Exceptional Point Degeneracy as Desirable Operation Point of Oscillator Array with Discrete Nonlinear Gain and Radiating Elements

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 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. Contrarily to the original expectation of zero phase shift associated to the designed EPD using small-signal gain, after reaching saturation, the time domain signal in consecutive unit cells displays a $\pi$ phase shift. Hence, we demonstrate that the saturated system oscillates at a distinct EPD, associated to a $\pi$ phase shift between consecutive cells, than the one at which the system was originally designed using small-signal gain. This new EPD at which the nonlinear system is landing is associated to higher power efficiency. 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.