  Reservoir computers (RC) are randomized recurrent neural networks well
adapted to process time series, performing tasks such as nonlinear distortion
compensation or prediction of chaotic dynamics. Deep reservoir computers
(deep-RC), in which the output of one reservoir is used as the input for
another one, can lead to improved performance because, as in other deep
artificial neural networks, the successive layers represent the data in more
and more abstract ways. We present a fiber-based photonic implementation of a
two-layer deep-RC based on frequency multiplexing. The two RC layers are
encoded in two frequency combs propagating in the same experimental setup. The
connection between the layers is fully analog and does not require any digital
processing. We find that the deep-RC outperforms a traditional RC by up to two
orders of magnitude on two benchmark tasks. This work paves the way towards
using fully analog photonic neuromorphic computing for complex processing of
time series, while avoiding costly analog-to-digital and digital-to-analog
conversions.
