The paper considers a general field of electromagnetic waves of a single frequency and identifies the salient structurally stable features of the three-dimensional pattern of polarization. The approach is geometrical rather than analytical, and it differs from previous treatments of this kind by being applicable even when the constituent plane waves are travelling in all directions. Lines and surfaces exist where the electric or magnetic vibration ellipse is singular. The field is divided into right-handed and left-handed regions by ‘T surfaces’ , the electric and magnetic T surfaces not being coincident. Lying in the T surfaces are ‘LT lines’ where the vibration is linear, and cutting through the T surfaces are ‘CT lines’ where the vibration is circular. Both kinds of lines are surrounded by characteristic patterns of vibration ellipses, which provide a singularity index, ± 1 for LT and ± ½ for CT. The analysis is applicable in a cavity, but a loss-free resonating cavity represents a highly degenerate case.
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