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The purpose of this sudy is to provide a complete optimization-based methodology to design waveguides with metamaterial walls. The present methodology is based on optimization. Indeed, the inverse problems of design are formulated as nonlinear black-box optimization problems with constraints. Two inequality black-box constraints are taken into account as penalized terms that are added to the objective function when the constraints are not satisfied. The numerical steps are done by using a finite element method solver (GetDP). Thus, different optimization software are tested to solve the nonlinear black-box optimization problems such as IPOPT, NLOPT and NOMAD from the Opti ToolBox in MatLab.

In this work, a methodology to design waveguides with metamaterial walls is proposed. The aim is to solve an inverse problem to find the best design where the electric field cartography is the closest to an imposed one.

The present methodology is applied to solve inverse problems of design and satisfactory results were provided by the three solvers IPOPT, NLOPT and NOMAD. Those numerical experiments show that NOMAD is the most efficient method to optimize the design of those cylindrical waveguide structures with metamaterial walls.

The model is set to find solutions using a specific pattern of metamaterials. This is promising to take those geometries as variables of the optimization problems. Moreover, in this exploratory work, no constraint on the fabrication limits has been taken into account.

The originality is to formulate design problems of waveguide with metamaterial walls into optimization problems. These optimization problems are difficult to solve because the objective function and two inequality constraints are computed via a numerical simulation code based on finite element methods. Thus, an original approach based on penalization is implemented and three optimization software are used. Hence, the authors propose an optimization-based methodology and apply to solve two inverse problems of design.