Propagation and self-imaging effect of deformed high-order Bessel beam

Based on the typical arrangement for generating high-order Bessel beam and decomposing it into high-order Bessel cosine beam and high-order Bessel sine beam,the analytical expression of a deformed high-order Bessel beam and its propagation properties in selffocusing lens were analyzed using the Collins formula in cylindrical coordinate system.The general analytical expression of the deformed high-order Bessel beam and its propagation properties of in self-focusing lens self-imaging process in free space were obtained.The numerical simulation results were also given,when the difference of transverse component of wave number between high-order Bessel cosine beam and high-order Bessel sine beam was 0.005 K.Experimental results show that the deformed high-order Bessel beam is still nondiffracting beam with self-imageing effect in free space.