Attention is called to a polarization basis formed by four Jones vectors that is reducible to two basic structures. In these states the field is linearly polarized at any point, but the polarization direction changes with the angular coordinate. Very simple equations hold for the field lines of these basis vectors. The adoption of this basis is of interest for beams possessing a single vortex of any order, say, m, as well as for beams with two vortices of opposite charges, n and -m. As an example, the application to vectorial Bessel-Gauss beams is briefly discussed. (C) 2001 Optical Society of America. [References: 34]
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