Note on Band Transmission in Multilayer Dielectric Filters

Abstract

The existence of pass and stop bands for periodically stratified media, in particular for multilayer dielectric filters, is well known, but there seems to be no way of demonstrating this either without the use of a good deal of algebra or by appeal to relatively unfamiliar ideas, such as those of transmission line theory. Our purpose here is to show that for an infinite medium, this result can be established by a direct adaptation of the Kronig-Penney (1931) model for metal lattices. Accounts of this model are given in a number of textbooks (Rojansky 1942; Brillouin 1946) and also in undergraduate courses in this country, so that it may be considered well known. Mathematical details will accordingly be abbreviated; they may be found in the references cited.