Estimating the Reflection Losses in the Passband of Edge Filters

Edge filters which block one spectral region and pass an adjacent region are normally constructed with periodic stacks of high and low index layers of equal quarter wave optical thickness at the center wavelength of the blocked band. A preliminary and a subsequent aperiodic structure of several layers which minimize the reflectance in the passband are usually needed to transition from the effective index of the substrate to the effective index of the periodic structure and from the structure to the final medium. This paper addresses the estimation of the possibilities and limitations of these antireflection or matching layers to reduce the reflections before the coating is actually designed. Equations are given for the estimation of the average reflectance in the passband as a function of the number of layers and the width of the passband for both short and long wavelength pass filters and for passbands on both sides of a “minus filter”.