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1. 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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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. Novel Regime for Antenna Array Oscillators Based on Exceptional Point of Degeneracy

   Abdelshafy, A.F.; Mealy, T; Kazemi, H; Othman, M; Capolino, F (June 2019, 2019 13th European Conference on Antennas and Propagation (EuCAP), Krakow, Poland, Poland, 31 March-5 April 2019.)

   We demonstrate a new regime of operation to conceive radiating array oscillators. This regime is based on the dispersion engineering of coupled transmission lines (CTLs) utilizing an exceptional point of degeneracy (EPD), which represents the coalescence of multiple eigenmodes. We propose the "gain and loss balance" regime for structures exhibiting significant radiation losses to enable an innovative regime for a class of coherent EPD-based radiating oscillators with stable oscillation frequency. Moreover, this class of radiating oscillators shows an interesting trend of how the oscillation threshold scales with the length of the structure. This EPD concept has potential applications in high power-efficiency oscillators and high-power radiation. 

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4. 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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5. Exceptional Points of Degeneracy in Electromagnetic Periodic Waveguides and the Role of Symmetries

   https://doi.org/10.23919/EuCAP53622.2022.9769037  

   Mealy, Tarek; Nada, Mohamed Y.; Abdelshafy, Ahmed F.; Hafezi, Ehsan; Capolino, Filippo (March 2022, Published in: 2022 16th European Conference on Antennas and Propagation (EuCAP))

   We investigate the role of reflection and glide symmetry in periodic lossless waveguides on the dispersion diagram and on the existence of various orders of exceptional points of degeneracy (EPDs). We use an equivalent circuit network to model each unit-cell of the guiding structure. Assuming that a coupled-mode waveguide supports N modes in each direction, we derive the following conclusions. When N is even, we show that a periodic guiding structure with reflection symmetry may exhibit EPDs of maximum order N . To obtain a degenerate band edge (DBE) with only two coupled guiding structures, reflection symmetry must be broken. For odd N,N+1 is the maximum EPD order that may be obtained, and an EPD of order N is not allowed. We present an example of three coupled microstrip transmission lines and show that breaking the reflection symmetry by introducing glide symmetry enables the occurrence of a stationary inflection point (SIP), also called frozen mode, which is an EPD of order three. 

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