Third-order nonlinearity with subradiance dark-state in ultra-strong excitons and surface plasmon coupling using self-antiaggregation organic dye

Abstract

A strong coupling regime with dressed states is formed when a propagating surface plasmon (PSP) mode coherently exchanges energy with an ensemble of excitons at a rate faster than the system’s losses. These states are superpositions of superradiance excitons and PSP modes, accompanied by remaining subradiance or ‘dark’ exciton states. Dark-states are ubiquitous, especially in disordered systems, and they rise in number as the number of excitons increases. Here, the ultra-strong coupling regime was experimentally observed with the coupling strength to bare energy as high as g/∼ 0.23 using a self-antiaggregation organic dye, BOBzBT2 in an Otto-SPR configuration. We show that the hybrid system of excitons in a nonlinear organic dye layer and a PSP mode can be described by employing dark-state in a theory of nonlinear third-order sum-frequency generation (TSFG). Close agreement between the theory and the experiment has been demonstrated. The study opens up a new perspective for establishing a relationship between the optical properties of a third-order nonlinear material and the extent of strong coupling.