Cylindrical to rectangular coordinate transformation for planar phase front synthesis

Abstract

Coordinate transformation technique is employed to engineer a metamaterial slab that enables planar wave emission from a planar or line localised source. First a rigorous cylindrical to rectangular coordinate transformation is applied resulting in with a sheet current generating a plane wave with impedance matching at the boundary between the device and the surrounding medium. Then, based on physical reasoning, the material constitutive parameters are further reduced to having only one entry of the spatially varying permeability tensor instead of two entries as discussed in the references. This further reduction is equivalent to modifying the near field in the transformed domain. Finally, due to a specific mu-near-zero condition near the origin, the sheet source is transformed to a localised one in the transformed domain and via full-wave simulations, the authors show that the field is still propagating as a plane wave. Moreover, the transmission line (TL) metamaterial implementation with discretised spatially varying permeability is designed. The capacitor- and inductor-loaded two-dimensional TL grid is used to synthesise the required spatially varying relative permeability in the wavefront converter metamaterial slab. The TL metamaterial design is proven to successfully synthesise a planar wave front using a microwave circuit simulator.