A novel decomposition of the transversal part of the electric field vector of a general non-paraxial electromagnetic field is presented, which is an extension of the radial/aximuthal decomposition and is known as gammazeta decomposition. Purely gamma and zeta polarized fields are examined and the decomposition is applied to propagation-invariant, rotating, and self-imaging electromagnetic fields. An experimental example on the effect of state of polarization in the propagation characteristics of the field: its is shown that a simple modification of the polarization conditions of the angular spectrum converts a self-imaging field into a propagation-invariant field.