Quantum statistical theory of fluorescence of low density Frenkel excitons in a crystal slab

The fluorescence of Frenkel excitons in low density regime is studied without the aid of rotating wave approximation and Markov approximation. The evolution of the emitted field is derived in terms of its initial conditions. It is found that the usual interaction Hamiltonian of ( e/mc)PiA type leads to unreasonable characteristic equation for decay rates. Only when the term ( e 2 /2mc 2 )A 2 is added to the ( e/mc)PiA, the result becomes reasonable. The case of single lattice layer is studied in detail. Different features of statistical properties of the superfluorescence are shown as compared with that of atom aggregate. Double and triple lattice-layer cases are also studied to show the effect of coupling between the excitons of different wave vectors.