Design of an achromatic beam splitter comprising a dielectric multilayer stack

The inverse transmittance (1/T) of a quarterwave all dielectric multilayer stack is expressed as a mixed series in sinø and cosø, where ø = (pi/2)[(lambda - lambda(0))/ lambda] and lambda(0) is the reference wavelength. This expression has been used to design achromatic beam splitters for the visible and near IR regions having different reflectance (R) to transmittance (T) ratios (e.g. R:T = 70:30, 30:70, 50:50, 60:40, 40:60, etc.). The theoretical design places emphasis on the selection of refractive indices which can be realized in practice.