Working with finite numbers of modes to describe, generate, and detect optical fields can be both mathematically economical and physically useful. Such a modal basis can map directly to various applications in communications, sensing, and processing. But, we need a way to generate and analyze such fields, including measurement and control of both the relative amplitudes and phases of the modal components. Ideally such an analysis scheme would operate directly on the field, without needing a separate, mutually coherent reference beam. Here, we show first how to measure all those relative amplitudes and phases automatically and simultaneously. The method repurposes a self-configuring network of ${2} \times {2}$ blocks, such as integrated Mach–Zehnder interferometers, that can automatically align itself to the optical field by a sequence of simple one-parameter power minimizations when network elements, such as phase shifters, are adjusted. The optical field is then directly deduced from the resulting settings of those elements. We show how the entire network can be calibrated for such measurements, automatically and with just two light beams. Then, using the same calibration and running the mesh backwards, we can also controllably generate an arbitrary multimode field. Explicit algorithms and formulas are given for operating this system.

中文翻译：

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使用自配置网络分析和生成多模光场

使用有限数量的模式来描述，生成和检测光场在数学上既经济又在物理上有用。这种模式基础可以直接映射到通信，传感和处理中的各种应用。但是，我们需要一种生成和分析此类场的方法，包括对模态分量的相对幅度和相位进行测量和控制。理想地，这种分析方案将直接在现场运行，而不需要单独的相互相干的参考光束。在这里，我们首先展示如何自动并同时测量所有这些相对振幅和相位。该方法重新调整了$ {2} \ times {2} $的自配置网络的用途模块，例如集成的Mach-Zehnder干涉仪，在调整网络元件（例如移相器）时，可以通过一系列简单的单参数功率最小化来自动将自身与光场对齐。然后，从这些元件的最终设置中直接推断出光场。我们展示了如何自动，仅用两个光束对整个网络进行此类测量的校准。然后，使用相同的校准并向后运行网格，我们还可以可控地生成任意多模场。给出了用于操作系统的显式算法和公式。