Generation of azimuthally modulated circular superlinear Airy beams

We demonstrate a new type of circular Airy beam, the azimuthally modulated circular superlinear Airy beam, generated by utilizing a diffraction element, whose transmission function is the sum of the transmission function of the element, generating a "petal" pattern and the transmission function of the element generating a circular Airy beam. We investigate the propagation dynamics of such beams and demonstrate that their autofocusing and self-healing properties are strongly dependent on the number of generated petals. In addition, we propose a simple way to control the shape of the caustic of the generated laser beams with a fixed number of generated petals. We believe that these results can be very useful for lensless laser fabrication and laser manipulation techniques, as well as for the development of new filament plasma multi-channel formation methods.