Topology optimization for cross-section designs of electromagnetic waveguides targeting guiding characteristics

Electromagnetic waveguides effectively conduct electromagnetic microwaves using resonance phenomena in RF-ranges, and are widely used in high-frequency electronic devices and equipment. The waveguide guiding characteristics related to eigen-frequencies and eigen-modes are critical factors determining the design performances pertaining to the bandwidth of appropriate response frequencies, and high performance electromagnetic waveguides can be obtained by designing cross-sections of waveguides that appropriately control such guiding characteristics at the conceptual design phase. This paper proposes a new application of a topology optimization method for the design of inhomogeneous electromagnetic waveguide cross-sections composed of dielectric material and air, with the resulting configurations performing according to specified guiding characteristics. First, the concept of topology optimization and a way to apply it to electromagnetic wave problems are explained. Next, design requirements for the design of waveguide cross-sections are clarified and corresponding objective functions and the optimization problem are formulated. A new multi-objective function is formulated to reduce grayscales since using a penalization parameter for physical property interpolation is ineffective in electromagnetic problems. The optimization algorithm is constructed based on these formulations, Sequential Linear Programming and the finite element method, where hybrid edge/nodal elements are used. Finally, several design examples of waveguide cross-sections are presented to confirm the usefulness of the proposed method.