Resonant Critical Coupling of Surface Lattice Resonances with Fluorescent Absorptive Thin Film

Surface lattice resonance supported on nanoparticle arrays is a promising candidate in enhancing fluorescent effects in both absorption and emission. The optical enhancement provided by surface lattice resonance is primarily through the light confinement beyond the diffraction limit, where the nanoparticle arrays can enhance light-matter interaction for increased absorption as well as providing more local density of states for enhanced spontaneous emission. In this work, we optimize the in-coupling efficiency to the fluorescent molecules by finding the conditions to maximize the absorption, also known as the critical coupling condition. We studied the transmission characteristics and the fluorescent emission of a $TiO_2$ nanoparticle array embedded in an index-matching layer with fluorescent dye at various concentrations. A modified coupled-mode theory that describes the nanoparticle array was then derived and verified by numerical simulations. With the analytical model, we analyzed the experimental measurements and discovered the condition to critically couple light into the fluorescent dye, which is demonstrated as the strongest emission. This study presents a useful guide for designing efficient energy transfer from excitation beam to the emitters, which maximizes the external conversion efficiency.