Coherent homodyne detection for amplified cross-beam electric-field induced second harmonic

The electric-field induced second harmonic (E-FISH) signal sensing is commonly used as a nonlinear optical technique to probe electric fields inside a plasma region. Cross-beam E-FISH is being investigated to improve spatial resolution by defining the interaction volume via a controlled geometry of two overlapping noncolinear optical beams. This drastic reduction in interaction length of the electric field and laser region results in a significant signal reduction. To overcome this signal reduction, we introduce coherent amplification of the cross-beam E-FISH signal by mixing the low E-FISH signal with a phase-locked bright local oscillator. We demonstrate enhancement of the signal. By introducing a local oscillator we can now derive the polarity of the measured electric field through the phase of the homodyne signal. To illustrate the technique, we, for the first time, to the best of our knowledge, measure the magnitude and the direction of the electric field in a cold atmospheric pressure plasma jet, which dynamically follows the profile of the applied bias current.