Detecting and Focusing on a Nonlinear Target in a Complex Medium

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 different 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.