Modelling photon condensation in a fluorescent dye filled optical microcavity

In this paper, a mathematical model for photon condensation in an optical microcavity is considered based on Gross-Pitaevskii equation. The interaction of photons with fluorescent dye molecules in an optical microcavity resembles electron-ion interaction in a periodic lattice. The system is modelled analogous to Kronig-Penney model for electrons in a one-dimensional periodic lattice. The laser used as the light source gives rise to nonlinearity due to the deformation of electron orbits in the fluorescent dye. To accommodate the optical Kerr effect which arises due to this nonlinear interaction, the resultant Schrödinger equation is modified, which assumes the form of Gross-Pitaevskii equation. The model is validated using equation of state, whose virial coefficients can be evaluated from grand canonical ensemble scheme taking into account the interaction between photons and fluorescent dye molecules. (paper)