Resonant interaction between excitons and intense coherent light

Starting from a Hamiltonian which describes the interaction of the many-electron system of a crystal with the quantized light field, we derive a set of nonlinear wave-equations for the field and exciton amplitude and the exciton occupation number. Our treatment comprises both Frenkel and Wannier excitons. Our equations form a sound basis for treating both pulse-propagation phenomena and giant polaritons in crystals.