A planar metamaterial Lüneburg lens that enables Fourier optics on-a-chip can be implemented in an SOI slab waveguide structure by patterning the silicon core with variable sized holes. The subwavelength patterning of binary nanocomposite material to form the metamaterial offers the major advantage of fabrication by a single etch step while demanding feature sizes that can be accessed by deep UV lithography in addition to e-beam lithography. A numerical calibration procedure is described that is used to find the relation between fill factor and the local homogenised effective refractive index and which improves upon the predictions of analytic effective media theory used by other researchers. The concept and designs were verified by the 2D FDTD simulation of a two lens telescope system with waveguide feeds implemented in a metamaterial that shows a low insertion loss of -0.45 dB with a reliable field profile at exit. A 3D FDTD simulation of the same two lens telescope system that takes full account of the SOI layers, their finite thickness, and the ridge waveguide feeds also predicts a low loss of -0.83 dB. Less reliance however can be placed on this result due to the coarseness of the computational grid that was necessary. Nevertheless both results are encouraging for planned fabrication trials. This structure can be used in optical transpose interconnection systems in optical switching architectures with the advantage of avoiding large number crossover waveguides in optical communication systems.