A Physical Interpretation of Imaginary Time Delay in Microwave Graphs

The time a wave spends in a scattering system before exiting is called time delay, which becomes complex in subunitary scattering systems [1]. The real part of this quantity has been examined thoroughly, but little has been done in exploring the physical meaning behind the imaginary part. In 2016, authors in [2] theoretically demonstrated a connection between complex time delay and the propagation properties of a Gaussian pulse. Specifically, they found that the real part of complex time delay corresponds to a shift in transmission time of the pulse, and the imaginary part to be a shift in the center frequency of the pulse. We were able to experimentally test these predictions using a two port microwave ring graph setup and found excellent agreement between the predictions made by the authors in [2] and our experimental results.

[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] M. Asano, K. Y. Bliokh, Y. P. Bliokh, A. G. Kofman, R. Ikuta, T. Yamamoto, Y. S. Kivshar, L. Yang, N. Imoto, S. K. Ozdemir, and F. Nori, Anomalous time delays and quantum weak measurements in optical micro-resonators, Nat. Comm. 7, 13488 (2016).