Analysis of Composite Structures Involving Near-Zero-Index Materials

We consider numerical solutions of electromagnetic problems involving near-zero-index materials with permittivity and/or permeability values close to zero. These types of problems are inherently multiscale due to the large variety of the wavelength from very large values to ordinary values in the same problem. In addition to developing a stable formulation for extreme values of the intrinsic impedance, we employ a broad-band multilevel fast multipole algorithm based on approximate diagonalization for efficient solutions. Examples involving near-zero-index materials inside ordinary waveguides are presented to demonstrate interesting electromagnetic responses of these exotic materials, as well as the effectiveness of the developed solver.