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Highly dispersive components enable photonic-integrated circuits for ultrafast optical pulse processing. This paper presents the design of an InP device with resonant giant group velocity dispersion. The waveguides have a dual layer, dual width geometry that enables tailoring of the group velocity resonance wavelength. By cascading sections with different resonance wavelengths we show how constant group velocity dispersion can be achieved over a 50-nm wavelength range. Depending on which one of two super modes is excited in this device, the dispersion can be either normal or anomalous with values of -23200 ps/(nm · km) or 8200 ps/(nm · km), respectively. Mode converters with >90% efficiency are designed to facilitate selective excitation of one or the other mode. The complete device is expected to be compatible with existing active/passive photonic integration technology in the InP/InGaAsP material system that should allow the creation of monolithic ultrafast optical pulse processing systems.