Measurement of inhomogeneous electric field based on electric field-induced second-harmonic generation

The electric field-induced second-harmonic generation (E-FISH) method can offer high spatiotemporal resolution in electric field measurement, but faces challenge in reconstructing the inhomogeneous electric field along the probing laser. This paper presents an inversion method to reconstruct the electric field profile by using E-FISH signals measured from multiple points along the probing laser. The relationship between the condition number of the inversion coefficient matrix and the parameters of E-FISH measurement system is clarified. The inversion method is validated through experimental investigations conducted in three different electrode configurations, namely the plate-to-plate gap, the rod-to-rod gap, and the rod-plate gap. With the inhomogeneity coefficient varies from 1 to 10.7, the maximum deviation between the measured electric field and the finite element simulation is less than 6%. This method does not rely on priori assumptions and electrode configurations, and exhibits good robustness in resisting the effect of measurement noise on the inversion accuracy.