Using Augmented Lagrangian Methods to Design Electromagnetic Surfaces with Far Field Constraints

This paper presents a method to synthesize passive and lossless electromagnetic surfaces, such as metasurfaces, by synthesizing their macroscopic surface parameters (namely their surface impedance) using optimization. A relaxation of this non-convex problem using the alternating direction method of multipliers is shown. An example where the surface impedance is optimized to satisfy a given sidelobe level and main beam level is then presented. Further directions for this work are proposed.