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A microstrip-technology three-way waveguide has been conceived to display exceptional modal degeneracy in the presence of periodic gain and radiation losses satisfying parity-time ( PT ) glide-symmetry. A third order exceptional point of degeneracy (EPD) is obtained in the modal dispersion relation, where three Floquet-Bloch eigenmodes coalesce at a single frequency, in their eigenvalues and polarization states. In the proposed structure, PT -glide-symmetry is achieved using periodically spaced lumped (radiation) loss and gain elements, each shifted by half a period. This particular degeneracy can be utilized in the design of devices such as radiating arrays with distributed amplifiers, arrays of oscillators, and sensors. 

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.