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1. Linear Time-Periodic Systems with Exceptional Points of Degeneracy

   https://doi.org/10.1109/ICEAA.2019.8879088  

   Kazemi, Hamidreza; Nada, Mohamed Y.; Mealy, Tarek; Abdelshafy, Ahmed F.; Capolino, Filippo (September 2019, 2019 International Conference on Electromagnetics in Advanced Applications (ICEAA))

   We show how exceptional points of degeneracy (EPDs), which a coalescence of multiple eigenmodes, emerge in a linear time-periodic (LTP) systems. We establish the necessary conditions that yield an EPD in a single LTP LC resonator, however, the presented theory can be generalized to any kind of resonator with a time varying element. Furthermore, we propose an application of the EPD in a LTP LC resonator as a sensing device and show the ultra-sensitivity of such system to external perturbations. 

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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. 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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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. Overcoming the rise in local deposit resistance during electrophoretic deposition via suspension replenishing

   https://doi.org/10.3389/fchem.2022.970407  

   Tiwari, Prabal; Ferson, Noah D.; Arnold, David P.; Andrew, Jennifer S. (August 2022, Frontiers in Chemistry)

   Nanomaterials have unique properties, functionalities, and excellent performance, and as a result have gained significant interest across disciplines and industries. However, currently, there is a lack of techniques that can assemble as-synthesized nanomaterials in a scalable manner. Electrophoretic deposition (EPD) is a promising method for the scalable assembly of colloidally stable nanomaterials into thick films and arrays. In EPD, an electric field is used to assemble charged colloidal particles onto an oppositely charged substrate. However, in constant voltage EPD the deposition rate decreases with increasing deposition time, which has been attributed in part to the fact that the electric field in the suspension decreases with time. This decreasing electric field has been attributed to two probable causes, (i) increased resistance of the particle film and/or (ii) the growth of an ion-depletion region at the substrate. Here, to increase EPD yield and scalability we sought to distinguish between these two effects and found that the growth of the ion-depletion region plays the most significant role in the increase of the deposit resistance. Here, we also demonstrate a method to maintain constant deposit resistance in EPD by periodic replenishing of suspension, thereby improving EPD’s scalability. 

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