Minimum layers for graded refractive index film approximation
Ideal gradient-index films are composed of heterogeneous structures of infinite increments in refractive index. In this paper, we studied the minimum layers to approximate the antireflective performance of an ideal GRIN film by comparing the angular and spectral reflectance of GRIN structures (of linear, cubic, and quintic profiles) between air-glass boundary while varying number of the layers. The accuracy of estimation was assessed using root mean square error (RMSE) method. An RMSE below 0.001 was found using at least 19, 13, and 12 layers for linear, cubic, and quintic profile, respectively. The average reflectivity without the GRIN, with GRIN film, and with a single layer quarter wave was also calculated. It was found that the GRIN film can reduce the average reflectivity of bare glass by about 8.25% against the 4% reduction using a single layer quarter wave. The result suggests that GRIN structures designed for omni-directional and broadband anti-reflectivity can be numerically approximated accurately using significantly less number of layers. The GRIN was also proven to be a better solution than a single quarter wave film as an anti-reflective coating.