Linear dynamics of an accelerating wave packet, which is produced by adding shifted copies of the fundamental Airy beam, due to parabolic optical potentials are investigated. A new type of self-imaging phenomenon, referred to as period-reversal accelerating self-imaging, is demonstrated theoretically and numerically. Unlike ordinary Talbot effects, where optical field pattern reappears at constant intervals and follows a straight line, here, the field pattern of this new self-imaging effect propagating along a periodic oscillating trajectory, can self-reproduces itself at nonconstant intervals, and begins to invert after the phase transition points, where the superposition of fundamental Airy beams forms multi-beams interference fringes. A completely spatially reversal replica of the initial field distribution is observed at odd multiplies of the period halves. Moreover, the properties of the multi-beams interference fringes are discussed in detail and can be used for the measurement of the system parameter. The above results can be generalized in the case of two transverse dimensions, where it can be treated as a product of two independent one-dimensional cases. The theoretical calculations and numerical simulations verify each other completely.
We investigate propagation dynamics of cosh- and cosine-Airy beams in Kerr nonlinear media. The cosh-Airy and cosine-Airy beam can be considered as a superposition of two Airy beams with different decay factors and different propagation trajectories, respectively. It is shown that the solitons shedding from cosh-Airy and cosine-Airy beams and their interaction in both in-phase and out-of-phase cases are strongly dependent on the modulation parameter associated with the cosh function. The interaction between two cosine-Airy beams can exhibit attraction or repulsion under proper interval and initial angle condition in both in-phase and out-of-phase cases.
The self‐imaging effect based on Airy beams with quadratic phase modulation (QPM) in 1 + 1 and 2 + 1 dimensions is studied both numerically and analytically. It is demonstrated that, in spite of spatial spectral shape being kept invariant, both the intensity pattern and the accelerating trajectory of this self‐imaging effect depend considerably on the QPM. When the QPM parameter is negative, the self‐imaging accelerating wave exhibits deceleration and then acceleration, and the self‐imaging scope can be expanded. In the opposite case, the self‐imaging extent would be narrowed and the self‐imaging accelerating wave will only accelerate during propagation. Numerical simulations agree with the theoretical results very well. This study shows the possibility of controlling the self‐imaging effect based on 1D and circular Airy beams, by purposely choosing appropriate QPM parameters.
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