Resonances in physical systems — electromagnetic cavities, mechanical oscillators, quantum states — are characterized by complex frequencies: a real part (the oscillation frequency) and an imaginary part (the decay rate). Measuring these complex frequencies from real-frequency experiments requires fitting models to response curves, which becomes ambiguous when resonances overlap or when the background is complicated.
Krasnok and Seletskiy (arXiv:2603.12519) bypass the fitting problem by probing directly in the complex-frequency plane. They synthesize chirped analytic pulses — finite-energy waveforms whose instantaneous frequency traces a prescribed contour through the complex-frequency plane rather than just sweeping along the real axis. The in-phase and quadrature components of these waveforms are constructed so that their analytic signal follows a trajectory that can circle around poles and zeros of the system's response function.
The extraction method computes a time-local input-output ratio — the instantaneous relationship between the probe and the response — which, under identified conditions, equals the system's complex-frequency response evaluated along the trajectory. Errors increase near resonant poles (where the response diverges) and at higher traversal speeds (where the finite-duration windowing distorts the trajectory), but both sources are characterizable.
The practical step: this requires only standard arbitrary waveform generation, I/Q modulation, and coherent detection — equipment already present in most microwave and optical labs. No specialized hardware, just a different choice of probe waveform. The complex-frequency plane, usually accessible only through analytic continuation of real-frequency data, becomes directly measurable by sending the right pulse shape.