Electric field profile measurement along probing laser path based on electric field-induced second-harmonic generation

Electric field measurement based on electric field-induced second-harmonic generation (E-FISHG) of gas molecules is a promising method that enables noninvasive field measurement in gases 1 , 2 . Although the probing laser beam is focused on the target area by a lens, the signal detected by the E-FISHG method is affected by the electric field along the probing laser path. The influencing path spans many tens of times the Rayleigh length front and rear the focused spot 3 . The E-FISHG signal has been frequently calibrated under uniform electric fields. However, this can yield a significantly incorrect calibrated value if the difference between the electric field profiles in the measurement and calibration is not considered. In this paper, we propose a new method to calibrate, and furthermore, restore the electric field profile along a probing optical path by measuring a series of E-FISHG signals by changing the focusing spot position. We obtained the confocal parameter of the probing light and the coefficient between the SHG and probing light intensities from the E-FISHG signals by moving cylindrical-to-cylindrical electrodes. Furthermore, we acquired the one-dimensional profile of the electric field from the distribution of the SHGs generated using cylindrical- to-cylindrical and sphere-to-sphere electrodes, which is verified by an experiment. Using the proposed restoration method, we successfully restored the electric field profiles generated between cylindrical-to-cylindrical and sphere-to- sphere electrodes within 2% deviation from the numerically computed ones.