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 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 polarizations 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.
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