Modeling molecular gain inside core-shell nanoparticles and their lattices. A way towards threshold-less amplification of light.

A model for the intensity-dependent optical properties of dye-doped transparent material is presented. This semi-classical model is built on the well-known rate equations for electronic population densities in a four-energy-level electronic system. This model is suitable for addressing the broadband nature of the dye molecules' transitions and the source. Also, it includes the saturation effect and the enhancement of absorption and emission decay rates, due to the presence of photonic states. The proposed material model is applied to investigate lasing phenomena in small core-shell particles and their hexagonal lattices, for which the optical response can be determined analytically. A frequency-domain numerical method is employed to solve the coupled Maxwell-Liouville equations, yielding self-consistent electronic populations, material properties, and both near- and far-field distributions. Numerical predictions for the lasing threshold are obtained and interpreted within a robust theoretical framework. For the lattices examined, the theory demonstrates that the complex polarizability of individual nanoparticles interacts with the effective polarizability of the lattice, thereby controlling or even eliminating the lasing threshold. Consequently, threshold-less amplification is achievable in non-propagating lattice modes and can be extended to light amplification in passive systems without intrinsic gain.