Generalization of Wigner time delay to subunitary scattering systems

We introduce a complex generalization of the Wigner time delay τ for subunitary scattering systems. Theoretical expressions for complex time delays as a function of excitation energy, uniform and nonuniform 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 the time delay and the determinant of the scattering matrix share a common feature in that the resonant behavior in Re[τ] and Im[τ] serves as a reliable indicator of the condition for coherent perfect absorption (CPA). By reinforcing the concept of time delays in lossy systems this work provides a means to identify the poles and zeros of the scattering matrix from experimental data. The results also enable an approach to achieving CPA at an arbitrary frequency in complex scattering systems.