Space-time focusing in a highly multimode fiber via optical pulse shaping

Fields propagating through a highly scattering material will be distorted in both space (intensity speckles) and time (spectral and temporal speckles), inhibiting tasks such as imaging and communication in both the optical and radio frequency regions. In optics, research thus far has demonstrated spatial focusing, image transmission, and short pulse delivery through bulk scattering materials and multimode fibers by taking advantage of spatial wavefront-shaping techniques. Here, we exploit spectral phase shaping for reference-free characterization of spectral and temporal speckle, and space-time focusing of broadband ultrafast pulses distorted by modal dispersion in a multimode fiber. We show that temporal speckle fields at different multimode fiber output locations are uncorrelated and demonstrate the ability to focus a short pulse at a specific output spatial location, while keeping the field at other output locations noise-like, offering opportunities to expand multimode fiber imaging and communication capacity.