Topological Valley Photonic Waveguides: Scattering matrix evaluation for linear computing

Topological boundary modes utilizing valley mode waveguides have opened opportunities in, for instance, the design of high transmission waveguides with tolerance to geometrical defects and sharp bends. Applications of these waveguides include linear computational processes and the emulation of logic gates using linear structures, among other scenarios. Here we present the design of a 6-port junction that exhibits equal power splitting to three other ports when excited at single port with no reflections. In studying this structure, a scattering matrix is extracted at telecom wavelengths (around 1550 nm). The linearity of the system along with the scattering matrix are exploited to produce linear operations such as routing of information considering two incident signals or multiple signals applied from different ports. Our work may be exploited to analytically design larger networks without the need of computationally expensive trial and error numerical methods.