Trajectory probing of complex-frequency scattering with chirped analytic pulses

TL;DR

This paper introduces complex-frequency chirped pulses for probing resonant scatterers, enabling direct characterization of their complex-frequency response along prescribed contours, improving accuracy near resonances.

Contribution

It presents a novel method for directly sampling complex-frequency responses using analytic waveforms and provides synthesis rules, analysis techniques, and validation through numerical tests.

Findings

Effective probing of complex-frequency responses along contours.

Finite-duration windowing causes deterministic distortions.

Validation on a coupled-mode resonator confirms method accuracy.

Abstract

Characterizing resonant scatterers is challenging because their poles and zeros usually lie away from the real-frequency axis, whereas most measurements sample only real frequencies and infer off-axis behavior from fitted models. Here we introduce complex-frequency chirped pulses: finite-energy analytic waveforms that probe a device continuously along a prescribed contour in the complex-frequency plane. We give a direct synthesis rule for an in-phase/quadrature (I/Q) waveform and show that finite-duration windowing deterministically distorts the realized trajectory, which makes it necessary to analyze only a central time interval where the window contribution is small. For stable linear time-invariant devices, we extract a time-local least-squares input--output ratio and identify when it follows the continued complex-frequency response, with errors that grow at higher traversal speeds and near resonant poles. Numerical tests on a coupled-mode resonator validate the method and show that closed contours enable an integer phase-winding consistency check. We also outline an implementation based on standard arbitrary waveform generation, I/Q modulation, coherent reception, and digital signal processing.