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Forming a desired optical field distribution from a given source requiresprecise spatial control of a field's amplitude and phase. Low-loss metasurfacesthat allow extreme phase and polarization control of optical fields have beendemonstrated over the past few years. However, metasurfaces that provideamplitude control have remained lossy, utilizing mechanisms such as reflection,absorption, or polarization loss to control amplitude. Here, we describe theamplitude and phase manipulation of optical fields without loss, by using twolossless phase-only metasurfaces separated by a distance. We first demonstratea combined beam-former and splitter optical component using this approach.Next, we show a high-quality computer-generated three-dimensional hologram. Theproposed metaoptic platform combines the advantage of lossless, complex-valuedfield control with a physically small thickness. This approach could lead tolow-profile, three-dimensional holographic displays, compact opticalcomponents, and high precision optical tweezers for micro-particlemanipulation.

Lossless, Complex-Valued Optical Field Control with Compound Metaoptics