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1. 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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2. Various Topologies of Coupled-Mode Structures Exhibiting Exceptional Points of Degeneracy

   https://doi.org/10.1109/ICEAA.2018.8520525  

   Nada, Mohamed Y.; Abdelshafy, Ahmed F.; Mealy, Tarek; Yazdi, Farshad; Kazemi, Hamidreza; Figotin, Alexander; Capolino, Filippo (September 2018, 2018 International Conference on Electromagnetics in Advanced Applications (ICEAA), Cartagena des Indias, Colombia)

   We investigate the modal characteristics of coupled-mode guiding structures in which the supported eigenmodes coalesce; the condition we refer to as an exceptional point of degeneracy (EPD). EPD is a point in a system parameter space at which the system eigenmodes coalesce in both their eigenvalues and eigenvectors, where the number of coalescing eigenmodes at the EPD defines the order of the degeneracy. First, we investigate the prospects of gain/loss balance and how it is related to realizing an EPD. Under geometrical symmetry in coupled resonators or coupled waveguides such scheme is often attributed to PT-symmetry; however, we generalize the concept of PT-symmetry to coupled waveguides exhibiting EPDs that do not necessarily have perfect geometrical symmetry. Secondly, we explore the conditions that lead to the existence of EPDs in periodically coupled waveguides that may be lossless and gainless. In general, we investigate properties associated to the emergence of EPDs in various cases: i) uniform, and ii) periodic, lossy or lossless, coupled-mode structures. Generally, the EPD condition is very sensitive to perturbations; however, it was shown recently with experimental and theoretical studies that EPDs' unconventionai properties exist even in the presence of loss and fabrication errors. Extraordinary properties of such systems at EPDs, such as the giant scaling of the quality factor and the high sensitivity to perturbation, provide opportunities for various applications in traveling wave tubes, pulse compressors and generators, oscillators, switches, modulators, lasers, and extremely sensitive sensors. 

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3. 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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4. Optical limiter based on PT-symmetry breaking of reflectionless modes

   https://doi.org/10.1364/OPTICA.497275  

   Riboli, Francesco; Kononchuk, Rodion; Tommasi, Federico; Boschetti, Alice; Suwunnarat, Suwun; Anisimov, Igor; Vitebskiy, Ilya; Wiersma, Diederik_S; Cavalieri, Stefano; Kottos, Tsampikos; et al (September 2023, Optica)

   The application of parity–time (PT) symmetry in optics, especially PT-symmetry breaking, has attracted considerable attention as an approach to controlling light propagation. Here, we report optical limiting by two coupled optical cavities with a PT-symmetric spectrum of reflectionless modes. The optical limiting is related to broken PT symmetry due to light-induced changes in one of the cavities. Our experimental implementation involves a three-mirror resonator of alternating layers of ZnS and cryolite with a PT-symmetric spectral degeneracy of two reflectionless modes. The passive optical limiting is demonstrated by measurements of single 532 nm 6 ns laser pulses and thermo-optical simulations. At fluences below 10mJ/cm², the multilayer exhibits a flattop passband at 532 nm. At higher fluences, laser heating combined with the thermo-optic effect in ZnS leads to cavity detuning and PT-symmetry breaking of the reflectionless modes. As a result, the entire multilayer structure quickly becomes highly reflective, protecting itself from laser-induced damage. The cavity detuning mechanism can differ at much higher limiting thresholds and include nonlinearity. 

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5. 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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