Polariton optics of semiconductor photonic dots: weak and strong coupling limits

We develop coherent optics of dipole-active, dispersionless excitons in spherical semiconductor photonic dots (PDs). In the absence of any incoherent scattering, both the strong and weak coupling regimes can intrinsically be realized simply by changing the parameters of the dot and surrounding medium. A criterion, which attributes the transition between these two regimes to a discrete topological change of the relevant dispersion curves, is found and approximated by an analytic expression. The transition depends upon the intrinsic radiative lifetime of the PD photon eigenstates, i.e. it is determined by the parameters of the structure (the oscillator strength of the exciton-photon interaction, PD radius and the ratio of the background dielectric constants inside and outside of the dot). We propose the use of high-precision modulation spectroscopy in order to visualize the above 'phase' transition between a well-developed polariton picture (the strong coupling regime) and weakly-interacting exciton and PD photon states (the weak coupling regime). It is shown that the radiative decay of optically dressed PD excitons, coherently distributed among the relevant PD eigenstates, is non-monotonous against the dot radius a: a size-dependent increase of the effective oscillator strength at small a saturates at a similar tolambda and with a increasing further towards a much greater than lambda the optical lifetime of excitons starts to increase proportionally to a, reflecting the ballistic escape of nearly bulk polaritons from the PD. The numerical simulations are scaled to dispersionless excitons in PDs fabricated from cyanine dye J aggregates.