Influence of magnetic fields up to 20 T on excitons and polaritons in CdS and ZnO

From an invariant expansion, we construct the exciton Hamiltonian for $A$ and $B$ excitons in CdS and ZnO represented by an 8\ifmmode\times\else\texttimes\fi{}8 matrix including the influences of the finite wave vector and an external magnetic field. We diagonalize the Hamiltonian matrix to obtain the exciton states. Then the excitons are coupled to the electromagnetic radiation field thus giving the polariton states. The theoretical dispersion curves are fitted to the results of two-photon Raman scattering, transmission, and reflection experiments in magnetic fields up to 20 T. From this fit we deduce precise values for eigenenergies, $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$-linear terms, exciton masses, $g$ factors, and diamagnetic shifts.