Exceptional-point degeneracy as a desirable operation point for an oscillator array with discrete nonlinear gain and radiative elements

We show that an oscillator array prefers to operate at an exceptional point of degeneracy (EPD) occurring in a waveguide periodically loaded with discrete nonlinear gain and radiating elements. The concept of the EPD is employed to conceptualize an exceptional synchronization regime, which leads to enhanced radiating power efficiency. The system maintains a steady-state degenerate mode of oscillation at a frequency of 3 GHz, even when the small-signal nonlinear gain values are nonuniform along the array. We designed the system using small-signal gain to work at the EPD of zero phase shift in consecutive unit cells. Contrarily to the original expectation of zero phase shift, after reaching saturation, the time-domain signal in consecutive unit cells displays a $\ensuremath{\pi}$ phase shift. Hence, we demonstrate that the saturated system tends to oscillate at a distinct EPD, associated to a $\ensuremath{\pi}$ phase shift between consecutive cells, than the one at which the system was originally designed using small-signal gain. This alternative EPD at which the nonlinear system is landing is associated to higher radiating power efficiency with respect to power provided by nonlinear gains. Finally, we demonstrate that the oscillation frequency is independent of the length of the array, contrarily to what happens ordinary oscillating systems based on one-dimensional cavity resonances. These findings may have a high impact on high-power radiating arrays with distributed active elements.