Step method: a new synthesis method for the design of optical filters with intermediate refractive indices

We propose a new synthesis method for the design of multilayer optical filters with intermediate refractive indices, the step method. This method consists in adding infinitesimally small index steps in the index profile at optimal positions and then reoptimizing the thickness and the refractive index of the layers. Application of the method to the design of an antireflective coating, a low-pass edge filter, and an immersed polarizing beam splitter shows that it provides interesting solutions, even in the absence of a proper starting design. The formalism developed for the method also serves to demonstrate that the optimal filter consists of either homogeneous layers that maximize the effective refractive index contrast, or of graded-index layers.