  Nonlinear optics is a rapidly growing field that has found a wide range of
applications. A major limitation, however, is the demand of high power,
especially for high-order nonlinearities. Here, by reconfiguring a
multiple-scattering system, we introduce 'structural nonlinearity' via a
nonlinear mapping between the scattering potential and the output light.
Experimentally we demonstrate high-order, tunable nonlinearities at low power.
The multiply-scattered light features enhanced intensity fluctuations and
long-range spatial correlations. The flexibility, robustness and energy
efficiency of our approach provides a versatile platform for exploring
structural nonlinearities for various applications.
