Aberration laser beams with autofocusing properties

We investigate theoretically, numerically, and experimentally a novel type of laser beam-an aberration laser beam (ALB). To generate the ALB, a diffractive optical element with a phase transmission function having an arbitrary radial dependence of power q and a periodic angular dependence of sin(mϕ) or cos(mϕ) form can be used. Such a light distribution is more general than classic aberrations including Zernike polynomials. We demonstrate that such radial nonuniformity results in autofocusing properties of ALBs. The autofocusing feature of ALBs is analogous to that of circular Airy beams, but the ALBs' autofocusing feature has more flexibility. The presence of the periodic angular dependence in the phase results in a diffraction pattern with mth-order symmetry. Transformation of ALBs during propagation in free space is analogous to transformation of the three-Airy beams; however, the generated light distributions have an arbitrary integer order of symmetry. The presence of an additional focusing lens leads to formation of an optical field in its focal plane with symmetry that depends on the parity of m: for even m, the generated light distribution has 2mth-order symmetry, and, for odd m, it has mth-order symmetry.