Compound Meta-Optic for Lossless Complete Field Manipulation

The ability to independently control the amplitude, phase, and polarization state of light is needed for a wide variety of scientific and industrial applications and generally requires multiple conventional optical elements such as lenses, polarizers, and amplitude masks. The need for multiple elements results in large systems that can be difficult to integrate into compact optical packages. Optical metasurfaces, comprising sub-wavelength scale meta-atoms, provide a versatile platform for manipulating optical waves in a compact form factor, and have been used to create a wide variety of optical elements such as lenses, beam splitters, and waveplates. Metasurfaces, moreover, can go beyond simple replacement of conventional optics by providing novel functionalities including multi-functional imaging, phase-mining, image processing, polarimetry, augment reality, holography.<br/>Although metasurface-based wavefront control has been demonstrated in the past, independent control of phase and amplitude using a single metasurface comes at the expense of a polarization-dependent response. The involvement of polarizer components introduces loss that can be as high as 90% in some circumstances. Moreover, the symmetric Jones matrix that dictates the transmission of each meta-atom prevents independent control over polarization conversion for orthogonal axis. Spatial multiplexing, on the other hand, can provide independent polarization manipulation over orthogonal states by using interference between the neighboring meta-atoms. However, this method leads to higher diffraction orders due to the use of a larger supercell, limiting the diffraction efficiency in the target order. An alternative approach is the use of multi-layer, compound meta-optics, which harness independent design degrees of freedom in each layer and allow for light redistribution during propagation for realizing near loss-less amplitude and phase functions.<br/>In this work, we expand on the multi-layer meta-optic platform to include polarization by employing end-to-end design optimization. In this platform, birefringent meta-atoms are used for both metasurfaces, enabling independent control over orthogonal polarization states as well as polarization conversion between those states. Redistribution of the wavefront between metasurface layers allows for loss-less, complex-valued wavefront and polarization control, that is not limited by the symmetric Jones matrix. As a proof of concept, we experimentally demonstrate a meta-optic for optical mode manipulation, including a spatial division multiplexer (SDM), an optical mode converter, and a vectorial hologram.<br/>All the demonstrated devices are optimized by an end-to-end inverse design algorithm, which is a stochastic gradient descent (SGD)-based platform, a common approach in machine learning applications. The use of multiple loss functions as well as <i>k</i>-space constraints during optimization avoids overfitting and scattering phase morphology for metasurfaces, allowing for highly improved device performance. In our case, all the devices achieve diffraction efficiency above 80% in experimental measurements. Meanwhile, the meta-optic platform that combines birefringence with the ability to redistribute the wavefront across the aperture, also demonstrates independent and decent control over the amplitude, phase and polarization state. We believe that the increased engineering freedom provided by compound meta-optics will open new avenues for the development of compact optical systems with novel functionalities and applications in quantum entanglement, optical encryption, and optical communications.