We present an optical measurement method using a femtosecond laser for nonintrusive measurements of electric field strength and orientation in virtually any gas or gas mixture via second-harmonic generation. This simple method takes advantage of the asymmetry in polarizability induced by an applied electric field, which enables the otherwise forbidden second-harmonic generation in any centrosymmetric or homogeneous media. The use of a femtosecond laser source permits high intensities without avalanche breakdown and leads to the measurement of electric field strength down to approximately $100\mathrm{V}/\mathrm{cm}$ in air with submillimeter spatial resolution governed by the confocal parameter and femtosecond temporal resolution governed by the laser-pulse duration.

The paper presents the results of time-resolved electric field measurements in a nanosecond discharge between two plane electrodes covered by dielectric plates, using picosecond four-wave mixing diagnostics. For absolute calibration, the IR signal was measured in hydrogen at a pressure of 440 Torr, for electrostatic electric field ranging from 0 to 8 kV cm ⁻¹ . The calibration curve (i.e. the square root of IR signal intensity versus electric field) was shown to be linear. By measuring the intensities of the pump, Stokes, and IR signal beam for each laser shot during the time sweep across the high-voltage pulse, temporal evolution of the electric field in the nanosecond pulse discharge was determined with sub-nanosecond time resolution. The results are compared to kinetic modeling predictions, showing good agreement, including non-zero electric field offset before the main high voltage pulse, breakdown moment, and reduction of electric field in the plasma after breakdown. The difference between the experimental results and model predictions is likely due to non-1D structure of the discharge. Comparison with the kinetic modeling predictions shows that electric field in the nanosecond pulse discharge is controlled primarily by electron impact excitation and charge accumulation on the dielectric surfaces.