Time-Domain Excitation of Finite-Lifetime Resonances and Their Exceptional Points

Abstract

Resonances associated with complex-frequency poles are ubiquitous across physics and can arise in any open system, ranging from subwavelength particles and cavities to biological structures. When two such resonances coalesce, they form exceptional points (EPs), non-Hermitian singularities known to produce unusual spectral and dynamical behavior. However, the dynamics of the response of such resonances and exceptional points to complex frequency drive remained largely unexplored. Here, we experimentally observe the temporal response of complex-frequency resonances and theoretically study this for exceptional points. We unveil a universal transient phenomenon of open cavities driven at complex frequencies: the system's initial response grows linearly, with enhanced growth at exceptional points (EPs), even though the system is passive and the excitation decays. Closed-form theory for general resonators, extended to higher-order modes, predicts efficient power transfer with $t$ and $t^2$ scaling for complex single poles and exceptional points (EPs), respectively, at all times. We demonstrate these effects in subwavelength optical scatterers and experimentally in an electrical circuit analogue, with excellent agreement, and explore configurations that capture EP-enhanced growth.