Second-Harmonic Generation in Optical Fibers Under an External Electric Field

A method for the second-harmonic generation (SHG) in optical fibers by exploiting the third-order nonlinearity under an external electric field is proposed. The analysis begins with the electric polarization vector of the SHG, and the analytical solution for the SHG is presented. When fiber birefringence is neglected, a mode-field matching condition is introduced. The nonlinearity-induced shift in propagation constant is provided based on Gaussian approximation. For a specific case, the power of SHG is calculated. The results show that the SHG power scales quadratically with the nonlinear coefficient. Reducing the effective area of the fiber and increasing the nonlinear coefficient can enhance the SHG power by 1–2 orders of magnitude. Since phase matching strongly affects the SHG process, optimizing the fiber design is crucial. Additionally, the polarization state of SHG is shown to have the same as the equivalent optical field of the injected fundamental wave. This work demonstrates potential for distributed sensing of electric fields and lightning events in high-voltage power grids using optical fibers.