We model the sub-millimetre polarization patterns that are expected for filamentary clouds that are threaded by helical magnetic fields. We previously developed a three parameter model of such clouds (Fiege & Pudritz 2000a), which are described by a concentration parameter $C$, and two flux to mass ratios $Gz$ and $Gphi$ to specify the mass loading of the poloidal and toroidal field lines respectively. Our models provide a simple and purely geometric explanation for the well-known ``polarization hole effect, in which the sub-millimetre polarization percentage decreases toward the regions of peak intensity. This occurs because of a cancellation between contributions to the polarization from the ``backbone of poloidal flux along the filaments axis and its surrounding envelope, which is dominated by the toroidal field component. A systematic exploration of our parameter space allows us to classify the polarization patterns due to filaments aligned approximately perpendicular to the plane of the sky into three basic types. The polarization vectors are parallel to filaments when $ratioappleq 0.1$, where $Bzs$ and $Bphis$ are respectively the poloidal and toroidal magnetic field components at the outer surface of the filament. The polarization vectors are perpendicular to filaments when $ratioappgeq 0.33$. Intermediate cases result in polarization patterns that contain $90^circ$ flips in the orientation of the polarization vectors. The flips are symmetric about the central axis for filaments oriented parallel to the plane of the sky, but more complicated asymmetric patters result from filaments that are inclined at some angle.
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