple system consisting of identical resonators placed near a waveguide. In contrast to the degeneracy in a Hermitian system (a diabolic point), an EP is a branch point in the complex energy surface where the Hamiltonian matrix becomes defective. Re(a) = Re(b), a − b is purely imaginary and c 1⁄4 dà 4,6–9 or when a − b is real and c = d is purely imaginary[28,29,30,31] In the former case, the non-Hermiticity comes from the asymmetric loss/gain of the two identical states, whereas in the latter case the non-
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