Effect of Substrate Index of Refraction on the Design of Antireflection Coatings

Formulae to estimate the average percent reflectance (Rave) of a broadband antireflection (AR) coating as a function of the bandwidth (B), the overall thickness (C), the index of refraction of the last layer (L), and the difference between the indices of the high-and low-index layers (D) were reported in 1991(1). Various refinements of these formulae and other insights into the underlying behavior of such coating designs have been reported up until the present time(2-5). Dobrowolski, et al.(6) and Tikhonravov, et al.(7) have also added independent viewpoints to this subject over this period. In the previous studies, the effects of the index of refraction of the substrate have mostly been ignored and have appeared to be very minor. This study has investigated the influence of the substrate index on the Rave results. It has been found that there seem to be two classes of designs with respect to the effect of substrate index. In the class of "step down"(8,9) AR designs, there is a significant effect, in the other class, there is no significant effect. Even in the step-down case, there is no effect of substrate index if any and all indices of refraction for the coating materials are available from that of the index of the substrate to the index of the media.