Anisotropic zero-index waveguide with arbitrary shapes

We design a series of waveguides composed of uniform anisotropic epsilon-near-zero media. Unlike normal waveguides in which the transmission rate strongly depends on the width and the boundary shape, such waveguides can achieve high transmission with almost arbitrary width and boundary shapes, leading to applications such as unusual waveguides, wave expanders and compressors, splitters, bends, and devices with combined purposes. The physical origin of such high transmission can be explained by using transformation optics and the condition for total transmission is derived. Numerical simulations with multilayers consisting of dielectric and negative-permittivity materials proved our theory. Our work provides a unified physical picture for waveguide structures based on anisotropic epsilon-near-zero media.