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Abstract

Fast radio bursts (FRBs) are bright radio transient events with durations on the order of milliseconds. The majority of FRB sources discovered so far have a single peak, with the exception of a few showing multiple-peaked profiles, the origin of which is unknown. In this work, we show that the strong lensing effect of a point mass or a point mass + external shear on a single-peak FRB can produce double peaks (i.e., lensed images). In particular, the leading peak will always be more magnified and hence brighter than the trailing peak for a point-mass lens model, while the point-mass + external shear lens model can produce a less magnified leading peak. We find that, for a point-mass lens model, the combination of lens mass M and redshift z_l in the form of M(1 + z_l) can be directly computed from two observables—the delayed time Δt and the flux ratio of the leading peak to the trailing peak R. For a point-mass + external shear lens model, upper and lower limits in M(1 + z_l) can also be obtained from Δt and R for a given external shear strength. In particular, tighter lens mass constraints can be achieved when the observed R is larger. Lastly, we show the process of constraining lens mass using the observed values of Δt and R of two double-peaked FRB sources, i.e., FRB 121002 and FRB 130729, as references, although the double-peaked profiles are not necessarily caused by strong lensing.