Generalized Brewster-angle conditions for quarter-wave multilayers at non-normal incidence*

Generalized Brewster-angle conditions for either the s or p plane of polarization are derived for periodic quarter-wave multilayers on a substrate, when the two layers of the basic period are matched to have equal effective optical thickness. By use of these relations, graphs for the design of reflecting polarizers for either the s or p plane of polarization are presented; two examples made with ZnS and MgF2 layers are treated in detail. The multilayer systems under consideration may also be used as transmitting polarizers, antireflection coatings for linearly polarized light, and for polarization-sensitive interference filters.