Limits to the Average Reflectance in a Broadband AR Coating Design and Avoiding Local Minima in the Design Process

When attempting to optimize an optical coating, such as minimizing the reflection from a glass surface, the optimization process often stops at a design which is indicated to be the minimum (best), but is only a "local minimum," since there exists another lower "real minimum" for those conditions. A procedure using constrained optimization has been employed to continue the optimization process past the local minimum and ultimately find the real minimum for any given overall thickness of the coating design. This procedure has been used to map the lower limits of the average reflectance (%Rave) in a given bandwidth versus the overall thickness of the coating design. To yield a low %Rave, a minimum thickness has been found necessary, and three times that overall thickness is judged to be a practical limit for a working broad band antireflection (BBAR) coating. The results of this mapping are explained from various viewpoints, and a formula is provided to estimate the minimum %Rave which can be achieved for a given bandwidth, thickness, and material choice.