Implementation of lossless Jones matrices using bilayer birefringent metasurfaces

Abstract

Metasurfaces are attractive options for the realization of on-chip optical systems because of their flat form factor and their ability to modify the wavefront, amplitude, and polarization of light with high efficiency. Several metasurface platforms have been reported that provide different levels of control over the polarization and phase of light, and it has been shown that a single layer birefringent metasurface can implement symmetric and unitary Jones matrices. Optical components with such Jones matrices can convert any arbitrary input polarization to any desired output polarization or perform independent wavefront transformations for two orthogonal polarizations while changing their handedness. However, the Jones matrices that describe the most general polarization and phase transformations are not symmetric, and this limits the range of possible devices that single layer birefringent metasurfaces can implement. For example, a single layer birefringent metasurface cannot impart two different phase shifts to x- and y-polarized light while simultaneously converting their polarizations to right- and left-handed circularly polarized. Here we show that bi-layer birefringent metasurfaces do not suffer from such limitations and can implement the most general form of Jones matrices that describe loss-less and reciprocal optical components. By using the Poincare sphere representation and closed-form relations, we identify the degrees of freedom in the design and present a procedure that allows for the design of large-scale devices based on bi-layer metasurfaces. As a proof-of-concept, we demonstrate a chiral bi-layer metasurface that focuses left- and right-handed polarized waves to two different points without changing their polarizations.