  In this manuscript, we develop an efficient algorithm to evaluate the
azimuthal Fourier components of the Green's function for the Helmholtz equation
in cylindrical coordinates. A computationally efficient algorithm for this
modal Green's function is essential for solvers for electromagnetic scattering
from bodies of revolution (e.g., radar cross sections, antennas). Current
algorithms to evaluate this modal Green's function become computationally
intractable when the source and target are close or when the wavenumber is
large. Furthermore, most state of the art methods cannot be easily
parallelized. In this manuscript, we present an algorithm for evaluating the
modal Green's function that has performance independent of both
source-to-target proximity and wavenumber, and whose cost grows as $O(m)$,
where $m$ is the Fourier mode. Furthermore, our algorithm is embarrassingly
parallelizable.
