Second-harmonic generation in plasmonic waveguides with nonlocal response and electron spill-out

Plasmonic waveguides provide an integrated platform to develop efficient nanoscale ultrafast photonic devices. Although metals display a rich variety of nonlocal optical effects and surface nonlinearities, the study of plasmonic waveguides has been limited to considering conventional bulk nonlinearities. Such analytical tools, however, do not allow us to incorporate the nonlocal optical effects on the studied phenomenon or the nonlinearities arising from it. In this work, we present a method based on the numerical calculation of the inhomogeneous solution that enables the study of nonlinear optical effects, such as second-harmonic generation, in waveguides displaying nonlocal response effects as well as surface nonlinearities. We use the proposed method to study the nonlinear response arising from the hydrodynamic description of free electrons in the metallic constituents of the waveguides, comparing local and nonlocal approximations. As a more general application of our method, we also consider nonlinearities arising from the quantum hydrodynamic theory with electron spill-out. Our results may find applicability in the design and analysis of integrated photonic platforms for nonlinear optics incorporating a wide variety of nonlinear materials such as heavily doped semiconductors for midinfrared applications.