Calculation and measurement of the effective chirality parameter of a composite chiral material over a wide frequency band

Materials that are effectively chiral at microwave frequencies can be fabricated by embedding identical, randomly oriented chiral inclusions, often metal helices, in a continuous matrix. We show that the chirality parameter can be calculated in the dilute limit using single scattering theory. The required tumble-averaged forward scattering by an individual inclusion is determined by the method of moments. Values of the effective chirality parameter are determined directly from the constitutive parameters of the matrix and the geometry and concentration of the inclusions. Comparisons are made with measurements previously reported in the literature. In addition, a chiral composite material was fabricated specifically to validate the calculations over frequencies including resonance. The measurements agree well with the calculations, providing quantitative values of the chirality parameter over a wide frequency band. It appears that the chirality parameter is appreciable only near the resonant frequencies of the inclusion. Finally, it is clear that an oscillator model can be used to describe the frequency dependence of the complex chirality parameter, and that therefore our results are consistent with the Kramers-Kronig relation