Modeling of dispersive media in ADI-FDTD method with complex–conjugate pole residue pairs

Abstract

This work presents an alternating-direction implicit (ADI) finite-difference time-domain (FDTD) scheme for the study of structures that involve materials with arbitrary frequency dispersion. The material dispersion is fitted to the complex–conjugate pole-residue (CCPR) terms model, and a novel, to the best of our knowledge, numerical formulation is presented based on auxiliary differential equations and two-step ADI methodology. Additionally, the proposed technique is combined with the concept of the perfectly matched layer, and a new implicit scheme is introduced for the termination of media with CCPR dispersion in the ADI-FDTD framework. The ADI-FDTD formulation is compared with the explicit FDTD scheme for several benchmark two-dimensional problems in terms of accuracy and efficiency. The suggested algorithm is proven to be robust and capable of simulating applications in different frequency regions, spanning from microwaves to optical frequencies. It can provide a powerful tool for the analysis of nanostructures involving both strongly dispersive and nanosized materials, such as plasmonic metasurfaces, antennas, core–shell nanoparticle systems, light-trapping plasmonic solar cells, surface-enhanced Raman spectroscopy substrates, or nanodevices based on epsilon-near-zero materials.