Fabry–Perot cavities are central to many optical measurement systems. In high-precision experiments, such as aLIGO and AdVirgo, coupled cavities are often required, leading to complex optical behavior. We show, for the first time to our knowledge, that discrete linear canonical transforms (LCTs) can be used to compute circulating optical fields for cavities in which the optics have arbitrary apertures, reflectance and transmittance profiles, and shape. We compare the predictions of LCT models with those of alternative methods. To further highlight the utility of the LCT, we present a case study of point absorbers on the aLIGO mirrors and compare it with recently published results.

中文翻译：

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使用离散线性正则变换对循环腔场进行建模

法布里-珀罗腔是许多光学测量系统的核心。在 aLIGO 和 AdVirgo 等高精度实验中，通常需要耦合腔，从而导致复杂的光学行为。据我们所知，我们第一次展示了离散线性规范变换 (LCT) 可用于计算光学具有任意孔径、反射率和透射率分布以及形状的腔的循环光场。我们将 LCT 模型的预测与替代方法的预测进行比较。为了进一步强调 LCT 的实用性，我们介绍了 aLIGO 反射镜上的点吸收器的案例研究，并将其与最近发表的结果进行了比较。