  Semiclassical catastrophes in the dynamics of a quantum rotor (molecule)
driven by a strong time-varying field are considered. We show that for strong
enough fields, a sharp peak in the rotor angular distribution can be achieved
via time-domain focusing phenomenon, followed by the formation of angular
rainbows and glory-like angular structures. Several scenarios leading to the
enhanced angular squeezing are proposed that use specially designed and
optimized sequences of pulses. The predicted effects can be observed in many
processes, ranging from molecular alignment (orientation) by laser fields to
heavy-ion collisions, and the squeezing of cold atoms in a pulsed optical
lattice.
