Deterministic light focusing in space and time through multiple scattering media with a time-resolved transmission matrix approach

We report a method to characterize the propagation of an ultrashort pulse of light through a multiple scattering medium by measuring its time-resolved transmission matrix. This method is based on the use of a spatial light modulator together with a coherent time-gated detection of the transmitted speckle field. Using this matrix, we demonstrate the focusing of the scattered pulse at any arbitrary position in space and time after the medium. Our approach opens different perspectives for both fundamental studies and applications in imaging and coherent control in disordered media.