  We study the control by electromagnetic fields of molecular alignment and
orientation, in a linear, rigid rotor model. With the help of a monotonically
convergent algorithm, we find that the optimal field is in the microwave part
of the spectrum and acts by resonantly exciting the rotation of the molecule
progressively from the ground state, i.e., by rotational ladder climbing. This
mechanism is present not only when maximizing orientation or alignment, but
also when using prescribed target states that simultaneously optimize the
efficiency of orientation/alignment and its duration. The extension of the
optimization method to consider a finite rotational temperature is also
presented.
