Perfect splitting in rectangular-waveguide junctions for analog computing

It has recently been shown how computing operations such as high-speed switching, routing, and solving partial differential equations can be performed by exploiting perfect splitting of electromagnetic waves in networks of waveguides from microwaves to the optical regime. Here we propose a technique to achieve perfect splitting of electromagnetic waves using junctions of rectangular waveguides. The structure consists of N air-filled rectangular waveguides interconnected at a junction. They are designed to have their cutoff frequency above the cutoff frequency of a further N waveguides used as inputs. The proposed structure is studied theoretically with use of transmission-line models, and it is demonstrated that perfect splitting can occur at frequencies below the cutoff frequency of the interconnected waveguides (evanescent coupling). Numerical results are used to validate the designs, and it is demonstrated that the theoretical model fits the numerical data well. As examples of computing operations, it is shown how the proposed structure can be used to compare the amplitude of two incident signals (comparison operation) and also for routing of information to different output ports by exploiting the linear superposition of scattered waves excited at the junction of rectangular waveguides, opening new opportunities and possibilities for future exploration and exploitation of electromagnetic waves for high-speed computing.