  Polarization measurements of the microquasar Cygnus X-1 exist at gamma-ray,
X-ray, UV, optical and radio frequencies. The gamma-ray emission has been shown
to be highly linearly polarized. Here, we present new infrared polarimetric
data of Cygnus X-1 taken with the 10.4-m Gran Telescopio Canarias and the 4.2-m
William Herschel Telescope. We show that the broadband, radio to gamma-ray flux
spectrum and polarization spectrum in the hard state are largely consistent
with a simple phenomenological model of a strongly polarized synchrotron jet,
an unpolarized Comptonized corona and a moderately polarized interstellar dust
component. In this model, the origin of the gamma-ray, X-ray and some of the
infrared polarization is the optically thin synchrotron power law from the
inner regions of the jet. The model requires the magnetic field in this region
to be highly ordered and perpendicular to the axis of the resolved radio jet.
This differs to studies of some other X-ray binaries, in which the magnetic
field is turbulent, variable and aligned with the jet axis. The model is able
to explain the approximate polarization strength and position angle at all
wavelengths including the detected X-ray (3 - 5 keV) polarization, except the
observed position angle of the gamma-ray polarization, which differs to the
model by ~ 60 degrees. Past numerical modelling has shown that a curved
synchrotron spectrum can produce a shift in position angle by ~ 60 degrees,
which may account for this.
