Metasurface design using electromagnetic inversion
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This thesis presents the theory and development of a framework for the design of electromagnetic metasurfaces. These metasurfaces can be used to systematically transform an incident electromagnetic field into a different transmitted field, providing new levels of control not typically possible with conventional materials. Although a metasurface is made up of subwavelength scattering elements, it can be macroscopically represented as a homogenized model using effective surface susceptibilities. These tensorial surface susceptibilities define the relationship between the tangential electric and magnetic fields on either side of the metasurface through a set of generalized boundary conditions known as the generalized sheet transition conditions. In this work we concern ourselves with macroscopic metasurface design, the goal of which is to find an appropriate set of surface susceptibilities to support a desired field transformation. Up until now, macroscopic design methods have been mostly limited to ideal cases in which analytical expressions of the input and output fields are fully known. While this limitation is acceptable for simpler applications such as refraction, reflection, or polarization manipulation of plane waves, more general transformations, such as producing a desired far-field radiation pattern, pose a challenge. To address the above limitation, we propose framing macroscopic metasurface design as an electromagnetic inverse source problem. We show that the equivalent currents produced by solving an appropriately constructed inverse source problem are directly related to the tangential transmitted fields required to compute the surface susceptibility parameters that characterize the metasurface. The design method is developed for several different types of field specifications, namely complex (amplitude and phase) fields, phaseless (amplitude-only) power patterns, and far-field performance criteria (e.g., main beam direction, beamwidth, null locations, etc.). We then show that local power conservation can be enforced during the inversion process, allowing for the design of metasurfaces that only require passive, lossless, and reciprocal elements. Lastly, we extend the framework to the design of cascaded metasurfaces. This introduction of a second metasurface removes the need to have equal input and output power distributions, thereby increasing the variety of supported field transformations.