Space Transformation Concept: Controlling the Path of Electromagnetic Waves

In this chapter, we will deal with devices designed using space transformation concept. Quasi-conformal transformation optics (QCTO) is applied for the design of electromagnetic devices at microwave frequencies. Antenna applications are targeted for focusing and collimating properties. Two lenses are studied and designed by solving the Laplace’s equation that describes the deformation of a medium in the space transformation. The material parameters of the lenses are derived from the analytical solutions of the Laplace’s equation. The first lens is conceived to produce an overall directive in-phase emission from an array of sources conformed on a cylindrical structure. The second lens allows steering a directive beam to an off-normal direction. Theoretical formulations are given to describe the transformations and full-wave simulations are performed to verify the functionality of the calculated lenses. Theoretical designs are adapted judiciously to be compatible with the constraints of realization technologies so as to have the best agreement between numerical calculations and experimental tests. Prototypes presenting a graded refractive index are fabricated through three-dimensional (3D) polyjet printing using all-dielectric materials and experimental measurements are carried out to validate the proposed lenses. Such easily realizable designs open the way to lowcost all-dielectric broadband microwave lenses for beam forming and collimation.