Owing to optical refraction, external rays that are incident upon a hi
gh-refractive-index medium fall within a small. internal cone angle. A
one-dimensionally periodic Bragg structure can reflect over an angula
r acceptance range that is greater than the small internal refraction
cone, if the internal refractive-index contrast is sufficient. Thus Wi
nn et al. [Opt. Lett. (to be published)] charted the range of refracti
ve indices at which omnidirectional external reflection occurs. A wide
spectral gap requires a high-index contrast. It is proposed that, by
chirping or grading the periodicity of the structure, one can cover an
arbitrarily wide spectral range with only a modest index contrast and
, furthermore, that arbitrary spectral shapes can be produced. The gra
ded-periodicity approach requires only a modest index contrast, provid
ed that the average refractive index is >2. (C) 1998 Optical Society o
f America.