Qualitative behaviour of time average power flow in electromagnetic fields can be studied by observing the critical points of the Poynting vector field, S. In order to analyze the behaviour of the flow lines of a plane Poynting vector field in the neighbourhood of a critical point, the S field is expanded in a Taylor series. Using this expansion, critical points can be classified according to their order and degeneracy. A formula for the index of rotation of the S field at a critical point is derived. The behaviour of the transverse electric or magnetic field component in the neighbourhood of the critical point is also studied. Lowest order critical points are always nondegenerate and they have interesting properties with regards to polarization and energy distribution. Examples involving linearly polarized system of interfering plane and/or cylindrical waves are given to show the critical points. The behaviour of flow lines is illustrated in these examples.
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