Arbitrary shaped abruptly autofocusing beams

•Theoretical model for arbitrary non-circular abruptly autofocusing beams (AAB) is first proposed and investigated.•The launch angle modulation method is first proposed for these beams to re-obtain their abruptly autofocusing properties.•The rectangle, star, ellipse shaped AAB are first generated in experiment, other shaped AAB could also be produced with this method. Arbitrary shaped abruptly autofocusing beam (AAB) with initial launch angle modulation is proposed and demonstrated in this paper. Usually, arbitrary shaped Airy beams, which are constructed by substituting various shape functions into circular model, do not own abruptly autofocusing properties because their parabolic trajectories would not intersect at a same point. The modulation for initial launch angles of trajectories is necessary for these beams to re-obtain abruptly autofocusing properties. With the launch angle modulation, the abruptness and intensity contrast of focusing could be as intensive as the circular AAB. The rectangle, star, ellipse shaped AAB are mainly investigated in this paper. Other shaped AAB can be constructed with similar method.