Anisotropic Inhomogeneous Metamaterials Using Nonuniform Transmission-Line Grids Aligned With the Principal Axes

We present a method for realizing electromagnetically inhomogeneous and anisotropic metamaterials using nonuniform transmission-line grids. The desired material parameter tensors are decomposed into their constituent eigenvectors and eigenvalues. Transmission lines are then aligned with the eigenvectors of the permeability tensor and loaded with reactive circuit elements to attain the desired eigenvalues (diagonal permeability and permittivity values). The method is shown for two separate 2-D transformation optical devices: a collimator and a field rotator. The collimator is simulated as a continuous inhomogeneous medium as well as a subwavelength-structured transmission-line grid, and the results closely agree.