Time-Domain Excitation of Complex Resonances

TL;DR

This paper develops a unified theoretical framework for the time-domain response of passive resonators under complex-frequency excitation, revealing a regime where they behave like active resonators and demonstrating its validity through analytical and experimental results.

Contribution

It introduces a closed-form solution for the time-domain behavior of passive resonators driven at complex resonances, unifying diverse systems and phenomena involving modal degeneracies.

Findings

Resonators exhibit a real-frequency-like evolution at short times.

The framework accurately predicts behavior in subwavelength particles and circuits.

Experimental results confirm enhanced power delivery and theoretical predictions.

Abstract

Passive resonators-systems that exhibit loss but no gain-are foundational elements across nearly every domain of physics and many types of of systems such as subwavelength particles, dielectric slabs, electric circuits, biological structures, and droplets. While their spectral properties are well characterized, their time-domain behavior under complex-frequency excitation remains largely unexplored, particularly near exceptional points where resonant modes coalesce. Here, we derive a closed-form time-domain response for passive resonators driven at complex resonance frequencies, uncovering a regime of real-frequency-like evolution at $t\ll1/\Gamma$ where they approximately function as active resonators. This framework unifies resonator behavior across disparate systems and accurately describes phenomena involving modal degeneracies and non-Hermitian effects. We verify this universality through analytical treatment of subwavelength particles and experimental demonstrations in passive electric circuits, showing excellent agreement with theory and enhanced power delivery efficiency. These results reveal a previously hidden structure in resonator dynamics and open new directions for time-domain control across across a variety of fields, including nanophotonics and circuit engineering.