Continuation method for synthesizing antireflection coatings

A continuation method for synthesizing antireflection multilayer coatings is presented. It takes into account the family of similar problems constituted by the syntheses of spectrally flat coatings that approximate different transmittance levels in the range 0-1. This method traces a path moving from the transmittance (in air) of the chosen substrate to the full transmittance. Whenever one or more thicknesses become too thin, this path is branched by investigating the existence of other local minima, so several optimal designs characterized by different numbers of layers are obtained. Some examples show the capabilities of the proposed synthesis.