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Abstract:Light scattering in inhomogeneous media induces wavefront distortions which pose an inherent limitation in many optical applications. Examples range from microscopy and nanosurgery to astronomy. In recent years, ongoing efforts have made the correction of spatial distortions possible by wavefront shaping techniques. However, when ultrashort pulses are employed scattering induces temporal distortions which hinder their use in nonlinear processes such as in multiphoton microscopy and quantum control experiments. Here we show that correction of both spatial and temporal distortions can be attained by manipulating only the spatial degrees of freedom of the incident wavefront. Moreover, by optimizing a nonlinear signal the refocused pulse can be shorter than the input pulse. We demonstrate focusing of 100fs pulses through a 1mm thick brain tissue, and 1000-fold enhancement of a localized two-photon fluorescence signal. Our results open up new possibilities for optical manipulation and nonlinear imaging in scattering media. 2The propagation of light in inhomogeneous media results in scattering and distortions of the propagating wavefront. Such distortions limit the effective focusing of optical intensity and degrade imaging quality through disordered or scattering media 1 . The problem of focusing light through inhomogeneous media is even more challenging when ultrashort pulses are considered, as in addition to the spatial distortions scattering also distorts the pulse shape in time [2][3][4][5] . The challenge of correcting the spatial distortions induced by scattering has been in the focus of many recent works [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] . Weak wavefront aberrations, such as those occurring in astronomical observations through the atmosphere, have been efficiently corrected using adaptive optics techniques [6][7][8] . These techniques, however, were considered inadequate for correcting distortions in highly scattering and turbid samples, which lead to diffusive light propagation and result in complex speckle patterns with no simple relation to the incident wavefront 1,20 . Recently, in a pioneering work, Vellekoop et al. have shown that adaptive optimization of the incident wavefront can increase the focused intensity of multiply scattered light by a factor that is roughly equivalent to the number of degrees of control [9][10][11][12] . Using a spatial light modulator (SLM) with 1000 degrees of control enabled a 1000-fold enhancement in the focused brightness after a turbid medium 9 . Following Vellekoop's works, other approaches for determining the optimal corrections were demonstrated either by measurement of the optical transmission matrix 13,14 or the complex-valued relation between spatial modes 15 , or alternatively by directly recording the distorted wavefront using optical phase conjugation 16,17 . These results, however, were only relevant for quasi-continuous light, and in spite of these remarkable achievements in the correction of spatial distortions, no work to date h...

Diffraction-limited imaging through complex scattering media is a long sought after goal with important applications in biomedical research. In recent years, high resolution wavefront-shaping has emerged as a powerful approach to generate a sharp focus through highly scattering, visually opaque samples. However, it requires a localized feedback signal from the target point of interest, which necessitates an invasive procedure in all-optical techniques. Here, we show that by exploiting optical nonlinearities, a diffraction-limited focus can be formed inside or through a complex sample, even when the feedback signal is not localized. We prove our approach theoretically and numerically, and experimentally demonstrate it with a two-photon fluorescence signal through highly scattering biological samples. We use the formed focus to perform two-photon microscopy through highly scattering, visually opaque layers.

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We show that the polarization state of coherent light propagating through an optically thick multiple scattering medium can be controlled by wavefront shaping, that is, by controlling only the spatial phase of the incoming field with a spatial light modulator. Any polarization state of light at any spatial position behind the scattering medium can be attained with this technique. Thus, transforming the random medium to an arbitrary optical polarization component becomes possible.