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Self‐Imaging Effect Based on Airy Beams with Quadratic Phase Modulation

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.