Transpose symmetry of the Jones matrix and topological phases

Abstract

The transmission Jones matrix of an arbitrary stack of reciprocal plane-parallel plates that has been turned through 180° about an axis in the plane of the stack is, in an appropriate basis, the transpose of the transmission matrix of the unturned slab with a change in the sign of the off-diagonal elements. We prove this convention-free result for the case where reflection at the interfaces can be ignored and use it to devise an experimental scheme to separate isotropic and topological phase changes in a reciprocal optical medium.