  The extragalactic radio source 1803+784 is a BL Lac object that shows rapid
variability and strong linear polarization. Very long baseline interferometry
observations reveal that the core possesses a distinctive structure in
polarized intensity with two maxima on axis and two minima symmetrically placed
on either side. The approximately radial pattern of electric field polarization
rods is reminiscent of the results obtained earlier by Cawthorne (2006) for
conical shocks, but, individually, these do not reproduce the main features of
the polarized intensity images. In numerical simulations and experiments, these
shocks occur in pairs and help to stabilize jets as they adjust to changes in
environment. Here, the polarization resulting from such structures is
investigated using an approximate, analytical approach, by making some simple
assumptions about the nature of the flow between two such shock waves. For
fairly small viewing angles, it is found that a reasonable representation of
the core polarization of 1803+784 can be obtained. The similarity between the
observed and model polarization supports the view that the core structure in
1803+784 represents a recollimation shock, and that such shock waves may be
responsible for the first disturbance and hence brightening of the quiescent
flow in astrophysical jets.
