A Reflective Metasurface for Perfect Cylindrical to Planar Wavefront Transformation

The problem of perfectly transforming an incident cylindrical wave into a reflected plane wave using a reflective metasurface is considered. The metasurface is a subwavelength-patterned metallic cladding that is placed above a ground plane. The subwavelength features of the textured metallic cladding are homogenized and represented as a purely reactive impedance sheet. The homogenization allows the mutual coupling between elements to be modeled efficiently and accurately. An integral equation is constructed which relates the surface impedance to the desired total electric field in the aperture. The integral equation is solved via the method of moments to find the required sheet impedance of the patterned metallic cladding. The resulting impedance is, in general, complex indicating the need for lossy and/or active elements, which is generally undesired. Here, we use an optimization strategy to remove the real part of the sheet impedance, while still achieving the field transformation of the complex sheet. In other words, a purely reactive sheet is maintained with no need for loss and/or gain. Hence, we show that shaping of amplitude and phase in the radiative near field can be achieved using a single, fully passive, electric impedance sheet.