Electric-field-induced second-harmonic generation
Second-harmonic generation (SHG) is a fundamental second-order nonlinear optical process that coherently doubles the frequency of incident light. However, in centrosymmetric materials, the bulk second-order nonlinear susceptibility χ(2) is strictly forbidden by inversion symmetry, suppressing SHG. Applying an external electric field breaks this inversion symmetry and 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 route for electrically tunable nonlinear nanophotonics. This review presents a comprehensive overview of the EFISH effect, covering its fundamentals, various material platforms (including bulk semiconductor crystals, ferroelectrics, van der Waals materials, and polymers), and diverse strategies for electric field engineering. We distinguish EFISH from related effects such as current-induced SHG and the quantum-confined Stark effect. Emerging applications of EFISH in tunable photonic devices, carrier dynamics probing, and nonlinear optical modulation across optical, electronic, and THz regimes are highlighted. Key challenges and prospects for the future development of electrically controlled nonlinear optical systems are outlined. The review consolidates the state of the art and provides a critical assessment of the field's trajectory.