  Metasurfaces are optically thin metamaterials that promise complete control
of the wavefront of light but are primarily used to control only the phase of
light. Here, we present an approach, simple in concept and in practice, that
uses meta-atoms with a varying degree of form birefringence and rotation angles
to create high-efficiency dielectric metasurfaces that control both the optical
amplitude and phase at one or two frequencies. This opens up applications in
computer-generated holography, allowing faithful reproduction of both the phase
and amplitude of a target holographic scene without the iterative algorithms
required in phase-only holography. We demonstrate all-dielectric metasurface
holograms with independent and complete control of the amplitude and phase at
up to two optical frequencies simultaneously to generate two- and
three-dimensional holographic objects. We show that phase-amplitude
metasurfaces enable a few features not attainable in phase-only holography;
these include creating artifact-free two-dimensional holographic images,
encoding phase and amplitude profiles separately at the object plane, encoding
intensity profiles at the metasurface and object planes separately, and
controlling the surface textures of three-dimensional holographic objects.
