Abstract: Poynting vector clearly, as well as simply, describes the longitudinal propagation momentum in homogeneous plane waves. However, for complex electromagnetic waves with vortex phase or inhomogeneous polarizations, Poynting vector can exhibit more characteristics about the momentum density. Based on the phasor representation, we decompose the Poynting vector into orbital and spin momenta, in addition to the usual longitudinal momentum, and paraxially discuss the characterisitcs of transverse orbital momentum and spin momentum, by listing some cases of typical complex electromagnetic waves with physically different transverse flows, which are also explained by corresponding phase gradient pictures. 

Key words: Poynting vector, density of momentum, orbital momentum, spin momentum, complex electromagnetic waves