Radio pulsars scintillate because their emission travels through the ionized
interstellar medium via multiple paths, which interfere with each other. It has
long been realized that the scattering screens responsible for the
scintillation could be used as interstellar lenses' to localize pulsar emission regions. Most scattering screens, however, only marginally resolve emission components, limiting results to statistical inferences and detections of small positional shifts. Since screens situated close to the source have better resolution, it should be easier to resolve emission regions of pulsars located in high density environments such as supernova remnants or binaries in which the pulsar's companion has an ionized outflow. Here, we report events of extreme plasma lensing in the Black Widow’ pulsar, PSR~B1957+20, near the
phase in its 9.2 hour orbit in which its emission is eclipsed by its
companion’s outflow. During the lensing events, the flux is enhanced by factors
of up to 70–80 at specific frequencies. The strongest events clearly resolve
the emission regions: they affect the narrow main pulse and parts of the wider
interpulse differently. We show that the events arise naturally from density
fluctuations in the outer regions of the outflow, and infer a resolution of our
lenses comparable to the pulsar’s radius, about 10,km. Furthermore, the
distinct frequency structures imparted by the lensing are reminiscent of what
is observed for the repeating fast radio burst FRB 121102, providing
observational support for the idea that this source is observed through, and
thus at times strongly magnified by, plasma lenses.

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