Transformation optics gives rise to numerous unusual optical devices, such as novel metamaterial lenses and invisibility cloaks. Very recently Mattheakis et al. [1] have suggested theoretical design of an optical waveguide based on a network of Luneburg lenses, which may be useful in sensing and nonlinear optics applications. Here we report the first experimental realization of such Luneburg waveguides. We have studied wavelength and polarization dependent performance of the waveguides. Explosive development of elecromagnetic metamaterials and transformation optics (TO) produced such novel and fascinating optical devices as perfect lenses [2], hyperlenses [3-5], invisibility cloaks [6-9], and perfect absorbers [10]. Very recently Mattheakis et al. [1] have suggested a theoretical design of an optical waveguide based on a network of TO-based lenses, such as a Luneburg lens [11], and suggested that such a waveguide may be useful in sensing and nonlinear optics applications. Here we report the first experimental realization of such Luneburg waveguides, which operate in the visible

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