Maxwell-Gaussian beams with cylindrical polarization.

It is common practice to work in the approximation that beam-like radiation fields are polarized transverse to the propagation axis. However, even in the paraxial approximation, this fails to correctly describe beam polarization and propagation characteristics. We present here the paraxial Maxwell's equations for beams having cylindrical polarization, which describe the full vector structure of these beams in the paraxial regime. The effect that these relations have on the polarization and propagation of cylindrically polarized Laguerre-Gauss and Bessel-Gauss beams is subsequently explored.