Graphical Method for Examining Complex Natural Frequencies of Dispersive Materials

A graphical method is extended to and applied for visual inspection of solution patterns (region of complex natural frequencies s
_n
) in the complex s-plane for dispersive materials characterized by the Debye and Lorentz models. These patterns are in the form of exponential decay and C-shaped profiles for the Debye and Lorentz models, respectively. Their forms are observed to be affected (e.g., moving left/right) in different manners with a variation of dispersion parameters. This method, thanks to its visual inspection capability, can help in analyzing/synthesizing filters and frequency-selective surfaces.