Accurately characterizing the width of a narrow (high $Q$) resonance can be quite challenging, requiring either a high-resolution grating spectrometer or a Fourier transform spectrometer with a long delay range. Here, we describe a new technique to determine the $Q$ of a resonance based on spatial measurements that is not subject to the same limitations as conventional methods. We theoretically show that this technique can give an accurate measurement of $Q$ for essentially any set of input beam parameters, even if the spectral resolution of the measurement is inadequate to resolve the linewidth of the resonance. We confirm this striking result with both numerical simulations and experimental measurements.

中文翻译：

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使用空间模式重塑来表征光学共振

准确表征窄幅（高 $问$共振可能非常具有挑战性，需要高分辨率的光栅光谱仪或具有较长延迟范围的傅立叶变换光谱仪。在这里，我们描述了一种新的技术来确定$问$基于空间测量的共振的分析不受与传统方法相同的限制。我们从理论上证明，该技术可以对$问$即使测量的光谱分辨率不足以解决共振的线宽，对于几乎任何一组输入光束参数来说，也是如此。我们通过数值模拟和实验测量证实了这一惊人的结果。