Mathematical and computational evidence that strongly suggests that op
timal solutions exist to single-band, normal-incidence antireflection
coating problems is presented. It is shown that efficient synthesis an
d refinement techniques can quickly and accurately iind such solutions
. Several visible and infrared antireflection coating examples are pre
sented to support this claim. Graphs that show the expected optimal pe
rformance for different representative substrates, refractive-index ra
tios, wavelength ranges, and overall optical thickness combinations ar
e given. Typical designs exhibit a pronounced semiperiodic clustering
of layers, which has also been observed in the past. Explanations of t
his phenomenon are proposed. (C) 1996 Optical Society of America