  Forming a desired optical field distribution from a given source requires
precise spatial control of a field's amplitude and phase. Low-loss metasurfaces
that allow extreme phase and polarization control of optical fields have been
demonstrated over the past few years. However, metasurfaces that provide
amplitude control have remained lossy, utilizing mechanisms such as reflection,
absorption, or polarization loss to control amplitude. Here, we describe the
amplitude and phase manipulation of optical fields without loss, by using two
lossless phase-only metasurfaces separated by a distance. We first demonstrate
a combined beam-former and splitter optical component using this approach.
Next, we show a high-quality computer-generated three-dimensional hologram. The
proposed metaoptic platform combines the advantage of lossless, complex-valued
field control with a physically small thickness. This approach could lead to
low-profile, three-dimensional holographic displays, compact optical
components, and high precision optical tweezers for micro-particle
manipulation.
