Reflection and Transmission Interference Filters Part I Theory

An interference filter of the reflection type consists in its simplest form of a perfectly reflecting mirror on which is placed a thin layer of a dielectric material. The outer surface of the dielectric is coated with a very thin metallic film. When properly constructed such a filter reflects 100 percent of radiation at the frequencies 2nν0, and 0 percent of radiation at the frequencies (2n + 1)ν0.A transmission filter consists of a thin dielectric layer, both sides of which are coated with very thin metallic films. A well made filter will transmit up to approximately 40 percent of the incident radiation at the frequencies nν0. The transmission bands can be made quite narrow, and the transmission between the maxima may be less than 1 percent although it does not fall to zero.The theory, which consists of a straightforward application of the Maxwell equations, is initially applied to a single metallic film backed by dielectric media. The reflection and transmission coefficients, as well as the phase shifts, are obtained and are given in terms of the thickness and the optical constants of the film.The reflection coefficient for the reflection filter is developed next and is expressed as a function of the properties of a single metallic film. The general formula is quite complicated but degenerates to a simple form when the wave-length becomes long (i.e. for the infra-red region). By using the filter at oblique incidence it is shown that polarized radiation may be produced.The transmission filter is studied and its properties may again be formulated in terms of the properties of a single metallic film. The values of the optical constants are deduced, which lead to the construction of an efficient transmission filter. Silver films have approximately these values in the visible region of the spectrum, but fail to possess them either in the ultraviolet or in the infra-red region. The theory shows that when the filter is tilted so that the angle of incidence is no longer normal, the transmission band shifts towards shorter wave-lengths, and splits into two bands, one of which is polarized parallel and the other perpendicular to the plane of incidence. This phenomenon is observed with experimental filters.