  Optical time-reversal techniques are being actively developed to focus light
through or inside opaque scattering media. When applied to biological tissue,
these techniques promise to revolutionize biophotonics by enabling deep-tissue
non-invasive optical imaging, optogenetics, optical tweezers and photodynamic
therapy. In all previous optical time-reversal experiments, the scattered light
field was well-sampled during wavefront measurement and wavefront
reconstruction, following the Nyquist sampling criterion. Here, we overturn
this conventional practice by demonstrating that even when the scattered field
is under-sampled, light can still be focused through or inside opaque media.
Even more surprisingly, we show both theoretically and experimentally that the
focus achieved by under-sampling is usually about one order of magnitude
brighter than that achieved by conventional well-sampling conditions. Moreover,
sub-Nyquist sampling improves the signal-to-noise ratio and the collection
efficiency of the scattered light. We anticipate that this newly explored
under-sampling scheme will transform the understanding of optical time reversal
and boost the performance of optical imaging, manipulation, and communication
through opaque scattering media.
