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The transmission matrix is a unique tool to control light through ascattering medium. A monochromatic transmission matrix does not allow temporalcontrol of broadband light. Conversely, measuring multiple transmissionmatrices with spectral resolution allows fine temporal control when a pulse istemporally broadened upon multiple scattering, but requires very longmeasurement time. Here, we show that a single linear operator, measured for abroadband pulse with a co-propagating reference, naturally allows for spatialfocusing, and interestingly generates a two-fold temporal recompression at thefocus, compared with the natural temporal broadening. This is particularlyrelevant for non-linear imaging techniques in biological tissues.

Temporal recompression through a scattering medium via a broadband transmission matrix