Dispersion compensating waveguide circuit

A method of processing an optical signal, comprising:

• spectrally decomposing the optical signal into a plurality of optical components using a first diffraction grating;
• directing different optical components along different optical paths to generate relative delays between the components, wherein the optical components impinge upon second, third, and fourth diffraction gratings optically connected in series;
• and
• recombining the delayed components using the fourth diffraction grating to produce a processed optical signal.

A dispersion compensator, comprising one or more diffraction gratings optically coupled to a light-routing device, wherein:

• the one or more diffraction gratings are configured to spectrally decompose an optical signal applied to the compensator into a plurality of optical components;
• the one or more diffraction gratings and the light-routing device are configured to direct different optical components along different paths to generate relative delays between the components;
• the one or more diffraction gratings are further configured to spatially recombine the delayed components to generate a processed optical signal;
• and
• the dispersion compensator further comprises a first section designed to operate in light transmission, wherein the first section comprises:
• first and second diffraction gratings;
• and
• a plurality of lenses configured to route light to and from the first and second diffraction gratings.