Exceptional Points of Degeneracy in Gyrator-Based Coupled Resonator Circuit

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.

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“…and M is the circuit matrix. The eigenfrequencies of this circuit are calculated by solving the characteristic equation [24,52],…”

Section: Lossless Configurationmentioning

confidence: 99%

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

et al. 2022

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“…In this paper, we study various schemes to get EPDs in gyrator-based sensing circuits, as well as their enhanced sensitivity when operating near an EPD. First, two series LC resonators are coupled via a gyrator, as explained in [55][56][57][58][59], leading to a second-order EPD. Next, we extend our study to a third-order EPD obtained using three LC resonators and two gyrators.…”

Section: Introductionmentioning

confidence: 99%

High-sensitivity in various gyrator-based circuits with exceptional points of degeneracy

et al. 2022

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Exceptional points of degeneracy (EPD) can enhance the sensitivity of circuits by orders of magnitude. We show various configurations of coupled LC resonators via a gyrator that support EPDs of second and third-order. Each resonator includes a capacitor and inductor with a positive or negative value, and the corresponding EPD frequency could be real or imaginary. When a perturbation occurs in the second-order EPD gyrator-based circuit, we show that there are two real-valued frequencies shifted from the EPD one, following a square root law. This is contrary to what happens in a Parity-Time (PT) symmetric circuits where the two perturbed resonances are complex valued. We show how to get a stable EPD by coupling two unstable resonators, how to get an unstable EPD with an imaginary frequency, and how to get an EPD with a real frequency using an asymmetric gyrator. The relevant Puiseux fractional power series expansion shows the EPD occurrence and the circuit's sensitivity to perturbations. Our findings pave the way for new types of high-sensitive devices that can be used to sense physical, chemical, or biological changes.

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“…Exceptional degeneracies are also observed in waveguides loaded with discrete gain and loss elements [18], and in lossless/gainless coupled-resonators optical waveguides [19]. Another way to get EPs is based on two resonators coupled by a gyrator [20].…”

Section: Introductionmentioning

confidence: 99%

Tuning exceptional points with Kerr nonlinearity

Ramezanpour

Bogdanov

2021

Phys. Rev. A

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Systems operating at exceptional points (EPs) are highly responsive to small perturbations, making them suitable for sensing applications. Although this feature impedes the system working exactly at an EP due to imperfections arising during the fabrication process. We propose a fast self-tuning scheme based on Kerr nonlinearity in a coupled dielectric resonator excited through a waveguide placed in the near-field of the resonators. We show that in a coupled resonator with unequal Kerr-coefficients, initial distortion from EP regime can be completely compensated. It provides an opportunity to reach very close to the EP in a coupled resonator with detuned resonant frequencies via tuning the intensity of the incident wave. Using time-modulation of the incident wave in nonlinear systems to control both the gain or loss, and resonant frequencies can be a possible approach to fully control the parameters close to an EP.

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Exceptional Points of Degeneracy in Gyrator-Based Coupled Resonator Circuit

Cited by 4 publications

References 11 publications

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

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

High-sensitivity in various gyrator-based circuits with exceptional points of degeneracy

Tuning exceptional points with Kerr nonlinearity

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