Optical activity in the Drude helix model

Abstract

An old classical one-particle helix model for optical activity, first proposed by Drude, is reconsidered here. The quantum Drude model is very instructive because the optical activity can be calculated analytically without further approximations apart from the Rosenfeld long wavelength approximation. While it was generally believed that this model, when treated correctly, is optically inactive, we show that it leads to optical activity when the motion of the particle is quantum mechanically treated. We also find that optical activity arises even in the classical regime at non-zero energy, while for zero energy the model is inactive, in accordance with previous results. The model is compared with other one-electron models and it is shown that its predicted optical activity is qualitatively different from those of other one-electron systems. The vanishing of optical activity in the classical zero-energy limit for the Drude model is due to the localization of the particle at the equilibrium position, whereas in the analogous model of a particle moving freely on a helix without a definite equilibrium position, optical activity does not vanish but the spectrum is rescaled. The model under study leads to interesting predictions about the optical properties of e. g. helicene derivatives.

Classical scattering of charged particles confined on an inhomogeneous helix

“…The formation of helical patterns and structures is common in many natural systems ranging from DNA molecules and amino-acids to non-neutral plasmas trapped in magnetic fields [1] and self-assembled configurations of charged particles confined in nanotubes [2]. Studying the motion of particles confined in a helix has proven to be a useful tool for the understanding of complex phenomena such as the optical activity of sugar solutions [3,4]. Certainly the problem of the confined motion of particles in a helical manifold is of fundamental interest since it reveals many intriguing phenomena.…”

Nonlinear coherent magneto-optical response of a single chiral carbon nanotube

“…It has long been thought that the notion of coupled oscillators is a necessary condition for the explanation of the rotatory power, until the Condon, Altar and Eyring model [5] demonstrated optical activity using a quantum mechanical single-oscillator model. In the 1970s, however, it was shown [8] that the Drude model exhibits optical activity in the nonlinear regime and recently 3 it has been demonstrated that it leads to optical activity if the motion of the particle is treated quantum mechanically [9].…”