Complex-Birefringent Dielectric Metasurfaces for Arbitrary Polarization-Pair Transformations

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 Poincare 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.