Simplified numerical modeling for Fano interference-induced asymmetric light reflectance effect using equivalent medium theory.

Localized surface plasmons exhibit promising capabilities in optoelectronic devices. In most cases, the metal nanoparticle arrays are located on interfaces or inside optical cavities. Fano interferences have been observed and explained via the interference between the waves generated by the localized surface plasmon and dielectric interfaces. Conventionally, these Fano interferences are modeled using the modified Fresnel equation. However, certain issues persist in the fundamental physics or in the numerical calculation process. Here, we adopt the equivalent medium theory (Maxwell-Garnett theory, MGT) to calculate and elucidate Fano interferences in different structures, in the region comprising nanoparticle arrays and dielectrics equivalent to a homogeneous layer of media via the mean field theory. Using this method, the Fano interference can be modeled by mixing different materials, i.e., metals and dielectrics in these cases. Furthermore, a multiple-layered equivalent medium theory is proposed to significantly improve the scalability of this simplified numerical method. In other words, this method can be easily extended to nanoparticles with different shapes, sizes, and materials; in addition, it exhibits robust practicability. Compared with the modified Fresnel equation and finite-difference time-domain methods, this MGT-based method can effectively minimize the calculation process, which is beneficial to the prospective application of plasmon photonics.