Slow–fast nonlinear dynamics and non-normal relaxation pulses near exceptional points in an autonomous Kerr dimer

Abstract

We study an active–passive Kerr dimer in which a slow saturable reservoir and unequal Kerr shifts make the optical state drive its own non-Hermitian spectral trajectory. Direct integration shows stable narrow relaxation pulses with T = 248.077 and I max = 24.604 , preceded by finite exceptional-point grazing, reduced phase rigidity, compressed eigenvalue splitting, and strong finite-window non-normal response. Pump continuation and frozen-subsystem analysis show that giant pulses appear after delayed passage through a local optical instability, not immediately at the closest EP approach. A signed-detuning control further shows that the weaker orbit can pass closer to the EP, so minimum EP distance alone is not a reliable predictor. We therefore use a cycle-integrated numerical-abscissa excess to include both non-normal strength and residence time. Across detuning, parameter variations, disorder, initial conditions, pump changes, and optical noise, this path-dependent action separates weak and giant-pulse cycles more reliably than minimum EP distance. The structural limitation of a nearest-point spectral metric is not specific to this dimer because a time-dependent non-normal response depends on the history of the operator; however, the quantitative classification performance of the proposed action is established here only for the present Kerr-dimer model and the parameter families tested.