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Exceptional Points of Degeneracy in a Transmission Line Periodically Loaded with Gain and Radiation Loss

We demonstrate that a periodic transmission line consisting of uniform lossless segments together with discrete gain and radiation-loss elements supports exceptional points of degeneracy (EPDs). We provide analytical expressions for the conditions that guarantee the coalescence of eigenvalues and eigenvectors. We show the dispersion diagram and discuss the tunability of the EPD frequency. Additionally, a special case is shown where the eigenvectors coalesce for all frequencies when a specific relationship between transmission line characteristic impedance, and gain/loss elements holds; in other words, in this situation, exceptional points merge to a line of frequency. The class of EPDs proposed in this work is very promising in many of applications that incorporate radiation losses.