Optimal single-band normal-incidence antireflection coatings

Mathematical and computational evidence that strongly suggests that optimal solutions exist to single-band, normal-incidence antireflection coating problems is presented. It is shown that efficient synthesis and refinement techniques can quickly and accurately find such solutions. Several visible and infrared antireflection coating examples are presented to support this claim. Graphs that show the expected optimal performance for different representative substrates, refractive-index ratios, wavelength ranges, and overall optical thickness combinations are given. Typical designs exhibit a pronounced semiperiodic clustering of layers, which has also been observed in the past. Explanations of this phenomenon are proposed.