Optical Inline Interferometer for Enhanced Low-Field Detection via Electric-Field Induced Second Harmonic Generation

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 1.7 V/(cm Hz^0.5). 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.非线性光学方法，例如电场诱导二次谐波（Electric-Field Induced Second Harmonic，E-FISH）生成技术，已成为等离子体环境中电场诊断的有力工具。E-FISH技术与待测电场呈二次方依赖关系，这导致其完全无法识别电场极性，且对弱电场幅值的检测灵敏度有所下降。近期提出的本地振荡器电场诱导二次谐波（Local Oscillator Electric-Field Induced Second Harmonic，LOE-FISH）技术则解决了这两大难题，该技术通过光学本地振荡器场实现微弱E-FISH信号的相干零差放大。早期的LOE-FISH演示实验依赖延迟线结构，由于干涉仪对环境噪声的敏感度较高，导致检测精度下降。本工作提出了一种采用最大程度共享公共光路的同轴干涉仪设计，并搭配平衡光电探测系统，由此大幅降低了对环境噪声与激光技术噪声的敏感度，进而提升了该技术的鲁棒性。为此，相较于E-FISH，LOE-FISH的信噪比（signal-to-noise ratio，SNR）提升了143倍。此外，我们在0.15秒的测量时长内，成功测得低至32 V/cm的电场，对应信噪比为7.4，估算得到前所未有的检测极限为1.7 V/(cm·Hz^0.5)。本工作为复杂等离子体环境下电场的实时高精度诊断迈出了重要一步——电场幅值波动会影响反应活性物种的生成与整体工艺效率。