Waveguide to laminated waveguide transition and methodology

An apparatus through at least a portion of which electromagnetic waves are to be propagated, comprising:

• a boundary structure, that defines at least a transition interior, said boundary structure comprising electrically-conductive materials, said boundary structure further defining a first opening and a second opening to said transition interior, said first opening configured to be open toward a first interior, of a first waveguide, said first waveguide being laminated on a substrate, and said second opening configured to be open toward a second interior, of a second waveguide, said second interior being defined by an electrically-conductive structure of said second waveguide, whereby an electromagnetic wave is capable of being propagated, in operation, via said transition interior, from one of said first interior and said second interior to the other of said first interior and said second interior, wherein said first interior has a dielectric constant that differs from a dielectric constant of content of said second interior, and said second waveguide is not laminated on the substrate on which the first waveguide is laminated, wherein said boundary structure along with said transition interior, is modeled by an equivalent circuit that includes at least two cascaded resonators.