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1. Highly Sensitive Exceptional Degeneracy in Coupled Transmission Lines With Balanced Gain and loss

   https://doi.org/10.23919/USNC-URSINRSM57467.2022.9881419  

   Nikzamir, Alireza; Kazemi, Hamidreza; Mealy, Tarek; Capolino, Filippo (January 2022, Published in: 2022 United States National Committee of URSI National Radio Science Meeting (USNC-URSI NRSM))

   We proposed a highly sensitive circuit scheme based on an exceptional point of degeneracy (EPD) using two finite-length coupled transmission lines terminated on balanced gain and loss. 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 the system's parameter. We demonstrate that two PT-symmetric finite-length coupled transmission lines (CTLs), can generate an EPD at a desired frequency. We find the EPDs in this circuit and the bifurcation diagram that exhibits the ultra-sensitivity behavior to the system's perturbations. The very high sensitivity induced by an EPD can be used to conceive a new generation of high-sensitive sensors. 

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2. Sensing Via Exceptional Points in Space and Time Periodic Systems and in PT-Symmetric Systems

   https://doi.org/10.1109/Metamaterials49557.2020.9285058  

   Nada, M. Y.; Mealy, T.; Hafezi, E.; Nikzamir, A.; Capolino, F. (September 2020, Published in: 2020 Fourteenth International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials))

   We review and explore sensor applications based on electromagnetic systems operating near an exceptional point of degeneracy (EPD). The EPD is defined as the point at which the system eigenmodes coalesce in both their eigenvalues and eigenvectors varying a system parameter. Sensors based on EPDs show sensitivity proportional to δ 1/m , where δ is a perturbation of a system parameter and m is the order of the EPD. EPDs manifest in PT-symmetric systems or periodic systems that can be periodic in either time or space. We review all the methods to obtain EPD based sensors, and we focus on two classes of ultra-sensitive EPD systems: i) periodic linear time-varying single oscillators, and ii) optical gyroscopes based on a modified coupled resonators optical waveguide (CROW) exhibiting 4th order EPD. 

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3. 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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4. 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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5. 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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