Demonstration of Exceptional Points of Degeneracy in Gyrator-Based Circuit for High-Sensitivity Applications

Nikzamir, Alireza; Rouhi, Kasra; Figotin, Alexander; Capolino, Filippo

doi:10.48550/arxiv.2107.00639

Cited by 4 publications

(24 citation statements)

References 31 publications

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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%

“…The main feature of an exceptional point is the strong full degeneracy of the relevant eigenmodes (including their eigenvectors), justifying the presence of "D" in EPD that stands for "degeneracy" [17]. Exceptional points have been observed in various circuits as in coupled resonators [18][19][20][21][22][23][24], temporally-periodic systems [25][26][27], and spatially periodic structures [28][29][30].…”

Section: Introductionmentioning

confidence: 99%

“…Also, we study the stability of the circuit, manifested in its eigenfrequencies. Details and analysis of the series configuration, not shown here, are discussed in [23,24,46,47]. In Section 4, we study the second-order EPD in two coupled resonators with balanced gain and loss satisfying PT-symmetry.…”

Section: Introductionmentioning

confidence: 99%

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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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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%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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%

“…This paper explores and reviews specific cases, whereas a mathematical framework for constructing lossless circuits for any conceivable Jordan structure using a gyrator has been presented in [55]. In addition, we consider lossless components in our study, and the analysis of stability or instability in some circuit configurations by adding small losses to the circuits is discussed in [57,58]. The analysis and circuit presented in this paper have great potential applications in novel ultra-high-sensitive schemes.…”

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

Rouhi

Nikzamir

Figotin

et al. 2022

2022 Sixteenth International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials)

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An exceptional point of degeneracy (EPD) occurs when both the eigenvalues and the corresponding eigenvectors of a square matrix coincide and the matrix has a nontrivial Jordan block structure. It is not easy to achieve an EPD exactly. In our prior studies, we synthesized simple conservative (lossless) circuits with evolution matrices featuring EPDs by using two LC loops coupled by a gyrator. In this paper, we advance even a simpler circuit with an EPD consisting of only two LC loops with one capacitor shared. Consequently, this circuit involves only four elements and it is perfectly reciprocal. The shared capacitance and parallel inductance are negative with values determined by explicit formulas which lead to EPD. This circuit can have the same Jordan canonical form as the nonreciprocal circuit we introduced before. This implies that the Jordan canonical form does not necessarily manifest systems' nonreciprocity. It is natural to ask how nonreciprocity is manifested in the system's spectral data. Our analysis of this issue shows that nonreciprocity is manifested explicitly in: (i) the circuit Lagrangian and (ii) the breakdown of certain symmetries in the set of eigenmodes. All our significant theoretical findings were thoroughly tested and confirmed by extensive numerical simulations using commercial circuit simulator software.

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Demonstration of Exceptional Points of Degeneracy in Gyrator-Based Circuit for High-Sensitivity Applications

Cited by 4 publications

References 31 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

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

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