Scattering of light is considered a nuisance in microscopy. It limits the penetration depth and strongly deteriorates
the achievable resolution. However, by gaining active spatial control over the optical wave front it is possible to
manipulate the propagation of scattered light far in the multiple scattering regime. These wave front shaping
techniques have given rise to new high-resolution microscopy methods based on strong light scattering. This is
based on the realization that scattering by stationary particles performs a linear transformation on the incident
light modes. By inverting this linear transformation, one can focus light through an opaque material and even
inside it. An extremely high resolution focus can be obtained using scatterers embedded in a high-index medium,
where the diffraction limit for focusing is reduced by a factor n. We have constructed a scattering lens made
of the high-index material gallium phosphide (GaP) which is transparent over most of the visible spectrum and
has the highest index of all nonabsorbing materials in the visible range. This yields a focal spot resolution of
less than 100 nm, and it seems theoretically possible to create a focus of order 70 nm. The system resolution of
a microscope based on this lens could be substantially higher.n
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