Modeling Reflection-Free One-Way Edge Modes Using Foldy-Lax Multiple Scattering Theory

The Foldy-Lax multiple scattering theory is applied to compute the reflection-free topological one-way edge modes induced by wave interactions with periodic gyromagnetic scatterers. The electromagnetic field response arising from a point source at the interface of two photonic crystals, one comprised of gyromagnetic scatterers, - yttrium-iron-garnet (YIG) scatterers, and the other of alumina scatterers, is studied. The T-matrices of a single cylindrical scatterer of circular cross-section, of both YIG and alumina materials, are derived and utilized to formulate the Foldy-Lax multiple scattering equations. The fields inside and outside the scatterers are derived. Field results of both single-scatterer scattering and multiple-scatterer scattering are compared with results from the method of moments (MoM) and from COMSOL simulations. The comparisons confirm the accuracy of the proposed method and show that the Foldy-Lax multiple-scattering theory is far more efficient than MoM and COMSOL. The proposed approach can be a useful tool for topological wave device analysis and design.