Hybrid graphene-black phosphorus plasmonic nanoribbons for strong terahertz third-harmonic generation

Two-dimensional (2D) materials with strong light-matter interactions have opened what we believe are new opportunities for nonlinear nanophotonics. Here, we present a theoretical study of third-harmonic generation (THG) in a hybrid graphene/black phosphorus (G/BP) nanoribbon array integrated with a metallic layer and dielectric substrate. The interplay between graphene's tunable plasmonic response and the in-plane anisotropy of BP gives rise to strong polarization-dependent nonlinear emission in the terahertz (THz) regime. Finite element method (FEM) simulations incorporating without compromising phase matching, both the third-order surface conductivity of graphene and the anisotropic conductivity tensor of BP reveal pronounced direction-dependent behavior: Notably, in the armchair (AC) orientation at a Fermi level of 0.4 eV, resonant enhancement near 10.2 THz yields a TH output power approximately three times higher than in the zigzag (ZZ) orientation at the same frequency, highlighting the strong anisotropic nonlinear response of the G/BP heterostructure. The THG efficiency can be dynamically modulated through electrostatic tuning of the graphene Fermi level (0.4-0.7 eV) or by varying the nanoribbon geometry, enabling precise spectral and amplitude control without compromising phase matching. Moreover, the structure maintains high efficiency over wide incident angles (±60°), confirming its robustness and suitability for integrated THz photonics. These results highlight G/BP heterostructures as a promising platform for polarization-sensitive, gate-tunable, and compact nonlinear THz sources.