Black plastic sandwiches demonstrating biaxial optical anisotropy

Abstract

Transparent overhead-projector foil is an anisotropic material with three different principal refractive indices. Its properties can be demonstrated very simply by sandwiching the foil between crossed polarizers and looking through it at any diffusely lit surface (e.g., the sky). Coloured interference fringes are seen, organized by a pattern of rings centred on two `bullseyes' in the directions of the two optic axes. The fringes are difference contours of the two refractive indices corresponding to propagation in each direction, and the bullseyes are degeneracies where the refractive-index surfaces intersect conically. Each bullseye is crossed by a black `fermion brush' reflecting the sign change (geometric phase) of each polarization in a circuit of the optic axis. Simple observations lead to the determination of the three refractive indices, up to an ordering ambiguity.