How to achieve exceptional points in coupled resonators using a gyrator or PT-symmetry, and in a time-modulated single resonator: high sensitivity to perturbations

Abstract

We study the rise of exceptional points of degeneracy (EPD) in various distinct circuit configurations such as gyrator-based coupled resonators, coupled resonators with PT-symmetry, and in a single resonator with a time-varying component. In particular, we analyze their high sensitivity to changes in resistance, capacitance, and inductance and show the high sensitivity of the resonance frequency to perturbations. We also investigate stability and instability conditions for these configurations; for example, the effect of losses in the gyrator-based circuit leads to instability, and it may break the symmetry in the PT-symmetry-based circuit, also resulting in instabilities. Instability in the PT-symmetry circuit is also generated by breaking PT-symmetry when one element (e.g., a capacitor) is perturbed due to sensing. We have turned this instability “inconvenience” to an advantage, and we investigate the effect of nonlinear gain in the PT-symmetry coupled-resonator circuit and how this leads to an oscillator with oscillation frequency very sensitive to perturbation. The circuits studied in this paper have the potential to lead the way for a more efficient generation of high-sensitivity sensors that can detect very small changes in chemical, biological, or physical quantities.

Two resonators with negative and positive reactive components to achieve an exceptional point of degeneracy

“…The circuit has only four elements which are all lossless and reciprocal. The nontrivial Jordan canonical form is already obtained in the gyrator-based nonreciprocal circuit (GNC) which has a nonreciprocal element [25,26,27,30,29], as shown in Figure 2(b). The list of components for reciprocal and nonreciprocal circuits and the necessary conditions to pick the equivalency value of gyration resistance is summarized in Table 1.…”

Thin film sensing near exceptional point utilizing terahertz plasmonic metasurfaces

“…The square root topology of the EP and enormous effect on such a system under minute perturbations has been noticed in recent times [37][38][39][40]. That is if the perturbation experienced is δ resulting in ∆ω frequency split, that leads to ∆ω ∝ √ δ [41]. Hence, EP has opened up new avenues of ultrasensitive optical and photonic-based sensors.…”

Extremely asymmetric absorption and reflection near the exceptional point for three-dimensional metamaterial

“…It has attracted a lot of research interest [16][17][18]. The EPs are non-Hermitian energy degeneracies at which the eigenvalues and corresponding eigenvectors simultaneously coalesce [19]. Near the EP of the parameter space, the eigenvalue spectrum of these systems from real-valued becomes complex due to its non-Hermitian nature [20].…”