In this paper, we reformulate a sensitivity analysis method for function-expansion-based topology optimization method without using gray area. In the conventional approach based on function expansion method, permittivity distribution contains gray materials, which are intermediate materials between core and cladding ones, so as to let the permittivity differentiable with respect to design variables. Since this approach using gray area dose not express material boundary exactly, it is not desirable to apply this approach to design problems of strongly guiding waveguide devices, especially for plasmonic waveguides. In this study, we present function-expansion-method-based topology optimization without gray area. In this approach, use of gray area can be avoided by replacing the area integral of the derivative of the matrix with the line integral taking into acount the rate of boundary deviation with respect to design variables. We verify the validity of our approach through applying it to design problems of a T-branching power splitter and a mode order converter.

In this paper, the topology optimization method is first applied to obtain high gain characteristics of dielectric flat lens. The topology optimization method used in this study is based on the gradient method with adjoint variable method. The FDTD method is used as the analysis method of electromagnetic fields. Results are compared with those obtained by using metaheuristic methods GA and PSO. As a result, it is shown that the proposed method can efficiently design a high gain dielectric flat lens in a wide frequency band.

We present a design optimization method of H-plane waveguide components, based on the level set method with the finite element method. In this paper, we propose a new formulation for the improvement of a level set function, which describes shape, location, and connectivity of dielectric in a design region. Employing the optimization procedure, we demonstrate that optimized structures of an H-plane waveguide filter and T-junction are obtained from an initial structure composed of several circular blocks of dielectric.

We investigate the usefulness of the topology optimization with the finite element method in the optimization of an H-plane waveguide component. Design sensitivity is computed efficiently using the adjoint variable method. Employing the optimization procedure, optimized structures of an H-plane waveguide filter and T-junction are obtained from an initial homogeneous structure.