Overcoming light scattering with high optical nonlinearity

While scattered light conveys most of the information we perceive, scattering may also distort that information before it reaches our detectors. The problem is acute in many applications, such as in high-resolution microscopy of biological tissue, where scattering degrades both resolution and signal-to-noise ratio. Here, for the first time, we demonstrate that uniting two intrinsic properties of scattered light: speckle statistics and the angular memory effect, with highly non-linear optical response yields, rather surprisingly, super-resolution, low-background, non-invasive imaging of objects completely hidden behind a strongly scattering, opaque layer. Crucially, our technique of non-invasive imaging through scatterers does not resort to wavefront shaping, adaptive optics, complicated optical setups, or iterative image reconstruction algorithms. Because the strategy relies solely on the properties of scattered light and high-order nonlinear response of the fluorophores, it can be applied to any speckle-forming propagation, from biological tissue to multicore fibres, combined with any type of phenomenon that exhibits a sufficiently high order nonlinearity.