Abstract

The Herpin equivalence theorem has been used for a long time in the design of multilayer interference coatings. It states that a layer of arbitrary thickness and index is equivalent to a symmetrical three-layer stack at one wavelength. The one-wavelength restriction limits its use, however. By considering five-layer symmetrical stacks, we have been able to extend the Herpin theorem to include equivalence at two wavelengths. Specifically, we can find five-layer symmetrical combinations that have quarterwave phase thickness and given equivalent index values at two wavelengths. Unfortunately, the location of the two wavelengths is not completely arbitrary. However, the selection available is useful for some applications.

© 1987 Optical Society of America