An optical fiber grating has theoretically been designed that would be
capable of compressing a dispersion-broadened pulse of 100 ps down to
the transform limit of 20 ps, with a total reflectance of approximate
ly 75%. A numerical recipe is presented for the design of a fiber grat
ing, whose spectral response closely follows an arbitrarily chosen pro
file, both for the reflectance and the phase factor. The resulting gra
ting consists of a number of subgratings, all of which have the same g
rating period but a different spatial phase and coupling coefficient.