Abstract

The analysis of multilayered films made up of homogeneous layers is well developed.¹ Much of the analysis of films with different, e.g., sinusoidal, profiles has been carried out through approximations, such as coupled-mode theory (CMT). An exact analysis can be undertaken by solving the wave equation for a given profile or class of profiles;² however, an even more useful approach is to make use of the concept of a characteristic admittance. All of the formulas which are familiar from the theory of homogeneous multilayered films¹ hold exactly for films with continuously varying refractive indices when expressed in terms of an appropriately defined characteristic admittance, η_c. It must be noted that η_c is a generalized admittance, and will be purely imaginary within a filter stop band. Away from the stop band, η_c approaches the mean index of the filter.

© 1988 Optical Society of America