Using an extended Tavis-Cummings model, we study the effect of the spin-orbit
coupling between the singlet and the triplet molecular excitons in organic
microcavities in the strong coupling regime. The model is solved in the single
excitation space for polaritons, that contain the bright (permutation
symmetric) singlet and triplet excitons, as well as the dark bands consisting
of the non-symmetric excitons of either type. We find that the spin-orbit
coupling splits the lower polariton into two branches, and also creates a novel
triplet polariton when the cavity mode is in resonance with the triplet
excitons. The optical absorption spectrum of the system that can reveal this
splitting in experiments is presented and the effect of disorder in exciton
energies and couplings is explored. An important consequence of the disorder in
the spin-orbit coupling - a weak coupling between the otherwise decoupled
bright and dark sectors - is explored and detailed calculations of the squared
transition matrix elements between the dark bands and polaritons are presented
along with derivation of some approximate yet quite accurate analytical
expressions. This new relaxation channel for the dark states contains an
interference between two transition paths that,
for a given polariton state, suppresses the relaxation of one dark band and
enhances it for the other.Comment: 16 pages, 10 figure