  As artificial neural networks (ANNs) continue to make strides in wide-ranging
and diverse fields of technology, the search for more efficient hardware
implementations beyond conventional electronics is gaining traction. In
particular, optical implementations potentially offer extraordinary gains in
terms of speed and reduced energy consumption due to intrinsic parallelism of
free-space optics. At the same time, a physical nonlinearity, a crucial
ingredient of an ANN, is not easy to realize in free-space optics, which
restricts the potential of this platform. This problem is further exacerbated
by the need to perform the nonlinear activation also in parallel for each data
point to preserve the benefit of linear free-space optics. Here, we present a
free-space optical ANN with diffraction-based linear weight summation and
nonlinear activation enabled by the saturable absorption of thermal atoms. We
demonstrate, via both simulation and experiment, image classification of
handwritten digits using only a single layer and observed 6-percent improvement
in classification accuracy due to the optical nonlinearity compared to a linear
model. Our platform preserves the massive parallelism of free-space optics even
with physical nonlinearity, and thus opens the way for novel designs and wider
deployment of optical ANNs.
