Transpose symmetry of the Jones Matrix and topological phases

TL;DR

This paper proves a general property of the Jones matrix for reciprocal optical stacks, showing how its transpose relates to the original matrix when rotated, and proposes an experimental method to distinguish phase changes.

Contribution

It establishes a transpose symmetry property of the Jones matrix for reciprocal stacks and introduces an experimental scheme to separate isotropic and topological phases.

Findings

Transpose symmetry holds for reciprocal stacks without interface reflection.

The scheme can distinguish isotropic from topological phase changes.

The result is basis-independent and applicable to various reciprocal media.

Abstract

The transmission Jones matrix of an arbitrary stack of reciprocal plane parallel plates which has been turned through 180 degrees 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.