UC Irvine

A coupled-oscillator system displays enhanced sensitivity of its saturated steady-state (SS) oscillation frequency to small parameter perturbations near an exceptional-point degeneracy (EPD), a property that can be used to realize EPD-based sensors. Linear PT-symmetric systems, consisting of two coupled resonators, exhibit EPDs around which square-root sensitivity is observed. However, linear models are insufficient for realistic systems that rely on nonlinear, saturable-gain elements, particularly when PT-symmetry is broken. Thus, we study the SS of a general system of two coupled oscillators featuring EPDs and saturable nonlinear gain, using coupled-mode theory. We do this by synthesizing and extending prior SS analyses of the system’s stability and its square-root and cubic-root oscillation frequency sensitivity at a unique third-order SS-EPD. We add an SS analysis of saturated gain, energy, and oscillation-frequency sensitivity in the vicinity of the third-order SS-EPD, enabling characterization of the various SS regimes. We determine that the stable and bistable regions in parameter space directly depend on the saturated-gain values; that the dynamic range of high sensitivity around degenerate conditions is extended by increasing losses, consequently reducing the system’s stored energy; and that, to exploit the cubic-root-like sensitivity associated with the third-order SS-EPD, the suggested working regime is best confined to operation within the weakly coupled regime and not exactly at the third-order SS-EPD. Finally, we apply the model to two electronic circuits that exhibit cubic-root sensitivity, demonstrating the application and limitations of this analysis.