Phase-resolved measurement of electric-field-induced second harmonics and its application to noninvasive electric field sensing

Abstract The electric-field-induced second-harmonic generation (E-FISH) method has gained attention as a non-contact, non-invasive, and highly sensitive technique for measuring electric fields. In this method, the electric field profile along the laser path influences the second harmonic (SH) signal and must be carefully characterized. Several approaches have been proposed to infer electric-field profiles from SH distributions obtained by changing the focus position along the laser optical axis. These include optimization-based methods and techniques that assume a predefined electric field shape. However, optimization-based methods are prone to local optima, while assumption-based methods cannot be applied to unknown electric fields. To address these challenges, we propose a novel phase-sensitive approach to infer an unknown electric-field profile without requiring optimization. We generated an additional second-harmonic reference beam using a local oscillator (LO) with a β –BBO crystal and observed interference fringes by superimposing the LO with the E-FISH beam. By analyzing changes in the interference fringes, we determined the phase distribution of the E-FISH beam along the laser optical axis. While larger errors were observed in regions of low electric field strength, using the obtained phase distribution, we successfully inferred the electric-field profile with a peak error of 0.3%. This work marks the first successful demonstration of a technique enabling unique measurements of arbitrary electric-field profiles.