83 research outputs found
The Nonlinear Talbot Effect of Rogue Waves
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.Comment: 4 pages, 4 figure
Fresnel diffraction patterns as accelerating beams
We demonstrate that beams originating from Fresnel diffraction patterns are
self-accelerating in free space. In addition to accelerating and self-healing,
they also exhibit parabolic deceleration property, which is in stark contrast
to other accelerating beams. We find that the trajectory of Fresnel paraxial
accelerating beams is similar to that of nonparaxial Weber beams. Decelerating
and accelerating regions are separated by a critical propagation distance, at
which no acceleration is present. During deceleration, the Fresnel diffraction
beams undergo self-smoothing, in which oscillations of the diffracted waves
gradually focus and smooth out at the critical distance
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