  We present Hubble Space Telescope Near-Infrared Camera and Multi-Object
Spectrometer coronagraphic imaging polarimetry of the TW Hydrae protoplanetary
disk. These observations simultaneously measure the total and polarized
intensity, allowing direct measurement of the polarization fraction across the
disk. In accord with the self-shadowing hypothesis recently proposed by Debes
et al., we find that the total and polarized intensity of the disk exhibits
strong azimuthal asymmetries at projected distances consistent with the
previously reported bright and dark ring-shaped structures (~45-99 au). The
sinusoidal-like variations possess a maximum brightness at position angles near
~268-300 degrees and are up to ~28% stronger in total intensity. Furthermore,
significant radial and azimuthal variations are also detected in the
polarization fraction of the disk. In particular, we find that regions of lower
polarization fraction are associated with annuli of increased surface
brightness, suggesting that the relative proportion of multiple-to-single
scattering is greater along the ring and gap structures. Moreover, we find
strong (~20%) azimuthal variation in the polarization fraction along the
shadowed region of the disk. Further investigation reveals that the azimuthal
variation is not the result of disk flaring effects, but instead from a
decrease in the relative contribution of multiple-to-single scattering within
the shadowed region. Employing a two-layer scattering surface, we hypothesize
that the diminished contribution in multiple scattering may result from
shadowing by an inclined inner disk, which prevents direct stellar light from
reaching the optically thick underlying surface component.
