Continuous-wave, high-resolution, ultra-broadband mid-infrared nonlinear spectroscopy with tunable plasmonic nanocavities

Vibrational sum- and difference-frequency generation (SFG and DFG) spectroscopy probes the nonlinear response of interfaces at mid-infrared (MIR) wavelengths while detecting upconverted signals in the visible. Recent work has moved from large-area films and colloids to nanoscale structures using dual-resonant plasmonic nanocavities that co-confine light and matter in deep-subwavelength volumes. Here we implement high-resolution ($<1$~cm$^{-1}$), continuous-wave ultrabroadband vSFG, vDFG, and four-wave mixing (FWM) coherent spectroscopy from 860 to 1670~cm$^{-1}$ on dual-resonant antennas under ambient conditions. Using a commercial, broadly tunable quantum-cascade laser and eliminating geometric phase matching simplify acquisition and expand spectral reach. The resulting spectra exhibit coherent interference between resonant (vibrational) and nonresonant (electronic) contributions to the effective $\chi^{(2)}$, previously accessible only under fs/ps excitation. Simultaneous measurement of SFG and DFG enables a {ratiometric} analysis that suppresses common-mode drifts and helps reveal vibrational resonances. We demonstrate versatility and reproducibility across several analytes that span distinct relative strengths of vibrational vs. electronic nonlinearities. Together, these capabilities position our approach as a scalable route to multiplexed, high-resolution MIR sensing and a practical basis for chip-level, label-free coherent spectroscopy. It opens a feasible path toward single- and few-molecule optomechanical studies using nanoscale trapping strategies.