Imaginary Time Delays Are For Real
A scattering material, such as a frosted window or a thin fog, will cause light to travel slower than it would if no material were in its path. The mathematical formula for this time delay has a real part—which is well studied—and a lesser-known imaginary part. “The imaginary time delay has been largely ignored and disregarded as unphysical,” says Isabella Giovannelli from the University of Maryland. But she and her advisor Steven Anlage have now measured this abstract quantity by recording a corresponding frequency shift in scattered light pulses [1].
The real part of the time delay has been observed in many experiments, particularly slow-light setups where light pulses can become effectively trapped inside a scattering medium (see Focus: Light Nearly Stopped in a Waveguide). By contrast, the imaginary part has been stuck in the realm of mathematics. Theoretical work from 2016, however, showed that the imaginary time delay can be related to a potentially observable frequency shift [2].
Giovannelli and Anlage have now uncovered this signal in a system where the frequency shift is expected to be large. As a stand-in for the scattering medium, they used a microwave circuit with a ring graph, which is a simple resonator often used as a filter or a switch. The researchers sent 5-GHz microwave pulses—with a narrow bandwidth of 5 MHz—through the resonator and recorded a shift of 0.48 MHz in the central peak of the pulses. This shift was in close agreement with theoretical predictions.
The researchers plan to look for similar shifts in more complex pulses, where measurements of the imaginary time delay could offer insights into the effects of scattering media on optical communication signals, Giovannelli says.
–Michael Schirber
Michael Schirber is the Deputy Editor of Physics Magazine.
References
- I. L. Giovannelli and S. M. Anlage, “Physical interpretation of imaginary time delay,” Phys. Rev. Lett. 135, 043801 (2025).
- M. Asano et al., “Anomalous time delays and quantum weak measurements in optical micro-resonators,” Nat. Commun. 7, 13488 (2016).