Terahertz Control of Optical Second-Harmonic Generation in Displacive Ferroelectrics: Electronic Bloch-State Reconstruction

Abstract

Optical second-harmonic generation (SHG) is a powerful probe of ferroelectric order, yet its microscopic origin and dynamical control are often understood primarily from symmetry considerations rather than from the underlying electronic processes. Here, we develop a microscopic theory of terahertz-controlled optical SHG in displacive ferroelectrics, establishing a direct connection between THz-driven polar lattice distortions and the resulting electronic nonlinear optical response. Starting from a complete Bloch-band representation, we show that an inversion-breaking lattice distortion reconstructs electronic Bloch wave functions, modifies optical dipole matrix elements, and activates nonlinear optical pathways that are forbidden in the centrosymmetric structure. We derive the second-order susceptibility in terms of the distortion-induced reconstruction of electronic states and optical transition matrix elements, and demonstrate that the electronic SHG susceptibility is linear in the polar distortion, $χ^{(2)}({\bf Q})\propto{\bf Q}$, leading to an SHG intensity quadratic in the inversion-breaking order parameter. When the polar mode is coherently driven by a terahertz electric field, the resulting time-dependent lattice distortion dynamically reconstructs the electronic states and thereby modulates the optical SHG response, with $I_{2ω}(t)\propto|{\bf Q}(t)|^2$ to leading order. This framework distinguishes the THz-driven lattice dynamics from the electronic interband processes responsible for optical SHG, which is particularly important in insulating ferroelectrics where low-energy carrier dynamics are absent. Our theory thus provides a microscopic bridge between nonequilibrium polar lattice dynamics and ultrafast electronic nonlinear optics.