The optical activity of an artificial non-magnetic uniaxial chiral crystal at microwave frequencies

Abstract

Constitutive relations which include electric quadrupole terms, in addition to electric and magnetic dipole terms, are used to predict the circular birefringence experienced by an electromagnetic wave propagating in an artificial uniaxial chiral crystal which is non-magnetic. The formulation is independent of the origin chosen for the computation of the multipole moments. Numerical values are presented, in the long wavelength regime, for the rotatory dispersion as a result of circular birefringence. It is shown that in this regime the rotatory dispersion has a quadratic frequency dependence, in accordance with the Drude model. The polarizability tensors which determine circular birefringence are computed from the multipole moments of a single structure. It is quantitatively demonstrated that neglect of the electric quadrupole contribution would lead to a serious error in the predicted value for the rotation angle of the polarization plane in the case of a uniaxial crystal. In fact, the contribution of the electric quadrupole moments to optical activity is comparable to that of the magnetic dipole moments. The geometry, dimensions and spacing of the chiral element were chosen for relative ease of fabrication of the crystal, and to allow experimentation at frequencies where microwave instrumentation is readily available. Hence it was possible to subject the numerical prediction of the expected rotatory dispersion, and the effect of the electric quadrupole contribution, to experimental investigation. This was done with good agreement.