On a heuristic point of view concerning the optical activity

TL;DR

This paper explores the quantum-mechanical basis of optical activity, revealing that polarization is linked to a quasi-spin property that depends on local coordinate systems, providing a new understanding of optical rotation.

Contribution

It introduces the concept that optical activity arises from changing local coordinate systems while keeping quasi-spin fixed, offering a novel perspective beyond traditional models.

Findings

Polarization relates to a quantum quasi-spin property.

Two mechanisms influence polarization: quasi-spin rotation and local coordinate change.

Optical activity is explained by the local coordinate system mechanism.

Abstract

Motivated by a recent finding that Fresnel's phenomenological description of the optical activity in the chiral medium is not self-consistent, we conduct a thorough investigation into the nature of the polarization of a plane light wave. We demonstrate that the polarization of light is the reflection of one of its quantum-mechanical properties, called the quasi-spin. Unexpectedly, the quasi-spin is not an observable with respect to the laboratory coordinate system. Instead, it is with respect to the momentum-dependent local coordinate system. The representative operators for the quasi-spin are the Pauli matrices. The wavefunction is the Jones vector. In order to completely determine a state of polarization, two different kinds of degrees of freedom are needed. One is the degrees of freedom to characterize the state of quasi-spin. They are the Stokes parameters, the expectation values of the Pauli matrices in the state described by the Jones vector. The other is the degrees of freedom to specify the local coordinate system, including the propagation direction and an angle of rotation about it. Accordingly, there are two independent mechanisms to change the state of polarization. One is to change the state of quasi-spin in a fixed local coordinate system. This is the traditional mechanism that can be expressed as an SU(2) rotation of the Jones vector. The other is to change the local coordinate system with the state of quasi-spin remaining fixed in it. At last, we show that it is the newly-identified mechanism that accounts for the optical activity.