Figure of merit for Kerr nonlinear plasmonic waveguides

Plasmonic waveguides are promising in many applications because of their subwavelength field confinement, which can strongly enhance light-matter interactions. Nevertheless, how to efficiently evaluate their Kerr nonlinear performance is still an open question because of the presence of relatively large linear losses. Here a simple and versatile figure of merit (FOM) is proposed for Kerr nonlinear waveguides with linear losses. To derive the FOM, a generalized full-vectorial nonlinear Schrodinger equation governing nonlinear pulse propagation in a lossy waveguide is developed, and an approximate analytic solution of the degenerate four wave mixing conversion efficiency is derived and validated. The effectiveness of the FOM is verified with an all-plasmonic and a hybrid-plasmonic waveguide configuration. Rigorous results show that the optimal waveguide length for the highest conversion efficiency is ln3 times the attenuation length. At this length, the upper limits of the conversion efficiency and the nonlinear phase shift are determined by the FOM. These results provide fundamental theory and useful guidance in exploring plasmonic waveguides for nonlinear optical applications.