Direct measurements of the effects of complex time delay in a simple scattering network

The Wigner-Smith delay time is a measure of how long an excitation lingers in the vicinity of a scattering potential before leaving through the asymptotic scattering channels. This delay time was originally defined only for unitary scattering systems, but over the past 10 years there has been increasing interest in defining a complex generalization of time delay (CTD) for non-Hermitian scattering systems [1]. Our earlier work has related the real and imaginary parts of CTD to the zeros and poles in the complex energy plane of the scattering matrix. We now examine the influence of CTD on the propagation of Gaussian time-domain pulses through a simple scattering network, namely a ring graph [2]. We find that the time delay and carrier frequency shift of the scattered pulses are well described by the real and imaginary parts of CTD, in agreement with theory.

References

[1] Lei Chen, Steven M. Anlage, and Yan V. Fyodorov, “Generalization of Wigner Time Delay to Sub-Unitary Scattering Systems,” Phys. Rev. E 103, L050203 (2021).

[2] Lei Chen and Steven M. Anlage, “Use of Transmission and Reflection Complex Time Delays to Reveal Scattering Matrix Poles and Zeros: Example of the Ring Graph,” Phys. Rev. E 105, 054210 (2022).