Phase-matched nonlinear second-harmonic generation in plasmonic metasurfaces

The phase matching between the propagating fundamental and nonlinearly generated waves plays an important role in the efficiency of the nonlinear frequency conversion in macroscopic crystals. However, in nanoscale samples, such as nanoplasmonic structures, the phase-matching condition is often ignored due to the sub-wavelength nature of the materials. Here, we first show that the phase matching of the lattice plasmon modes at the fundamental and second-harmonic frequencies in a plasmonic nanoantenna array can effectively enhance the surface-enhanced second-harmonic generation. Additionally, a significant enhancement of the second-harmonic generation is demonstrated using stationary band-edge lattice plasmon modes with zero phase.