Here we use the following notation for the nuclear coordinate to emphasize the angular dependance of the Wigner functions. The expansion ( ) is plugged into the time-dependent Schrödinger equation with a subsequent projection onto the electronic and rotational basis functions. This yields a set of coupled differential equations defining the ro-vibrational dynamics of on two potential energy surfaces (6) where is the transition dipole. The matrix elements correspond to projecting the local electric field, , that follows (3) in laboratory frame to the molecular frame. The general expressions for