Dual-band higher-order topological states and four-wave mixing in plasmonic valley-Hall metasurfaces

Abstract

Higher-order topological states in plasmonic metasurfaces are of great importance in practice for their tight confinements and high field enhancements, providing many promising nonlinear applications such as robust quantum light source through four-wave mixing (FWM). However, previous works are limited to single-band modes and FWM processes based on second-order topological corner states have still not been revealed. In this work, we propose a plasmonic valley-Hall topological metasurface, which is modelled based on coupled dipole approximation with dyadic Green's functions containing retarded long-range interaction terms. Simultaneous lifting of Dirac degeneracies in two bandgaps due to inversion-symmetry breaking results in dual-band second-order topological states, which are robust against structural disorder. We present a theoretical approach for considering the nonlinear interaction in dipole arrays and numerically show nonlinear generation of corner mode at signal frequency via the FWM process by pumping with edge modes. The results presented in this work will pave a broad way towards the wide applications of topological plasmonic metasurfaces.