  Using an extended Dicke model, we study the effect of the spin-orbit coupling
between the singlet and the triplet molecular excitons in organic
microcavities. We exactly solve the model in the strong coupling regime in the
single excitation space. We calculate the polaritonic states and the optical
absorption spectrum of the system and explore the spin-orbit induced splitting
of the lower polariton into two branches. The effect of this splitting in the
ultra strong coupling regime on the superradiant phase transition is explored
using a variational approach. We find that the spin-orbit coupling pushes the
system towards the superradiant phase and reduces the critical matter-light
coupling required for it.
