Geometric phases in twisted strips

We compute the optical phase shifts between the left and the right-circularly polarized light after it traverses non-planar cyclic paths described by the boundary curves of twisted closed strips of various widths. While the phase shift increases monotonically with the width of the strip for multi-twisted closed strips, it has a minimum at a certain critical width for the Mobius. In our detailed study of various twisted strips, this intriguing property singles out the Mobius geometry. Possible applications are pointed out. (C) 2009 Elsevier B.V. All rights reserved.