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)∝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 I2ω(t)∝|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.
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BibTeX
@misc{liu2026terahertz,
title = {{Terahertz Control of Optical Second-Harmonic Generation in Displacive Ferroelectrics: Electronic Bloch-State Reconstruction}},
author = {Hong-Kui Liu and Zi-Chen Qin and Jun-Song Wu and Yue Yuan},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30665},
eprint = {2608.30665},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30665},
}
RIS
TY - UNPB
TI - Terahertz Control of Optical Second-Harmonic Generation in Displacive Ferroelectrics: Electronic Bloch-State Reconstruction
AU - Hong-Kui Liu
AU - Zi-Chen Qin
AU - Jun-Song Wu
AU - Yue Yuan
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30665
UR - https://arxiv.org/abs/2608.30665
AB - 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)∝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)∝|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.
ER -