Non-linear modeling of active or passive optical lamellar nanostructures

A universal approach to modeling the refraction of a monochromatic plane wave incident on an optical metamaterial arranged of arbitrary (passive, active, or plasmonic) layers of linear or feebly non-linear elemental materials is examined. The approach is built on an alternative formulation of the method of single expression, which works well upon different combinations (non-linear lossy dielectric, graded-index Kerr medium, and gain medium with metal) upon either ppolarized or s-polarized light. We show that although the formulation for s-polarized light is straightforward, the ppolarization case is more complicated, since solving an implicit material equation is required. Numerical validation of the proposed method indicates good agreement with the results taken from other numerical solvers (based on finite element and mode matching methods).