Optical inline interferometer for enhanced low-field detection via electric-field induced second harmonic generation

Abstract Nonlinear optical methods, such as Electric-Field Induced Second Harmonic (E-FISH) generation, have emerged as powerful tools for diagnosing electric fields in plasma environments. The E-FISH technique depends quadratically on the electric field under study, which results in complete insensitivity to its polarity and diminished sensitivity to its low amplitudes. Both of these challenges have been recently resolved in a Local Oscillator Electric-Field Induced Second Harmonic (LOE-FISH) technique, introducing coherent homodyne amplification of a weak E-FISH signal using of an optical local oscillator field. Early LOE-FISH demonstrations relied on a delay line, resulting in decreased accuracy due to the higher sensitivity of the interferometer to environmental noise. In this work, we introduce an "inline" design of the interferometer with maximally shared common paths and a balanced photodetection system, thus greatly reducing sensitivity to environmental noise and laser technical noise and hence improving the robustness of the technique. To this end, we achieve a factor of 143 increase in signal-to-noise ratio (SNR) when LOE-FISH is compared to E-FISH. Furthermore, we successfully measured an electric field as low as 32 V/cm with an SNR of 7.4 during 0.15 s measurement time, estimating an unprecedented detection limit of 12.1 V/(cm √Hz). Our work represents a significant step toward real-time, high-precision diagnostics of electric fields in complex plasma environments, electric field amplitude fluctuations can influence reactive species' generation and overall process efficiency.