Calculation of Effective Electromagnetic Parameters of Helix Loaded Composites

There is currently a great interest in studying the electromagnetic response of helix loaded composites. There have been many works in the literature that model such materials as artificial chiral media. The objective is to understand the dependence of the electromagnetic response of the artificial medium on the inclusion and the host medium parameters. Therefore, a theoretical model is needed to express this dependence and to be used in the design of composites with desirable absorption and polarization characteristics. In this work, a theoretical model is proposed for characterizing the response of artificial media made up of randomly oriented helices in a host medium, based on a description of these materials with the constitutive relations of effective chiral media. The macroscopic electromagnetic parameters are calculated in terms of helix and host medium parameters. The approach taken is to first solve the scattering by a single helix numerically using the method of moments (MoM) under a thin wire approximation in order to calculate the helix polarizabilities. The effective electromegnetic parameters of the composite medium are then obtained by applying an extension of the standard Maxwell-Garnett mixing formula to include chirality. Using the effective electromagnetic parameteters that are calculated by this approach, reflection and transmission calculations are performed. It is found that the variation of the electromagnetic response with frequency is well predicted by the theoretical model and the expected resonance frequencies are obtained due the accuracy of the method of moments. However, the comparison with published measurement results reveals the limitations of the model to low inclusions and low frequencies. Due to these limitations an alternate approach is investigated for periodic structures consisting of infinite two-dimensional arrays of aligned helices. This approach is based on an exact MoM solution of the integral equation for the induced currents, using a periodic Green's function. The formulation derived can be used to find the scattered fields. The reflection and transmission coefficients for a given incidence could then be inverted to give the effective EM parameters. Thesis Supervisor: Jin Au Kong Title: Professor of Electrical Engineering Thesis Supervisor: R. T. Shin Title: Assistant Group Leader, MIT Lincoln Laboratory