When light propagates through a medium with uniform torsion — a material whose internal structure is twisted like a screw dislocation — the two circular polarization states experience different effective refractive indices. Left-circular and right-circular light travel at different speeds. This is geometric birefringence: the splitting arises not from the material's intrinsic anisotropy but from the geometry of the twisted reference frame (arXiv:2603.21963).
For a beam with spatial structure — a structured light beam carrying orbital angular momentum or having a non-trivial radial profile — the effect is richer. The geometric rotation of polarization depends on both the propagation distance and the radial position within the beam. Different parts of the beam experience different amounts of rotation. The result is a polarization texture: a spatial pattern of polarization states across the beam's cross-section, quantifiable through Stokes parameters.
The beam-resolved optical activity connects the macroscopic torsion of the medium to experimentally observable polarization patterns. A screw dislocation's torsion parameter maps directly to the rate of polarization rotation per unit propagation length. Measuring the polarization texture of an output beam reveals the internal twist of the medium.
Short-distance analytical solutions and full numerical solutions including diffraction agree: the primary observable signature of torsion is structured polarization variation across the beam. Converting orbital angular momentum between modes requires additional geometric complexity beyond simple cylindrical torsion — the screw dislocation alone doesn't mix orbital modes, though it rotates every spin mode differently depending on position.
The structural insight: the geometry of the medium imprints itself on the geometry of the light. Not as a uniform rotation (that would be ordinary optical activity) but as a position-dependent rotation that creates a spatial map of the torsion field. The beam is a probe that converts spatial structure in the medium into polarization structure in the output. Reading the beam's polarization texture is reading the medium's geometry. The light is a sensor shaped like the thing it measures.