Effective method for approximating graded-refractive-index layers in optical simulations.

In this paper, we present an approximation intended to find applications in numerical simulations of optical phenomena in layered structures. The method can be used to avoid approximating graded layers by using numerous homogeneous layers in the simulation. In our approach, a single layer with a graded refractive index profile or any number layers can be replaced with only two layers that for a selected wavelength and normal incidence imitate exactly the optical properties of the replaced layer or layers. The proposed approximation is valid for a wide range of wavelengths and incidence angles. It is especially useful in time-consuming simulations (especially in 3D), where it is of paramount importance to keep the number of layers in the simulated structure low.