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Quantum-mechanical-model calculations of radiative properties of a molecular crystal. II. A transition to coherence in the spontaneous emission from disordered two-dimensional excitons.

A general theory is devised for treating the emission of two-dimensional disordered excitons strongly coupled to the radiation field. We show that a transition to coherence in the spontaneous emission occurs at a critical value of the extended disorder, static (substitutional limit) or thermal (adiabatic limit). For weak disorder the coherent emission of ``superradiant'' states is established by long-range retarded forces, while for strong disorder the emissions of microscopic domains are incoherent. We discuss this competition using model Hamiltonians either for small- or for large-sized crystals when compared with the light wavelength, and we connect it with recent observations of picosecond emission rates: emission of the monolayer surface of anthracene crystals (at low temperatures) and emission of J aggregates in dye monolayers at room and low temperatures.