Dispersion of optical fibers with far off-resonance gratings

We derive analytic expressions for the quadratic and cubic dispersion of optical fiber Bragg gratings, at frequencies far from the Bragg condition, where the usual coupled-mode theory (CMT) fails. We use these to design fibers that have no quadratic dispersion at a particular wavelength, but find that the cubic dispersion then increases. We also show that it is possible to design a fiber link with vanishing average quadratic and cubic dispersion by combining a length of standard fiber and a length of dispersion compensating fiber with an off-resonance grating.