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Physical Interpretation of Imaginary Time Delay

Isabella L. Giovannelli* and Steven M. Anlage

  • *Contact author: igiovann@umd.edu
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Phys. Rev. Lett. 135, 043801 – Published 24 July, 2025

DOI: https://doi.org/10.1103/nnk7-xy4v

Abstract

The scattering matrix S linearly relates the vector of incoming waves to outgoing wave excitations, and contains an enormous amount of information about the scattering system and its connections to the scattering channels. Time delay is one way to extract information from S, and the transmission time delay τT is a complex (even for Hermitian systems with unitary scattering matrices) measure of how long a wave excitation lingers before being transmitted. The real part of τT is a well-studied quantity, but the imaginary part of τT has not been systematically examined experimentally, and theoretical predictions for its behavior have not been tested. Here we experimentally test the predictions of Asano et al. [Nat. Commun. 7, 13488 (2016)] for the imaginary part of transmission time delay in a nonunitary scattering system. We utilize Gaussian time-domain pulses scattering from a two-port microwave graph supporting a series of well-isolated absorptive modes to show that the carrier frequency of the pulses is changed in the scattering process by an amount in agreement with the imaginary part of the independently determined complex transmission time delay, Im[τT], from frequency-domain measurements of the subunitary S matrix. Our results also generalize and extend those of Asano et al., establishing a means to predict pulse propagation properties of non-Hermitian systems over a broad range of conditions.

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synopsis

Imaginary Time Delays Are For Real

Published 24 July, 2025

The time delay experienced by a scattered light signal has an imaginary part that was considered unobservable, but researchers have isolated its effect in a frequency shift.

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Phys. Rev. Lett. 135, 043801– Published 24 July, 2025
  • Received 17 December 2024
  • Revised 20 May 2025
  • Accepted 3 June 2025
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