Exceptional Points of Degeneracy in Nonlinear Systems: Two Coupled Oscillators and Arrays of Oscillators

We discuss the effect of nonlinearities in two different systems with an exceptional point of degeneracy (EPD). First, we discuss a highly sensitive oscillator scheme employing coupled resonators with gain and loss with nonlinearity in the gain component (as in realistic devices) to achieve ultra-sensitivity of the oscillation frequency to perturbations. This scheme contrasts with traditional linear systems, revealing a marked improvement in sensitivity. Nonlinearity leads to low phase noise, showing the potential of this circuit to exhibit measurable high sensitivity to perturbations. Second, we incorporate discrete distributed nonlinear gain and radiating elements within a periodically loaded waveguide. We demonstrate that an oscillator array will select an EPD as a favorable operation point after saturation, achieving an exceptional synchronization regime and improving radiating power efficiency. These findings underscore the profound impact of nonlinearity on the design of high-power radiating arrays and offer potential applications across a broad spectrum of sensing and modulation technologies.