Fast radio bursts are a coherent cosmological probes. Searching for the phase correlations of a fast radio burst in the voltage data of radio telescopes can allow for the detection of a gravitational lens. The papers below link to the technique used to search for this signature and how this search allows us to constrain dark matter in the form of compact objects.

Papers:

Coherent Search Algorithm
Constraints on Dark Matter 

By simulating from first principles how the propagation of electromagnetic radiation through astrophysical mediums appears to observers, we can model the detection signatures that can change depending on the astrophysical lens. The paper linked below provides a simulation toolset to model different types of astrophysical lenses and provides a overview of how different propagation signatures may appear in data.  

Paper:

Simulating Astrophysical Lensing 

Code:

Github Repo 

FRB 202201413B detected by CHIME/FRB featured a time-lag signature suggestive of a coherent phase response. We performed a morphology analysis and a scintillation analysis of this burst and found this event could be modelled by a simple plasma lens.  We also found the time-lag signature could be explained by a scattering through the Milky Way alone and that the phase coherence observed only suggests part of the propagation path was coherent. The paper below details all the analyses done that suggest this conclusion.

Paper:

Detection of partial phase coherence