A new formulation of the Auxiliary Difference Equation (ADE) Finite Difference Time Domain (FDTD) algorithm for the simulation of dispersive materials has been presented in the literature. Although flexible and efficient, this algorithm suffers from instability when modelling lossy high contrast dielectrics. In this paper we adapt this ADE-FDTD formulation and present alternative algorithms for modelling static conductivity and Debye dispersion. The stability of these algorithms is assessed by numerical simulation in a wide variety of dielectricmedia and their performance is compared to the existing algorithm by means of a simulation of the reflection of a plane wave from a dielectric boundary. Results and comparison with theory demonstrate the stability and accuracy of the new methods. The flexibility, computational efficiency and ability to model a wide range of materials make these new methods highly attractive compared to other dispersive FDTD algorithms, particularly for modelling materials with multiple dispersion models.
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