  We present a novel paradigm for dispersion engineering in coupled
transmission lines (CTLs) based on exceptional points of degeneracy (EPDs). We
develop a theory for fourth-order EPDs consisting of four Floquet-Bloch
eigenmodes coalescing into one degenerate eigenmode. We present unique wave
propagation properties associated to the EPD and develop a figure of merit to
assess the practical occurrence of fourth-order EPDs in CTLs with tolerances
and losses. We experimentally verify for the first time the existence of a
fourth EPD (the degenerate band edge), through dispersion and transmission
measurements in microstrip-based CTLs at microwave frequencies. In addition, we
report that based on experimental observation and the developed figure of
merit, the EPD features are still observable in structures that radiate (leak
energy away), even in the presence of fabrication tolerances and dissipative
losses. We investigate the gain and loss balance regime in CTLs as a mean of
recovering an EPD in the presence of radiation and/or dissipative losses,
without necessarily resorting to Parity-Time (PT)-symmetry regimes. The
versatile EPD concept is promising in applications such as high intensity and
power-efficiency oscillators, spatial power combiners, or low-threshold
oscillators and opens new frontiers for boosting the performance of large
coherent sources.
