Möbius strips and twisted ribbons in intersecting Gauss-Laguerre beams

Circularly polarized, intersecting Gauss-Laguerre beams are shown to give rise to a rich array of unusual polarization structures whose properties can be tuned by varying the angle between the beams. These structures include Möbius strips with arbitrarily large, odd numbers of half twists, twisted ribbons with arbitrarily large, even numbers of half twists, and coronets (crowns). Six topological/geometrical indices are used to characterize these structures. Analytical expressions are given for some indices; others, which still present a considerable theoretical challenge, are treated numerically and illustrated graphically. It is argued that the polarization structures described here are, or soon will be, amenable to experiment.