  Akhmediev and Kuznetsov-Ma breathers are rogue wave solutions of the
nonlinear Schr\"odinger equation (NLSE). Talbot effect (TE) is an image
recurrence phenomenon in the diffraction of light waves. We report the
nonlinear TE of rogue waves in a cubic medium. It is different from the linear
TE, in that the wave propagates in a NL medium and is an eigenmode of NLSE.
Periodic rogue waves impinging on a NL medium exhibit recurrent behavior, but
only at the TE length and at the half-TE length with a \pi-phase shift; the
fractional TE is absent. The NL TE is the result of the NL interference of the
lobes of rogue wave breathers. This interaction is related to the transverse
period and intensity of breathers, in that the bigger the period and the higher
the intensity, the shorter the TE length.
