A rigorous electromagnetic theory of the common sidewall, single‐hole directional coupler is presented. The characteristics of the directional coupler are obtained retaining the propagating modes as well as the evanescent modes, and the effect of the evanescent modes is determined. The standing‐wave ratio at the input port, the directivity, the transmission, and the coupling factors, together with their spectral responses, are investigated. Maximization of the power coupled to the output port with respect to the aperture width and the optimization with respect to the variation in the width of the waveguide are also discussed.