A programmable metasurface inside an electromagnetic cavity can compute. The input data is encoded into the tunable scattering elements of the metasurface, not into the input wavefront. The cavity's electromagnetic modes process the data through multiple reflections and inter-element coupling. The output is read from the resulting field pattern.
Hammami, Le Magoarou, and colleagues analyze what makes this physical neural network expressive. The answer is coupling. When the mutual coupling between metasurface elements is strong, the mapping from element configurations to electromagnetic fields is strongly nonlinear — even a single-layer system performs well on complex tasks. The inter-element electromagnetic interaction is the computational resource.
The counterintuitive finding: adding physical layers (stacking metasurfaces in the cavity) improves expressivity without increasing the number of trainable parameters. The additional layers don't add weights — they add physical depth. Each layer introduces new wave interactions, new scattering paths, new nonlinear mixing of the encoded information. The computation happens in the physics, not in the parameterization.
When coupling is weak, depth compensates. When coupling is strong, even a single layer suffices. The two mechanisms — coupling strength and physical depth — are substitutable sources of nonlinearity, both arising from the electromagnetic interactions rather than from any designed nonlinear activation function.
The waves do the computation. The engineer's job is to let them.