I ' m just beginning my foray into Quantum Optics but I ' ll try and help . I ' d have to see the the exact setups in question with certainty but here are my first thoughts . Atomic transitions are dependent on the transition dipole moment . The probability has a dependence on the dot product of this dipole moment and the photon polarisation . In an isolated atom we have spherical symmetry but it you ' re applying a electricmagnetic field you break that symmetry and see the dependence . Other reasons for employing this might be Birefringent media have different indices of refraction on their axes labelled ordinary and extraordinary Polarisation dependent fluorescence , in some long life timed media the polarisation of the outgoing photons is dependent on that of the incoming . Hope this helps