Semicircular Ridges in Rectangular Waveguides

The two-dimensional Hehnholtz equation is solved in a rectangle having two semicircular projections in the center of its broad faces. More particularly, the lowest two eigenvalues are determined for Nenmann´s boundary condition, and the lowest eigenvalue for Dirichlet´s boundary condition. The results are of interest in various fields of physics, such as vibrations of a membrane, but are of particular importance in the study of waveguide propagation. The latter application is stressed in the article, in accordance with the practical, importance of ridged waveguides.