Abstract

The efficiency enhancement of nonlinear optical processes in extremely confined volumes ($\sim 100{\mathrm{nm}}^3$) is a great challenge in the field of nanophotonics, and has an important role in modern applications such as all-optical signal processing and ultrafast switching. Due to their opacity and large absorption, metals are usually considered a hindrance to high efficiency in traditional photonic systems. However, light interaction with metal nanoparticles, i.e., plasmonics, gives unmatched possibilities of both miniaturization and electromagnetic field enhancement. These properties, together with the large intrinsic nonlinear susceptibilities of metallic systems, make plasmonic systems ideal candidates for nonlinear optics applications. Here, we present the design of a plasmonic system for efficient difference frequency generation (DFG), performing a theoretical and numerical analysis of linear and nonlinear properties of the structure. In particular, we model the system using a hydrodynamic theory for the electron dynamics inside the metal. A key element for the implementation of these equations is to write the nonlocal contributions as purely surface current terms. This may be done by exploiting the particular mathematical form of the nonlinear surface terms, which can be approximated as a function of the bulk and external values of the electric field. As a result, we obtain a parameter-free model for DFG in plasmonic systems. Finally, as an application of our method, we have designed a doubly resonant gold nanostructure, estimating an effective second-order nonlinear susceptibility ${\chi }_{\mathrm{eff}}^{(2)}\approx 1\mathrm{nm}/\mathrm{V}$.

© 2019 Optical Society of America

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