  We consider the optimal control of quantum systems interacting non-linearly
with an electromagnetic field. We propose new monotonically convergent
algorithms to solve the optimal equations. The monotonic behavior of the
algorithm is ensured by a non-standard choice of the cost which is not
quadratic in the field. These algorithms can be constructed for pure and
mixed-state quantum systems. The efficiency of the method is shown numerically
on molecular orientation with a non-linearity of order 3 in the field.
Discretizing the amplitude and the phase of the Fourier transform of the
optimal field, we show that the optimal solution can be well-approximated by
pulses that could be implemented experimentally.
