The theory of double-layer antireflection coatings

The theory of double-layer antireflection coatings using non-quarter-wave films is reviewed and extended. Normal incidence only is considered.The spectral reflectance of a double-layer coating depends on the refractive indices of the layers and the adjacent media, and on Ø₁ and Ø₂, the phase thickness of the layers. It is known that the reflectance is theoretically zero if the refractive indices satisfy certain inequalities and if the phase thicknesses are those calculated from certain equations.To obtain a fuller appreciation of double-layer coatings, the reflectance throughout the whole (Ø₁, Ø₂) plane is studied analytically. The pattern formed by the lines of constant reflectance exhibits translational symmetry, and the unit pattern which generates the whole pattern has a twofold axis of symmetry. The shape of the unit pattern depends on the refractive indices of the four media. Numerical examples are given to illustrate the similarities and differences between the unit patterns of some double-layer systems.