  Wavefront shaping techniques allow waves to be focused on a
diffraction-limited target deep inside disordered media. To identify the target
position, a guidestar is required that typically emits a frequency-shifted
signal. Here we present a noninvasive matrix approach operating at a single
frequency only, based on the variation of the field scattered by a nonlinear
target illuminated at two incident powers. The local perturbation induced by
the nonlinearity serves as a guide for identifying optimal incident wavefronts.
We demonstrate maximal focusing on electronic devices embedded in chaotic
microwave cavities and extend our approach to temporal signals. Finally, we
exploit the programmability offered by reconfigurable smart surfaces to enhance
the intensity delivered to a nonlinear target. Our results pave the way for
deep imaging protocols that use any type of nonlinearity as feedback, requiring
only the measurement of a monochromatic scattering matrix.
