Length reduction of a short-slot directional coupler in a single-layer dielectric substrate waveguide by removing dielectric near the side walls of the coupler

A method for reducing the size of a short-slot directional coupler by changing the dielectric constant near the side walls in the coupled region is proposed. The coupled length can be reduced by 51 % for the hybrid and by 57 % for the cross coupler, respectively. The distance between the couplers is also shortened, and the total size of the Butler matrix is reduced by 48 %.