  This paper characterizes a realistic feed for cylindrical metasurfaces,
allowing it to be included in metasurface design. Specifically, it investigates
a coaxial feed which is displaced from the center (off-center) of
concentrically-cascaded cylindrical metasurfaces. Formulas are reported to
quickly compute the multimodal S-matrix (scattering properties) of a displaced
feed from that of the central feed. The theory is rigorously derived based on
the addition theorem of Hankel functions for all azimuthal modes. Moreover, the
resulting multimodal S-matrix is combined with the multimodal wave matrix
theory used to model cylindrical metasurfaces, allowing devices to be designed
that realize arbitrary field transformations from a displaced coaxial feed. A
design example is reported, which opens new opportunities in the realization of
realistic, high-performance cylindrical-metasurface-based devices.
