  Wavefront shaping has revolutionized imaging deep in scattering media, being
able to spatially and temporally refocus light through or inside the medium.
However, wavefront shaping is not compatible yet with polarization-resolved
microscopy given the need of polarizing optics to refocus light with a
controlled polarization state. Here, we show that wavefront shaping is not only
able to restore a focus, but it can also recover the injected polarization
state without using any polarizing optics at the detection. This
counter-intuitive effect occurs up to several transport mean free path thick
samples, which exhibit a speckle with a completely scrambled state. Remarkably,
an arbitrary rotation of the input polarization does not degrade the quality of
the focus. This unsupervised re-polarization - out of the originally scrambled
polarization state - paves the way for polarization-resolved structural
microscopy at unprecedented depths. We exploit this phenomenon and demonstrate
second harmonic generation (SHG) structural imaging of collagen fibers in
tendon tissues behind a scattering medium.
