Perturbation of Transmission Matrices in Nonlinear Random Media

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In this paper, published in Annalen der Physik, we present the direct measurement of the nonlinear transmission matrix of complex materials, exploiting the strong optothermal nonlinearity of scattering silica aerogel. It is shown that the dephasing effects due to nonlinearity are both controllable and reversible, opening the road to applications based on the nonlinear response of random media