Electric-field-induced second-harmonic generation

Second-harmonic generation (SHG) is a fundamental nonlinear optical process widely used in photonics; however, it is strictly forbidden in the bulk of centrosymmetric materials due to their inversion symmetry. Nevertheless, applying an external electric field breaks this inversion symmetry. It induces an effective second-order nonlinear response known as the electric-field-induced second-harmonic generation (EFISH) effect. This mechanism enables SHG in centrosymmetric media and provides a effective mechanism for electrically tunable nonlinear nanophotonics. Here, we present a comprehensive overview of the EFISH effect, covering the fundamentals, various material platforms (including bulk semiconductor crystals, ferroelectrics, van der Waals materials, and polymers), as well as diverse strategies for electric field engineering. We distinguish EFISH from related effects including current-induced SHG and the quantum-confined Stark effect, and highlight emerging applications of EFISH in tunable photonic devices, carrier dynamics probing, and nonlinear optical modulation across optical, electronic, and THz regimes. Finally, we outline key challenges and prospects for the future development of electrically controlled nonlinear optical systems.