  Since the discovery of kiloparsec-scale X-ray emission from quasar jets, the
physical processes responsible for their high-energy emission have been poorly
defined. A number of mechanisms are under active debate, including synchrotron
radiation, inverse-Comptonized CMB (IC/CMB) emission, and other Comptonization
processes. In a number of cases, the optical and X-ray emission of jet regions
are inked by a single spectral component, and in those, high- resolution
multi-band imaging and polarimetry can be combined to yield a powerful
diagnostic of jet emission processes. Here we report on deep imaging photometry
of the jet of PKS 1136$-$135 obtained with the {\it Hubble Space Telescope.} We
find that several knots are highly polarized in the optical, with fractional
polarization $\Pi>30%$. When combined with the broadband spectral shape
observed in these regions, this is very difficult to explain via IC/CMB models,
unless the scattering particles are at the lowest-energy tip of the electron
energy distribution, with Lorentz factor $\gamma \sim 1$, and the jet is also
very highly beamed ($\delta \geq 20$) and viewed within a few degrees of the
line of sight. We discuss both the IC/CMB and synchrotron interpretation of the
X-ray emission in the light of this new evidence, presenting new models of the
spectral energy distribution and also the matter content of this jet. The high
polarizations do not completely rule out the possibility of IC/CMB
optical-to-X-ray emission in this jet, but they do strongly disfavor the model.
We discuss the implications of this finding, and also the prospects for future
work.
