摘要： Metasurfaces composed of arrays of nano-resonators are a powerful tool for manipulation of polarization of light. All-dielectric metasurfaces do not suffer absorption losses and are highly transparent in contrast to metallic structures, and combined with recent advances in their design and fabrication, have enabled efficient polarization manipulation and arbitrary phase shaping. A new regime of complex-valued birefringence has been recently suggested, extending the notion of real-valued birefringence through the specially introduced polarization-sensitive loss or gain. This can enable fundamentally new possibilities for polarization control, such as amplifying the angle between polarization vectors to improve detection sensitivity. However, a practical realization of complex-valued birefringence concept was missing. In particular, the theoretical approach in Ref. [4] was based on a complicated metamaterial with loss and gain, which is challenging to fabricate and not suitable for quantum applications. Here, we report on a new conceptual approach for implementing arbitrary complex-valued birefringence with pairwise birefringent elements using high-index dielectric nanostructures. We formulate a practical design principle, which is optimal for achieving any desirable polarization transformation. While loss is inherently necessary for implementing complex birefringence, our all-dielectric metasurface design achieves the mathematically minimum required amount of loss through tailored diffraction without any material absorption.