Simple model of saturable localised surface plasmon

Localised surface plasmons (LSPs) are now applied to various fields, such as bio-sensing, solar cell, molecular fluorescence enhancement and quantum-controlled devices at nanometre scale. Recent experiments show that LSPs are optically saturated by high-intensity light. Absorption saturation arises as a result of strong optical nonlinearity and cannot be explained by the conventional boson model of LSPs. Here, we propose a simple model of saturable LSPs using an effective dipole approximation. The strategy is to directly compare the classical linear optical response of an LSP with that obtained from a saturable quantum two-level system in the limit of weak excitation. The second quantization can then be performed by replacing a classical polarizability with a quantum dipole operator. Taking an ellipsoidal nanometal as an example, we analyse in detail the optical response of a single ellipsoidal nanometal to validate our model. Our numerical results show that the plasmon resonance frequency and spectral linewidth decrease as the aspect ratio of the ellipsoid increases, which is similar to the size dependence observed in early experiments.