Birefringent materials introduce phase retardance between different polarization states and underpin the operation of wave plates for control of classical and quantum light. However, such transformation always preserves the angle between two polarization states on the Poincaré sphere and does not allow for amplification of the polarization differences between two proximate states. Here we develop birefringent metasurfaces with judiciously tailored radiative loss for nonconservative class of complex-birefringence that combines polarization-dependent loss and phase retardance. We prove that the presence of loss enables the mapping of any nonorthogonal pair of polarizations to any other pair at the output. We establish an optimal design-framework for metasurfaces based on pairwise nanoresonators and experimentally demonstrate the amplification of small polarization differences with unconventional phase control. As an important example, we reveal that such metasurfaces can perform arbitrary transformations of biphoton quantum states and tailor their degree of polarization entanglement.

中文翻译：

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任意极化-对转换的复双折射介电超表面。

双折射材料在不同的偏振态之间引入了相位延迟，并为控制经典光和量子光提供了支撑波片的基础。但是，这样的变换总是保持庞加莱球上两个偏振态之间的角度，并且不允许放大两个邻近态之间的偏振差异。在这里，我们针对非保守类的复杂双折射，结合了偏振相关的损耗和相位延迟，开发了具有明智剪裁的辐射损耗的双折射超表面。我们证明损耗的存在使输出的任何非正交偏振对都可以映射到任何其他偏振对。我们建立了基于成对的纳米谐振器的超颖表面的最佳设计框架，并通过非常规的相位控制实验证明了小的极化差异的放大。作为一个重要的例子，我们揭示了这种超表面可以执行双光子量子态的任意转换并调整其偏振纠缠度。