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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. 

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. 

We propose a pulse generation scheme based on a fourth-order degeneracy in the dispersion relation. We take advantage of the loaded quality factor enhancement and the ultra-sensitivity to external perturbations due to the high order degeneracy in such a structure. The proposed scheme is able to produce a train of nanosecond pulses with several watts of output power. Such a design offers a flexibility that allows to conceive either high output power pulses or high frequency train of pulses. 

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. 

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. 

We investigate wave properties in coupled transmission lines (CTLs) under a special condition known as the exceptional point of degeneracy (EPD) at which two or more of the supported eigenmodes of the system coalesce. At an EPD, not only the eigenvalues (resonances or wavenumbers) of the system (a resonator or a waveguide) coalesce but also the eigenvectors (polarization states) coalesce, and the number of coalescing eigenmodes defines the order of the degeneracy. We investigate different structures, either periodic or uniform CTLs, that are capable of exhibiting EPDs in their dispersion diagram. Secondly, we show an experimental verification of the existence of EPDs through measuring the dispersion of microstrip-based CTLs in the microwave spectrum. For antenna array configurations, we discuss the effect of CTLs radiative and dissipative losses on EPDs and how introducing gain to the CTLs compensate for such losses restoring the EPD in a fully radiating array, in what we define as the gain and distributed-radiation balance regime. Therefore, we show how to obtain large linear and planar arrays that efficiently generate microwave oscillations, and by spatial combination they are able to generate collimated beams with large radiation intensity. Finally, we show other promising applications based on the concept of EPDs in ultra-sensitive sensors or reconfigurable antennas.