Method and apparatus for higher-order chromatic dispersion compensation

An optical arrangement provides dispersion slope compensation to a received dispersion distorted input signal comprising NxM wavelength multiplexed channels. In the optical arrangement, a major dispersion compensating fiber (DCF) provides a first predetermined chromatic dispersion correction value to the NxM wavelength channels. A plurality of fiber Bragg gratings (FBGs) are serially coupled along an optical fiber. Each FBG is arranged to reflect a separate one of N groups of wavelength channels received in the input signal back along the optical fiber in order to provide a second dispersion slope compensating value. Either, the FGBs can chirped to compensate for the dispersion slope within each group of wavelength channels, or each FBG only reflects one group or wavelength channels and small DCFs introduce dispersion slope compensation into the FBG reflected signals. The combination of the first and second dispersion compensating values provided by major DSC and in the reflected signals from the plurality of FBGs, respectively, are used to generate a NxM wavelength multiplexed channel dispersion compensated output signal from the optical arrangement wherein the dispersion found in the input signal is substantially eliminated. A counter-propagating Raman pump signal in the major DCF can also be used to compensate for insertion losses of the FBGs and small DCFs.