Terahertz-driven four-wave mixing at glass surfaces: Probing vibrational resonances and structural regimes

Disordered materials such as glasses exhibit complex structural dynamics that are challenging to probe with conventional spectroscopies. We demonstrate that terahertz-driven four-wave mixing (FWM) at glass surfaces provides direct access to low-frequency vibrational modes and structural evolution in amorphous solids. Applied to a compositional series of PbO-silicate glasses (20-54 mol% PbO), this technique resolves distinct contributions from collective Boson-peak excitations and Pb-O / Si-O network stretching modes, and tracks their systematic evolution across structurally distinct compositional regimes. The dominant vibrational frequency blueshifts with PbO content, reflecting the progressive evolution of the Pb$^{2+}$ network role from silicate-modifier to ward network-former. A pronounced enhancement of the FWM signal near 44 mol% PbO coincides with the emergence of medium-range Pb-Pb correlations, while in-plane-to-out-of-plane FWM intensity ratio ($I_{\rm SS}/I_{\rm PS}$) tracks $\chi^{(3)}$ tensor anisotropy tied to Pb$^{2+}$ lone-pair spatial correlations. The non-monotonic peak in both observables at 44 mol% PbO - a composition where NMR finds no change in local Pb-O coordination and Pb-O-Pb free-oxide linkages are negligible - provides direct evidence that a collective lone-pair reorganization occurs in the medium-range structure independently of nearest-neighbor bonding. These results establish terahertz-driven FWM as a bulk-sensitive, near-surface depth-confined ($\sim$50 nm) nonlinear spectroscopy sensitive to vibrational and electronic structural fingerprints inaccessible to linear infrared, Raman, and terahertz time-domain probes.