The electric and magnetic fields of a plane electromagnetic wave are orthogonal to each other and the direction of propagation. This suggests that the maximum number of waves with the same frequency that can be superposed without any interference is three. This can be done by choosing three waves travelling in mutually orthogonal directions and choosing all three polarisations orthogonal to each other.
If one is content with only the mean square of the electric field being homogeneous without requiring that the mean square of the magnetic field also be homogeneous, larger superpositions are allowed. For many practical purposes, such superpositions can still be considered noninterfering, as it is the electric field that interacts most with matter, including fluorescent dyes, CCDs and the light-sensitive pigments in the human eye. The inhomogeneity in the magnetic field is relatively difficult to detect.
The helicity density, a quantity that indicates the handedness of the light, is in general inhomogeneous for our noninterfering superpositions. It will vary in space in a pattern that is quite often, although not necessarily, periodic and resembles the intensity variations in optical lattices. There is enough freedom left in our superpositions to allow for a large variety of helicity
lattices.
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