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1. Theory of Periodically Time-Varying Induced Exceptional Points of Degeneracy

   https://doi.org/10.1109/MetaMaterials.2019.8900902  

   Kazemi, H.; Nada, M. Y.; Marosi, R.; Mealy, T.; Abdelshafy, A.; Capolino, F. (September 2019, 2019 Thirteenth International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials))

   We present the novel concept of exceptional points of degeneracy (EPDs), which denote a coalescence of multiple eigenmodes, that directly emerge in systems when a linear time-periodic (LTP) variation is applied. Though the presented theory is general, as an example we establish the general conditions that yield an EPD in a single LTP LC resonator with a capacitance that varies periodically in time. We show a potential application of the proposed LTP system in making sensors to exploit the ultra-sensitivity associated with operating at an EPD. 

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

   https://doi.org/10.1051/epjam/2022005  

   Rouhi, Kasra; Nikzamir, Alireza; Figotin, Alexander; Capolino, Filippo (January 2022, EPJ Applied Metamaterials)

   Mann, Sander; Vellucci, Stefano (Ed.)

   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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3. Experimental demonstration of exceptional points of degeneracy in linear time periodic systems and exceptional sensitivity

   https://doi.org/10.1063/5.0084849  

   Kazemi, Hamidreza; Nada, Mohamed Y.; Nikzamir, Alireza; Maddaleno, Franco; Capolino, Filippo (April 2022, Journal of Applied Physics)

   We present the experimental demonstration of the occurrence of exceptional points of degeneracy (EPDs) in a single resonator by introducing a linear time-periodic variation of one of its components. This is in contrast with the requirement of two coupled resonators with parity time-symmetric systems with precise values of gain and loss. In the proposed scheme, only the tuning of the modulation frequency is required, which is easily achieved in electronic systems. The EPD is a point in a system parameters’ space at which two or more eigenstates coalesce, and this leads to unique properties not occurring at other non-degenerate operating points. We show theoretically and experimentally the existence of a second-order EPD in a time-varying single resonator. Furthermore, we measure the sensitivity of the proposed system to a small structural perturbation and show that the two shifted system’s eigenfrequencies are well detected even for relative perturbations of [Formula: see text], with distinguished peaks well above the noise floor. We show that the regime of operation of the system at an EPD leads to a unique square-root-like sensitivity, which can devise new exceptionally sensitive sensors based on a single resonator by simply applying time modulation. 

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

   https://doi.org/10.1109/Metamaterials54993.2022.9920844  

   Rouhi, K.; Nikzamir, A.; Figotin, A.; Capolino, F. (September 2022, Published in: 2022 Sixteenth International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials))

   We present a scheme supporting an exceptional point of degeneracy (EPD) using connected Foster and non-Foster resonators. One resonator contains positive components, whereas the second resonator contains negative components. We show a second-order EPD where two eigenvalues and eigenvectors coalesce. This circuit can be used to make ultra-sensitive sensors. 

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5. Exceptional Points of Degeneracy in Gyrator-Based Coupled Resonator Circuit

   https://doi.org/10.1109/Metamaterials52332.2021.9577154  

   Nikzamir, A.; Rouhi, K.; Figotin, A.; Capolino, F. (September 2021, Published in: 2021 Fifteenth International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials))

   We propose a high-sensitive circuit scheme based on an exceptional point of degeneracy (EPD) using two LC resonators coupled with a gyrator. EPD is a point in a system’s parameter space in which two or more eigenmodes coalesce in both their resonance frequency and eigenvectors into a single degenerate eigenmode by varying a parameter in the system. We present the conditions to obtain EPDs in this circuit and the typical bifurcation diagram that shows the extreme sensitivity of such a circuit operating at an EPD to system’s perturbations. The very high sensitivity induced by an EPD can be used to explore a new generation of high-sensitive sensors. 

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