Enhanced Sensitivity of Degenerate System Made of Two Unstable Resonators Coupled by Gyrator Operating at an Exceptional Point

TL;DR

This paper demonstrates that a circuit with two unstable resonators coupled by a gyrator can support an exceptional point of degeneracy, significantly enhancing sensitivity for sensing applications, despite potential instability due to losses.

Contribution

It introduces a novel gyrator-coupled resonator system supporting an exceptional point with real eigenfrequencies, enabling highly sensitive detection of small perturbations.

Findings

Eigenfrequency response follows square-root dependence on perturbation.

Losses induce instability in the system.

Eigenfrequency bifurcation described by Puiseux fractional power series.

Abstract

We demonstrate that a circuit comprising two unstable LC resonators coupled via a gyrator supports an exceptional point of degeneracy (EPD) with purely real eigenfrequency. Each of the two resonators includes either a capacitor or an inductor with a negative value, showing purely imaginary resonance frequency when not coupled to the other via the gyrator. With external perturbation imposed on the system, we show analytically that the resonance frequency response of the circuit follows the square-root dependence on perturbation, leading to possible sensor applications. Furthermore, the effect of small losses in the resonators is investigated, and we show that losses lead to instability. In addition, the EPD occurrence and sensitivity are demonstrated by showing that the relevant Puiseux fractional power series expansion describes the eigenfrequency bifurcation near the EPD. The EPD has the great potential to enhance the sensitivity of a sensing system by orders of magnitude. Making use of the EPD in the gyrator-based circuit, our results pave the way to realize a new generation of high-sensitive sensors to measure small physical or chemical perturbations.