  Gamma-ray bursts (GRBs) are the most luminous transients in the universe and
are utilized as probes of early stars, gravitational wave counterparts, and
collisionless shock physics. In spite of studies on polarimetry of GRBs in
individual wavelengths that characterized intriguing properties of prompt
emission and afterglow, no coordinated multi-wavelength measurements have yet
been performed. Here, we report the first coordinated simultaneous polarimetry
in the optical and radio bands for the afterglow associated with the typical
long GRB 191221B. Our observations successfully caught the radio emission,
which is not affected by synchrotron self-absorption, and show that the
emission is depolarized in the radio band compared to the optical one. Our
simultaneous polarization angle measurement and temporal polarization
monitoring indicate the existence of cool electrons that increase the estimate
of jet kinetic energy by a factor of $>$ 4 for this GRB afterglow. Further
coordinated multi-wavelength polarimetric campaigns would improve our
understanding of the total jet energies and magnetic field configurations in
the emission regions of various types of GRBs, which are required to comprehend
the mass scales of their progenitor systems and the physics of collisionless
shocks.
