There are many kinds of waveguides. The most common waveguide cross-section "shapes" are rectangular and circular/elliptical.
Waveguides can carry electromagnetic energy in many modes, although these modes are usually designated as the basic mode with the most ideal loss and bandwidth characteristics. This mode is usually transverse wave mode (TE), in which the electric field direction is perpendicular to the propagation direction. This mode has an electric field directed towards and away from the sidewall of the waveguide. Adding an internal ridge to the waveguide will change the behavior of the electric field in the waveguide, because the wall of the waveguide is grounded. Therefore, the addition of internal ridges moves the ground plane and limits the distance that the electric field must propagate in the waveguide, and also increases the capacitance between the walls compared with the waveguide without ridges.
Like single ridge waveguide, double ridge waveguide uses this concept to further "shrink" the electric field in the waveguide. As a result, the impedance is reduced and the low-frequency cut-off point of the waveguide is also reduced. Compared with the case where there is no ridge in the waveguide, this basically allows the waveguide of smaller size to adapt to lower frequency. In addition, adding ridges in the waveguide also leads to the creation of higher-order waveguide modes that may have new internal structures. Through proper design and manufacture, the size and depth of ridges can be controlled to achieve very specific behaviors, including pushing unwanted patterns beyond the frequency of interest and reducing the need for filtering in some cases. The ability to control waveguide impedance using ridges also allows impedance matching without additional components or equipment, or reduces the impedance matching margin to a more manageable level. This can greatly reduce the design cost and complexity. In many applications where physical space and weight constraints exist, it may be desirable to have a waveguide with a smaller physical size but still be able to work at low frequencies.