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We consider accurate and iteratively efficient solutions of electromagnetic problems involving homogenized near-zero-index (NZI) bodies using surface-integral-equation formulations in the frequency domain. NZI structures can be practically useful in a plethora of optical applications, as they possess near-zero permittivity and/or permeability values that cannot be found in nature. Hence, numerical simulations are of the utmost importance for rigorous design and analysis of NZI structures. Unfortunately, small values of electromagnetic parameters bring computational challenges in numerical solutions of homogeneous models. Conventional formulations available in the literature encounter stability issues that make them inaccurate and/or inefficient as permittivity and/or permeability approach zero. We propose a novel formulation that involves a well-balanced combination of operators and that can provide both accurate and efficient solutions for all NZI cases. Numerical results are presented to demonstrate the superior properties of the developed formulation in comparison to the conventional ones.

We present surface-integral-equation formulations for accurate and stable solutions of electromagnetic problems involving near-zero-index materials with arbitrarily small permittivity and/or permeability values. The formulations are developed for conventional discretizations, while they can be implemented by using interaction routines of existing solvers. Initial results on canonical objects clearly demonstrate the superiority of the developed formulations in comparison to the conventional ones.

We present novel surface-integral-equation formulations for efficient and accurate iterative solutions of electromagnetic problems involving zero-index (ZI) and near-zero-index (NZI) materials. When applied to materials with small permittivity and/or permeability values, conventional implementations employing traditional formulations tend to become inefficient, inaccurate, or both. Such numerical issues arise mainly due to low-frequency breakdowns related to inner problems, as well as due to deteriorating balance of inner and outer terms. By investigating formulations in limit cases, we develop novel formulations by properly balancing integral-equation operators. We show that the resulting formulations can provide efficient, accurate, and stable analysis of three-dimensional structures having ZI and NZI materials with arbitrarily small permittivity/permeability values.