Microscopic circular polarizabilities (rotabilities) and the macroscopic properties of chiral media

The concepts of canonical sources and canonical circular polarizabilitìes, which are referred to as “rotabilities” in this paper, appropriate for a chiral medium are used to describe circularly polarized fields in a medium containing a distribution of chiral (handed) particles. Due to the introduction of different rotabilities for right and left handed particles, we avoid mode conversion between left and right circularly polarized fields at the microscopic level which is also absent at the macroscopic level in an infinite homogeneous chiral medium. The transition from the microscopic to the macroscopic picture is hence smooth and involves just an ensemble average of the microscopic fields and the introduction of macroscopic constitutive equations, but does not involve the use of any extinction theorems. Extinction theorems are needed in other models that permit mode conversion in the microscopic picture but not in the macroscopic medium. Explicit relations are obtained between macroscopic material properties and microscopic polarizabilitìes in the long wavelength limit. These are similar to the Clausius–Mossotti relations between the dielectric permittivity and the electric polarizability, but are not a trivial generalization for chiral media.