Abstract
We studied the critical dynamics of spectral singularities. The system investigated is a coupled resonator array with a side-coupled loss (gain) resonator. For a gain resonator, the system acts as a wave emitter at spectral singularities. The reflection probability increased linearly over time. The rate of increase is proportional to the width of the incident wave packet, which served as the spectral singularity observer in the experiment. For a lossy resonator, the system acts as a wave absorber. The emission and absorption states at spectral singularities coalesce in a finite parity-time (PT ) symmetric system that combined by the gain and loss structures cut from corrresponding scattering systems at spectral singularities; in this case, the PT -symmetric system is at an exceptional point with a 2 * 2 Jordan block. The dynamics of the PT -symmetric system exhibit the characteristic of exceptional points and spectral singularities.
Highlights
A non-Hermitian Hamiltonian can possess peculiar features that have no counterpart in a closed Hermitian system
We qualitatively studied the dynamic phenomena of wave emission and absorption in the coupled resonator array through a side-coupled gain resonator using an exact solution of a concrete tight-binding system
We demonstrated that the PT -symmetric system was at an exceptional point with a 2 × 2 Jordan block when the two semi-infinite scattering systems were at spectral singularities
Summary
A non-Hermitian Hamiltonian can possess peculiar features that have no counterpart in a closed Hermitian system. The steady-states at spectral singularities in scattering systems have the form of propagating plane wave emission and (or) absorption [39]. We qualitatively studied the dynamic phenomena of wave emission and absorption in the coupled resonator array through a side-coupled gain (loss) resonator using an exact solution of a concrete tight-binding system. We demonstrated that the PT -symmetric system was at an exceptional point with a 2 × 2 Jordan block when the two semi-infinite scattering systems were at spectral singularities. (c) After symmetric and antisymmetric combination of the uniform chain, we obtained a semi-infinite chain array with gain (loss) resonator coupled at the end.
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