  Wave-based analog signal processing holds the promise of extremely fast,
on-the-fly, power-efficient data processing, occurring as a wave propagates
through an artificially engineered medium. Yet, due to the fundamentally weak
non-linearities of traditional wave materials, such analog processors have been
so far largely confined to simple linear projections such as image edge
detection or matrix multiplications. Complex neuromorphic computing tasks,
which inherently require strong non-linearities, have so far remained
out-of-reach of wave-based solutions, with a few attempts that implemented
non-linearities on the digital front, or used weak and inflexible non-linear
sensors, restraining the learning performance. Here, we tackle this issue by
demonstrating the relevance of Time-Floquet physics to induce a strong
non-linear entanglement between signal inputs at different frequencies,
enabling a power-efficient and versatile wave platform for analog extreme deep
learning involving a single, uniformly modulated dielectric layer and a
scattering medium. We prove the efficiency of the method for extreme learning
machines and reservoir computing to solve a range of challenging learning
tasks, from forecasting chaotic time series to the simultaneous classification
of distinct datasets. Our results open the way for wave-based machine learning
with high energy efficiency, speed, and scalability.
