Proof of realizing arbitrary unitary light transformation based on polarized diffractive optical networks

Diffractive optical networks (DONs) enable arbitrary unitary transformations but are typically limited to scalar light fields. This limitation is overcome by introducing polarized diffractive optical networks (PDONs) composed of cascaded birefringent metasurfaces. In this work, we prove that a cascade of birefringent metasurfaces provides sufficient degrees of freedom to synthesize any unitary transformation on the joint polarization and spatial mode space. In addition, the results also indicate that PDONs can realize arbitrary unitary transformations even under non-paraxial conditions, confirming that their operational regime extends beyond the paraxial approximation.