  We have developed a new coherent dedispersion mode to study the emission of
Fast Radio Bursts that trigger the voltage capture capability of the Australian
SKA Pathfinder (ASKAP) interferometer. In principle the mode can probe emission
timescales down to 3 ns with full polarimetric information preserved. Enabled
by the new capability, here we present a spectropolarimetric analysis of FRB
181112 detected by ASKAP, localized to a galaxy at redshift 0.47. At
microsecond time resolution the burst is resolved into four narrow pulses with
a rise time of just $15 \mu$s for the brightest. The pulses have a diversity of
morphology, but do not show evidence for temporal broadening by turbulent
plasma along the line of sight, nor is there any evidence for periodicity in
their arrival times. The pulses are highly polarized (up to 95%), with the
polarization position angle varying both between and within pulses. The pulses
have apparent rotation measures that vary by $15\pm 2\, {\rm rad \,m^{-2}}$ and
apparent dispersion measures that vary by $0.041\pm 0.004\,{\rm pc\,cm^{-3}}$.
Conversion between linear and circular polarization is observed across the
brightest pulse. We conclude that the FRB 181112 pulses are most consistent
with being a direct manifestation of the emission process or the result of
propagation through a relativistic plasma close to the source. This
demonstrates that our method, which facilitates high-time-resolution
polarimetric observations of FRBs, can be used to study not only burst emission
processes, but also a diversity of propagation effects present on the
gigaparsec paths they traverse.
