Recent advances in optical metasurfaces enable control of the wavefront, polarization and dispersion of optical waves beyond the capabilities of conventional diffractive optics. An optical design space that is poised to highly benefit from these developments is the folded optics architecture where light is confined between reflective surfaces and the wavefront is controlled at the reflective interfaces. In this manuscript we introduce the concept of folded metasurface optics by demonstrating a compact high resolution optical spectrometer made from a 1-mm-thick glass slab with a volume of 7 cubic millimeters. The spectrometer has a resolution of 1.2 nm, resolving more than 80 spectral points in a 100-nm bandwidth centered around 810 nm. The device is composed of three different reflective dielectric metasurfaces, all fabricated in a single lithographic step on one side of a transparent optical substrate, which simultaneously acts as the propagation space for light. An image sensor, parallel to the spectrometer substrate, can be directly integrated on top of it to achieve a compact mono- lithic device including all the active and passive components. Multiple spectrometers, with similar or different characteristics and operation bandwidths may also be integrated on the same chip and fabricated in a batch process, significantly reducing their costs and increas- ing their functionalities and integration potential. In addition, the folded metasystems design can be applied to many optical systems, such as optical signal processors, interferometers, hyperspectral imagers and computational optical systems, significantly reducing their sizes and increasing their mechanical robustness and potential for integration.
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