Polarization-resolved microscopy through scattering media via wavefront shaping

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.