Abstract: Optical imaging through highly disordered media such as biological tissue or white paint remains a challenge as spatial information gets mixed because of multiple scattering. Nonetheless, spatial light modulators (SLM) offer millions of degrees of freedom to control the spatial speckle pattern at the output of a disordered medium with wavefront shaping techniques. However, if the laser generates a broadband ultrashort pulse, the transmitted signal becomes temporally broadened as the medium responds disparately for the different spectral components of the pulse.
We have developed several transmission matrix approaches to control the spatio-temporal profile of the pulse at the output of a thick scattering medium. By measuring either the Multispectral or the Time-Resolved Transmission Matrix, we can fully describe the propagation of the broadband pulse either in the spectral or in the temporal domain. With wavefront shaping techniques, one can control both spatial and spectral/temporal degrees of freedom with a single SLM via the spectral diversity of the scattering medium. We have demonstrated deterministic spatio-temporal focusing of an ultrashort pulse of light after the medium, with a temporal compression almost to its initial time-width in different space-time position, as well as different temporal profile such as double pulses. We exploit this spatio-temporal focusing beam to enhance a non-linear process that is two-photon excitation. It opens interesting perspectives in coherent control, light-matter interactions and multiphotonic imaging.