  We discuss optical (HST/WFPC2 F555W) and radio (15 GHz VLA) polarimetry
observations of the M87 jet taken during 1994-1995. Many knot regions are very
highly polarized ($\sim 40-50%$, approaching the theoretical maximum for
optically thin synchrotron radiation), suggesting highly ordered magnetic
fields. High degrees of polarization are also observed in interknot regions.
  While the optical and radio polarization maps share many similarities, we
observe significant differences between the radio and optical polarized
structures, particularly for bright knots in the inner jet, giving us important
insight into the jet's radial structure. Unlike in the radio, the optical
magnetic field position angle becomes perpendicular to the jet at the upstream
ends of knots HST-1, D, E and F. Moreover, the optical polarization decreases
markedly at the position of the flux maxima in these knots. In contrast, the
magnetic field position angle observed in the radio remains parallel to the jet
in most of these regions, and the decreases in radio polarization are smaller.
More minor differences are seen in other jet regions. Many of the differences
between optical and radio polarimetry results can be explained in terms of a
model whereby shocks occur in the jet interior, where higher-energy electrons
are concentrated and dominate both polarized and unpolarized emissions in the
optical, while the radio maps show strong contributions from lower-energy
electrons in regions with {\bf B} parallel, near the jet surface.
