A higher-order dispersion compensator including a chromatic dispersion compensator coupled to receive an input signal; a phase modulator optically coupled to the chromatic dispersion compensator, wherein the phase modulator selectively chirps portions of the data pulses; and a tunable dynamic dispersion element coupled to receive the phase modulated signal. The tunable dynamic dispersion element includes a first waveguide having a first non-linearly chirped grating tuned to reflect the polarization controlled signal and having a first reference reflection point; and a first tuning mechanism that tunes the first grating.