  We present results from deep, wideband, high spatial and spectral resolution
observations of the nearby luminous radio galaxy Cygnus A with the Jansky Very
Large Array. The high surface brightness of this source enables detailed
polarimetric imaging, providing images at $0.75''$, spanning 2 - 18 GHz, and at
0.30$''$ (6 - 18 GHz). The fractional polarization from 2000 independent lines
of sight across the lobes decreases strongly with decreasing frequency, with
the eastern lobe depolarizing at higher frequencies than the western lobe. The
depolarization shows considerable structure, varying from monotonic to strongly
oscillatory. The fractional polarization in general increases with increasing
resolution at a given frequency, as expected. However, there are numerous lines
of sight with more complicated behavior. We have fitted the $0.3''$ images with
a simple model incorporating random, unresolved fluctuations in the cluster
magnetic field to determine the high resolution, high-frequency properties of
the source and the cluster. From these derived properties, we generate
predicted polarization images of the source at lower frequencies, convolved to
0.75$\arcsec$. These predictions are remarkably consistent with the observed
emission. The observations are consistent with the lower-frequency
depolarization being due to unresolved fluctuations on scales $\gtrsim$ 300 -
700 pc in the magnetic field and/or electron density superposed on a partially
ordered field component. There is no indication in our data of the location of
the depolarizing screen or the large-scale field, either, or both of which
could be located throughout the cluster, or in a boundary region between the
lobes and the cluster.
