Far-Field Synthesis from Complex Point Souces via Transformation Metamaterials

It is well known that an electromagnetic field can be expanded as a weighted sum of Gaussian beams. Convergence to a given field distribution is guaranteed by adding enough beams and controlling individual beam characteristics such as beam waist and propagation direction. At the same time, a Gaussian beam can be recognized as the field produced paraxially by a complex point source with imaginary displacement along the axial beam direction. In this work, we propose a design methodology for metamaterials (flat transformation media) enabling the synthesis of electromagnetic far-field patterns based on such complex source representations. The methodology is based on the application of complex transformation optics to derive constitutive tensors that map point sources in real-space to effective complex point sources.