Reciprocity is a fundamental principle of wave physics and directly relates to the symmetry in the transmission through a system when interchanging the input and output. The coherent transmission matrix (TM) is a convenient method to characterize wave transmission through general media. Here, we demonstrate the optical reciprocal nature of complex media by exploring their TM properties. We measured phase-corrected TMs of forward and round-trip propagation in a single polarization state through a looped 1 m-long step-index optical multimode fiber (MMF) to experimentally verify a transpose relationship between the forward and backward transmission. This symmetry impedes straightforward MMF calibration from proximal measurements of the round-trip TM. Furthermore, we show how focusing through the MMF with digital optical phase conjugation is compromised by system loss since time reversibility relies on power conservation. These insights may inform the development of new imaging techniques through complex media and coherent control of waves in photonic systems.

中文翻译：

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复杂系统往返传输中互易引起的对称性


互易性是波动物理学的基本原理，与交换输入和输出时通过系统传输的对称性直接相关。相干传输矩阵（TM）是一种表征波在一般介质中传输的便捷方法。在这里，我们通过探索复杂介质的 TM 特性来展示其光学互易性质。我们通过环形 1 m 长阶跃折射率光纤多模光纤 (MMF) 测量了单偏振态下前向和往返传播的相位校正 TM，以通过实验验证前向和反向传输之间的转置关系。这种对称性阻碍了从往返 TM 的近端测量中直接进行 MMF 校准。此外，我们还展示了通过具有数字光学相位共轭的 MMF 聚焦如何受到系统损耗的影响，因为时间可逆性依赖于节能。这些见解可能会为通过复杂介质和光子系统中波的相干控制来开发新成像技术提供信息。