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Radio pulsars scintillate because their emission travels through the ionizedinterstellar medium via multiple paths, which interfere with each other. It haslong been realized that the scattering screens responsible for thescintillation could be used as `interstellar lenses' to localize pulsaremission regions. Most scattering screens, however, only marginally resolveemission components, limiting results to statistical inferences and detectionsof small positional shifts. Since screens situated close to the source havebetter resolution, it should be easier to resolve emission regions of pulsarslocated in high density environments such as supernova remnants or binaries inwhich the pulsar's companion has an ionized outflow. Here, we report events ofextreme plasma lensing in the `Black Widow' pulsar, PSR~B1957+20, near thephase in its 9.2 hour orbit in which its emission is eclipsed by itscompanion's outflow. During the lensing events, the flux is enhanced by factorsof up to 70--80 at specific frequencies. The strongest events clearly resolvethe emission regions: they affect the narrow main pulse and parts of the widerinterpulse differently. We show that the events arise naturally from densityfluctuations in the outer regions of the outflow, and infer a resolution of ourlenses comparable to the pulsar's radius, about 10\,km. Furthermore, thedistinct frequency structures imparted by the lensing are reminiscent of whatis observed for the repeating fast radio burst FRB 121102, providingobservational support for the idea that this source is observed through, andthus at times strongly magnified by, plasma lenses.

Pulsar emission amplified and resolved by plasma lensing in an eclipsing binary