Understanding the Accuracy of Electric Field Induced Second Harmonic Generation (E-FISH) Measurements in Fast Ionization Waves

E-FISH has shown significant potential for measuring electric fields in non-equilibrium plasmas, especially for its high sensitivity and temporal resolution. Yet, a recent study has shown that the E-FISH signal is a function of the entire electric field profile that overlaps with the laser beam path. This raises the possibility that measured field strengths could be in error if the electric field profiles in the plasma are not well matched with that of the calibration. To assess the accuracy of such measurements, we utilize field profiles from numerical simulations to theoretically predict the results of an E-FISH experiment. We apply this approach to analyzing the electric field evolution in a fast ionization wave for a diffuse, atmospheric pressure, nanosecond discharge in a pin-plane geometry. We find that the discharge development is characterized by three distinct phases: an initial phase before the arrival of the front, a second phase after the passage of the front, and a final conduction phase when the interelectrode gap is closed. Each of these phases has an associated field shape that produces a different signal response. Our results suggest that measurements in phase 1 and 3 are likelier to be more accurate, and supports the continued use of E-FISH in these regimes.