Fig. 1: Different matching mechanisms for different interconnections.
a Mode matching (MM) for the interconnection of two different slab waveguides (WG). For the ordinary two-dimensional slab waveguide coupling with widths W1 and W2, the waveguide coupling mechanism is more accurately described by vector mode matching (VMM). The rule of vector mode matching is the input and output interface vector mode profile matching. In order to match the mode profile, an optimized taper can be used to tune the mode profile adiabatically, and enhance the transmittance (T = 1). In fact, for the sake of simplicity, only complex electric field amplitude is usually considered in mode matching. b Transverse spin matching (TSM) for the coupling of a slab waveguide and a topological waveguide (TWG). b1 Although the vector mode matching degree at positions P1 and P2 is very low to α(P1P2) ~ 0 (Eq. (1)), the TS matching degree of is up to β(P1P2) ~ 0.6 (Eq. (3)), which results in T ~ 0.8. This phenomenon hints that the mode matching principle is not suitable for the design of topological structure coupling. b2 An optimized coupler tunes the TS profiles and gradually enhances the matching degree of TS from 0.6 (P1) to 1 (P4). As a result, a high transmittance T ~ 1 is obtained.
