Fast and Accurate Analysis of Three-Dimensional Structures Involving Near-Zero-Index Materials

We present efficient and accurate frequency-domain analysis of three-dimensional structures involving near-zero-index (NZI) materials with very small permittivity and/or permeability values. Accurate simulations are required to analyze these homogenized models that represent metamaterials with exotic NZI properties, which can be useful in a plethora of applications. When traditional solution methods are directly applied, however, instability and inaccuracy issues arise, making solutions inefficient and inaccurate particularly when electrically large models need to be studied. Identifying that numerical problems are due to unbalanced equations, extremely small/large terms, as well as the traditional low-frequency breakdown, we develop alternative implementations based on novel surface integral equations and broadband multilevel fast multipole algorithm. Numerical examples demonstrate excellent accuracy, stability, and efficiency of the developed solvers for NZI structures.