Complete vectorial optical mode converter using multi-layer metasurface

A vectorial optical mode converter that can transform an orthogonal set of multiple input vector beams into another orthogonal set of vector beams is attractive for a wide range of applications in optics and photonics. While multi-plane light conversion (MPLC) and metasurface (MS) technologies have been explored to individually address multiple spatial mode conversion and polarization mode manipulation, there has been no universal methodology to simultaneously convert a set of multiple vectorial modes, having non-uniform spatial distributions in both their complex amplitude and polarization, to another set of multiple vectorial modes. In this paper, we demonstrate versatile devices based on the MPLC concept incorporating multi-layer locally birefringent MSs and present a general design formalism for complete vectorial mode conversion in arbitrary cases. The effectiveness of our proposed method is confirmed experimentally by demonstrating a 6-mode (3 spatial modes $\times$ 2 polarization modes) multiplexer, fabricated on a compact chip with a ~0.65 mm$^2$ lateral size in a folded MS configuration. Additionally, we verify its applicability to more advanced functional devices through numerical demonstration of a mode-division-multiplexed dual-polarization coherent receiver and spatial-mode-multiplexed vectorial holography. The versatility of our protocol makes it suitable for designing a myriad of multi-input-multi-output devices, providing a powerful tool for realizing universal optical mode converters for a wide range of applications.