Designing Optical Coatings with Incorporated Thin Metal Films

In the world of nanomaterials and meta-materials, thin films are used which are an order of magnitude thinner than historically used in optical thin film coatings. A problem stems from the island structure that is seen as the film nucleates and grows until there is coalescence or percolation of the islands into a nearly continuous film. The application problem is that the indices of refraction, n and k, vary with thickness from zero thickness up to some thickness such as 30 or 40 nanometers for silver. This behavior will be different from material to material and deposition process to deposition process; it is hardly modeled by simple mathematical functions. It has been necessary to design with only fixed thicknesses and associated indices instead. This paper deals with a tool for the practical task of designing optical thin films in this realm of non-bulk behavior of indices of refraction; no new research is reported here. Historically, two applications are known to have encountered this problem because of their thin metal layers which are on the order of 10 nm thick: (1) architectural low emittance (Low-E) coatings on window glazing with thin silver layers, and (2) black mirrors which transmit nothing and reflect as little as possible over the visible spectrum with thin layers of chromium or related metals. The contribution reported here is a tool to remove this software limitation and model thin layers whose indices vary in thickness.