Complete spatiotemporal characterization and optical transfer matrix inversion of a 420 mode fiber.

The ability to measure a scattering medium's optical transfer matrix, the mapping between any spatial input and output, has enabled applications such as imaging to be performed through media which would otherwise be opaque due to scattering. However, the scattering of light occurs not just in space, but also in time. We complete the characterization of scatter by extending optical transfer matrix methods into the time domain, allowing any spatiotemporal input state at one end to be mapped directly to its corresponding spatiotemporal output state. We have measured the optical transfer function of a multimode fiber in its entirety; it consists of 420 modes in/out at 32768 wavelengths, the most detailed complete characterization of multimode waveguide light propagation to date, to the best of our knowledge. We then demonstrate the ability to generate any spatial/polarization state at the output of the fiber at any wavelength, as well as predict the temporal response of any spatial/polarization input state.