The Design of Optical Filters

According to Herpin’s theorem, a symmetrical thin-film combination is equivalent, at one wavelength, to a single film, characterized by an equivalent index and equivalent thickness. If a large number of identical nonabsorbing thin-film combinations are combined, the resulting periodically stratified medium acts as a band-stop filter. In a stop band, the equivalent index of a symmetrical period is a pure imaginary; in a pass band, it is real. Equivalent indices are given for some commonly used periods. These may have values not possessed by any existing substance. These periods have proved useful in the design of optical filters and antireflection coatings.