Lensless Formation and Turbulence Response of Airy-Type Beams Generated by Direct Fresnel Propagation

We investigate a lensless Airy-type optical beam generated by direct Fresnel propagation of a Gaussian apodized real space cubic phase. Starting from the scalar Fresnel diffraction integral, we derive a closed-form expression showing that the propagated field can be written in terms of an Airy function, but with an argument different from that of the conventional finite energy Airy beam. This difference leads to distinct free space dynamics: the conventional beam is already formed at the input plane and follows a parabolic trajectory, whereas the lensless beam forms during propagation and undergoes stronger transverse reshaping and broadening. The two fields are also compared under atmospheric turbulence using a phase screen approach and multiple performance metrics. The comparison shows that no single beam performs best for all detection scenarios: the lensless field gives lower scintillation at the beam maximum, the two beams provide comparable aperture collected power, and the conventional Airy beam gives higher coherent fiber coupling efficiency.