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When fast radio burst (FRB) waves propagate through the local (< 1 pc)environment of the FRB source, electrons in the plasma undergo large-amplitudeoscillations. The finite-amplitude effects cause the effective plasma frequencyand cyclotron frequency to be dependent on the wave strength. The dispersionmeasure and rotation measure should therefore vary slightly from burst to burstfor a repeating source, depending on the luminosity and frequency of theindividual burst. Furthermore, free-free absorption of strong waves issuppressed due to the accelerated electrons' reduced energy exchange in Coulombcollisions. This allows bright low-frequency bursts to propagate through anenvironment that would be optically thick to low-amplitude waves. Given a largesample of bursts from a repeating source, it would be possible to use thedeficit of low-frequency and low-luminosity bursts to infer the emissionmeasure of the local intervening plasma and its distance from the source.Information about the local environment will shed light on the nature of FRBsources.

Imprint of local environment on fast radio burst observations