Foreground power dominates the measurements of interferometers that seek a
statistical detection of highly-redshifted HI emission from the Epoch of
Reionization (EoR). The inherent spectral smoothness of synchrotron radiation,
the dominant foreground emission mechanism, and the chromaticity of the
instrument allows these experiments to delineate a boundary between spectrally
smooth and structured emission in Fourier space (the "wedge" or "pitchfork",
and the "EoR Window", respectively). Faraday rotation can inject spectral
structure into otherwise smooth polarized foreground emission, which through
instrument effects or miscalibration could possibly pollute the EoR Window.
Using data from the Hydrogen Epoch of Reionization Array (HERA) 19-element
commissioning array, we investigate the polarization response of this new
instrument in the power spectrum domain. We confirm the expected structure of
foreground emission in Fourier space predicted by Thyagarajan et al. (2015a,
2016) for a HERA-type dish, and detect polarized power within the pitchfork.
Using simulations of the polarized response of HERA feeds, we find that almost
all of the power in Stokes Q, U and V can be attributed to instrumental leakage
effects. Power consistent with noise in the EoR window suggests a negligible
amount of spectrally-structured polarized power, to the noise-levels attained.
This lends confidence to deep integrations with HERA in the future, but with a
lower noise floor these future studies will also have to investigate their