Generalization of Wigner Time Delay to Sub-Unitary Scattering Systems

TL;DR

This paper extends the concept of Wigner time delay to lossy, sub-unitary scattering systems, providing theoretical expressions, experimental validation, and insights into coherent perfect absorption and scattering matrix poles.

Contribution

It introduces a complex generalization of Wigner time delay for lossy systems, linking it to CPA conditions and enabling pole-zero identification from experimental data.

Findings

Good agreement between theory and microwave graph experiments.

Time delay features indicate conditions for Coherent Perfect Absorption.

The method allows identifying scattering matrix poles and zeros.

Abstract

We introduce a complex generalization of Wigner time delay $\tau$ for sub-unitary scattering systems. Theoretical expressions for complex time delay as a function of excitation energy, uniform and non-uniform loss, and coupling, are given. We find very good agreement between theory and experimental data taken on microwave graphs containing an electronically variable lumped-loss element. We find that time delay and the determinant of the scattering matrix share a common feature in that the resonant behavior in $\text{Re}[\tau]$ and $\text{Im}[\tau]$ serves as a reliable indicator of the condition for Coherent Perfect Absorption (CPA). This work opens a new window on time delay in lossy systems and provides a means to identify the poles and zeros of the scattering matrix from experimental data. The results also enable a new approach to achieving CPA at an arbitrary energy/frequency in complex scattering systems.