Automated analytic continuation method for the analysis of dispersive materials

All dielectrics are dispersive. This frequency dependence of materials must be modeled in a well-defined way whenever microwave structures are expected to operate over broad bands of frequency. The well known analytic properties of the permittivity can be used to generate such models by fitting them to experimental data using non-linear optimizers. However, in that approach the questions of convergence to the true global solution and the sensitivity to experimental noise remain open. Here it is shown that an automated deterministic approach to generate such a model for the important case of multi-Debye relaxation materials can be implemented. The method is compared to a recently proposed alternate approach: hybrid particle swarm-least squares optimization method (PSO/LS) that was demonstrated on idealized data sets with bandwidths in excess of 10 000:1. In our case no arbitrary parameters need be set to guarantee convergence nor need any constants be added after the fact to match the data. The case of materials with DC conductivity (imaginary permittivity growing to infinity at DC) is as easily dealt with as the conventional pure Debye case. Physically realizable results are generated even when the data is realistically noisy and spans a frequency bandwidth as small as 18:1.