Electric field induced second harmonic generation (E-FISH) has recently demonstrated significant potential as a method for making absolute electric field measurements in non-equilibrium plasmas and gas discharges. Previous studies have relied on the plane-wave approximation in quantifying these measurements, while in reality, focused laser beams are almost always used. In this work, we perform a theoretical and experimental study using focused Gaussian beams, and examine the consequent effects on the E-FISH signal. We show that in addition to important parameters such as the external electric field strength, wave vector mismatch and Rayleigh range, the signal is strongly influenced by the full length and shape of this external field profile. We attribute this to the Gouy phase shift associated with focused beams, and note that analogous effects have been previously observed in second and third harmonic generation microscopy. This dependence of the E-FISH signal on the spatial profile of the external field is worth highlighting since it is often not easily determined a priori in a plasma, and neglecting its influence could lead to an incorrect electric field measurement. To minimize any inaccuracies associated with this issue, we propose several recommendations to consider when using the E-FISH diagnostic with focused beams.

电场感应二次谐波（E-FISH）作为一种用于在非平衡等离子体和气体放电中进行绝对电场测量的方法，最近已显示出巨大的潜力。先前的研究在量化这些测量值时依赖于平面波近似，而实际上，几乎总是使用聚焦激光束。在这项工作中，我们使用聚焦的高斯光束进行了理论和实验研究，并检查了对E-FISH信号的影响。我们表明，除了重要的参数（例如外部电场强度，波矢量失配和瑞利范围）外，该信号还受到此外部场轮廓的全长和形状的强烈影响。我们将其归因于与聚焦光束相关的Gouy相移，并注意，以前在第二和三次谐波产生显微镜中已经观察到类似的效果。E-FISH信号对外部场空间分布的这种依赖性值得强调，因为它通常不容易确定等离子体中的先验知识，而忽略其影响可能会导致错误的电场测量。为了最大程度地减少与此问题相关的不准确之处，我们提出了在聚焦光束下使用E-FISH诊断时要考虑的一些建议。