  We consider the nonlinear Schrodinger equation, with mass-critical
nonlinearity, focusing or defocusing. For any given angle, we establish the
existence of infinitely many functions on which the scattering operator acts as
a rotation of this angle. Using a lens transform, we reduce the problem to the
existence of a solution to a nonlinear Schrodinger equation with harmonic
potential, satisfying suitable periodicity properties. The existence of
infinitely many such solutions is proved thanks to a constrained minimization
problem.
