Plastic optical parts require antireflective as well as hard coatings. A novel design concept for coating plastics combines both functions. Symmetrical three-layer periods with a phase thickness of 3/2π are arranged in a multilayer to achieve a step-down refractive-index profile. It is shown mathematically that the equivalent index of symmetrical periods can be lower than the lowest refractive index of a material used in the design, if the phase thickness of the symmetrical period is set equal to 3/2π instead of the usual π/2. The straightforward application of the concept to the design of antireflection coatings in general is demonstrated by example.
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