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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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There are two kinds of exceptional points of degeneracy (EPD) in waveguides: those in the absence of loss and gain, related to slow light, and those where the waveguide has distributed gain and/or loss. Here, we discuss both kinds and highlight their differences. We show EPDs of order 2, 3, 4 and 6 in waveguides supporting two or three modes in each direction, and how the coalescence parameter is a good tool to measure the degree of degeneracy by measuring the angle between the eigenvectors (polarization states). In highlighting the differences between the two kinds of EPDs, we also show different sets of applications, which include sensors, delay lines, distributed amplifiers, antennas, and oscillators.more » « less
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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.more » « less
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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.more » « less
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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.more » « less
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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.more » « less
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A degenerate band edge is a resonant dispersive behavior of coupled transmission lines arising from a fourth-order degeneracy due to the coalescence of two propagating and two evanescent modes. It leads to a so-called giant resonance resulting in field enhancement inside the transmission line. In this paper, we propose a SIW periodic line supporting a degenerate band edge and we study the impact of losses. Conductor and dielectric losses are analyzed in the full-wave simulations of the unit cell and of truncated structures.more » « less
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