Despite the tremendous progresses in wavefront control through or inside
complex scattering media, several limitations prevent reaching practical
feasibility for nonlinear imaging in biological tissues. While the optimization
of nonlinear signals might suffer from low signal to noise conditions and from
possible artifacts at large penetration depths, it has nevertheless been
largely used in the multiple scattering regime since it provides a guide star
mechanism as well as an intrinsic compensation for spatiotemporal distortions.
Here, we demonstrate the benefit of Transmission Matrix (TM) based approaches
under broadband illumination conditions, to perform nonlinear imaging. Using
ultrashort pulse illumination with spectral bandwidth comparable but still
lower than the spectral width of the scattering medium, we show strong
nonlinear enhancements of several orders of magnitude, through thicknesses of a
few transport mean free paths, which corresponds to millimeters in biological
tissues. Linear TM refocusing is moreover compatible with fast scanning
nonlinear imaging and potentially with acoustic based methods, which paves the
way for nonlinear microscopy deep inside scattering media