Sub-wavelength, phase-sensitive microscopy of third-order nonlinearity in terahertz frequencies

Light-induced coherent phonon dynamics provides both structural characterization of materials and ultrafast manipulation of materials’ properties. Infrared-active phonons in centrosymmetric materials can be optically probed from their χ³ spectra via terahertz electric field induced second harmonic generation (TEFISH). We report phase-sensitive heterodyne TEFISH microscopy offering simultaneous temporal, spectral, and spatial resolution in the frequency range between 5 — 15 THz, which is the phonon bands of most quantum materials. The method combines intense and frequency-tunable narrowband terahertz source in the frequency range and stable colinear heterodyne detection. It reveals ultrafast phonon dynamics in sub-wavelength two-dimensional crystals and polaritonic resonators, enabling quantitative measurement of χ³. This far-field vibrational spectroscopy with resolution as low as 3 μm and high sensitivity to the monolayer limit is suitable for studying electron-phonon and spin-phonon coupling in a broad range of quantum materials.