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Second-order nonlinearity in solids gives rise to a plethora of uniquephysical phenomena ranging from piezoelectricity and optical rectification tooptical parametric amplification, spontaneous parametric down-conversion, andthe generation of entangled photon pairs. Monolayer transition metaldichalcogenides (TMDs), such as MoS$_2$, exhibit one of the highest knownsecond-order nonlinear coefficients. However, the monolayer nature of thesematerials prevents the fabrication of resonant objects exclusively from thematerial itself, necessitating the use of external structures to achieveoptical enhancement of nonlinear processes. Here, we exploit the 3R phase of amolybdenum disulfide multilayer for resonant nonlinear nanophotonics. The lackof inversion symmetry, even in the bulk of the material, provides a combinationof a massive second-order susceptibility, an extremely high and anisotropicrefractive index in the near-infrared region ($n>$~4.5), and low absorptionlosses, making 3R-MoS$_2$ highly attractive for nonlinear nanophotonics. Wedemonstrate this by fabricating 3R-MoS$_2$ nanodisks of various radii, whichsupport resonant anapole states, and observing substantial ($>$ 100-fold)enhancement of second-harmonic generation in a single resonant nanodiskcompared to an unpatterned flake of the same thickness. The enhancement ismaximized at the spectral overlap between the anapole state of the disk and thematerial resonance of the second-order susceptibility. Our approach unveils apowerful tool for enhancing the entire spectrum of optical second-ordernonlinear processes in nanostructured van der Waals materials, thereby pavingthe way for nonlinear and quantum high-index TMD-nanophotonics.

Combining ultrahigh index with exceptional nonlinearity in resonant transition metal dichalcogenide nanodisks