  Spatial light modulators (SLMs) are central to numerous applications ranging
from high-speed displays to adaptive optics, structured illumination
microscopy, and holography. After decades of advances, SLM arrays based on
liquid crystals can now reach large pixel counts exceeding 10^6 with phase-only
modulation with a pixel pitch of less than 10 {\mu}m and reflectance around
75%. However, the rather slow modulation speed in such SLMs (below hundreds of
Hz) presents limitations for many applications. Here we propose an SLM
architecture that can achieve high pixel count with high-resolution phase-only
modulation at high speed in excess of GHz. The architecture consists of a
tunable two-dimensional array of vertically oriented, one-sided microcavities
that are tuned through an electro-optic material such as barium titanate (BTO).
We calculate that the optimized microcavity design achieves a {\pi} phase shift
under an applied bias voltage below 10 V, while maintaining nearly constant
reflection amplitude. As two model applications, we consider high-speed 2D beam
steering as well as beam forming. The outlined design methodology could also
benefit future design of spatial light modulators with other specifications
(for example amplitude modulators). This high-speed SLM architecture promises a
wide range of new applications ranging from fully tunable metasurfaces to
optical computing accelerators, high-speed interconnects, true 2D phased array
beam steering, and quantum computing with cold atom arrays.
