I. Introduction
Artificial materials having very small (near-zero) refractive index values, namely near-zero-index (NZI) materials, are well-known with their potential usages in a plethora of applications at radio, microwave, and optical frequencies [1]–[3]. While they are practically obtained by arranging unit cells in the form of metamaterials, homogeneous models of NZI objects using effective permittivity and permeability values can be useful to efficiently investigate and analyze their electromagnetic responses. In fact, well-known solution approaches, such as surface integral equations (SIEs), have been successfully employed for this purpose [4]. On the other hand, as permittivity and/or permeability values become close to zero, traditional SIEs tend to possess inaccuracy and/or instability issues. In this work, we present new formulations that are accurate and stable for arbitrarily small values of permittivity and permeability values. Initial results on canonical problems demonstrate excellent properties of new formulations, in contrast to the conventional ones.