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Subwavelength waveguide gratings (SWG) are locally periodic structures with parameters that may vary slowly on the scale of a wavelength. Here the implementation of a Lüneburg lens as a SWG to provide Fourier optics on a chip and the design of the adiabatic structures that must be provided to interface SWG structures to conventional waveguides are considered. Preliminary findings are reported on the dispersion engineering of multimode interference couples towards the ideal port phase relations needed in coherent applications.