Atomic-vibration-induced nonlinear electronic polarization for terahertz detection

Terahertz (THz) has broad applications for imaging, spectroscopy, and high-data-rate communication. However, THz detection at room temperature remains a significant challenge. By model Hamiltonian including electron-phonon coupling and photon-electron interaction within dipole approximation, we demonstrate that atomic displacement $\stackrel{P\vec}{A}(t)$ driven by THz field $\stackrel{P\vec}{E}(t)$ can induce static nonlinear electronic polarization in semiconductors without spatial inversion symmetry by nonlinear optic effect (${\ensuremath{\alpha}}_{ijk}{E}_{j}{E}_{k}$), Raman effect (${\ensuremath{\beta}}_{ijk}{A}_{j}{E}_{k}$), and nonlinear phononic effect (${\ensuremath{\gamma}}_{ijk}{A}_{j}{A}_{k}$). Our numerical calculations also reveals that nonlinear phononic effect dominates the change of static polarization in ferroelectric semiconductor ${\mathrm{BaTiO}}_{3}$ irradiated by THz field. This work presents a design principle for efficient THz detection at room temperature by monitoring the change of surface polarization induced by THz-driven lattice vibration.