The properties of periodical multi-layers are surveyed in respect of width, shape and phase change of the stopping band. It is shown that for a given range of possible refractive indices the widest stopping band is obtained with, in effect, a two-layer fundamental period with the maximum ratio of refractive indices; this can also be expressed as a symmetrical three-layer period with the same stopping band width, but with different properties. The application of the results obtained to the polarizing beam-splitters is briefly indicated.