Electric field distribution in dielectric barrier discharge plasma actuators powered by nanosecond pulse and AC waveforms are measured by picosecond second harmonic generation. In a ns pulse actuator, the measurement results demonstrate a significant electric field offset before the discharge pulse, due to the surface charge accumulation during previous discharges pulses. This shows that charge accumulation is a significant factor affecting the electric field in the discharge, even at very low pulse repetition rates. The time scale for the electric field reduction in the plasma after breakdown is fairly long, several tens of ns, including the conditions when the discharge develops as a diffuse ionization wave. This suggests that a considerable fraction of the energy is coupled to the plasma at a relatively low reduced electric field, several tens of Townsend. At these conditions, the discharge energy fraction thermalized as rapid heating remains fairly low, limiting the effect on the flow caused by the high-amplitude localized thermal perturbations. In an AC actuator, the horizontal electric field during the negative voltage half-period exceeds the field measured during the positive half-period. This indicates the dominant effect of negative ions generated in the plasma on the ion wind, resulting in the flow entrainment away from the high-voltage electrode. This result is consistent with previous measurements of electrohydrodynamic body force distributions, which show that the body force peaks during the negative going half-cycle.