Directional sources realized by toroidal dipoles

Directional optical sources can give rise to the directional excitation and propagation of light. The directionality of the conventional directional dipole (CDD) sources is attributed to the interference of the electric and/or magnetic dipoles, while the effect of the toroidal dipole on optical directionality remains unexplored. Here, we numerically and analytically investigate the directional properties of the toroidal dipole. We show that the toroidal dipole can replace the electric dipole in the CDD sources to form the pseudo-directional dipoles (PDDs), which can be applied to achieve analogous near-field directional coupling with a silicon waveguide. Moreover, the directionality of the PDDs can be flexibly controlled by changing the geometric parameters of the toroidal dipole, leading to tunable asymmetric coupling between the sources and the waveguide. These alternative types of directional sources provide more degrees of freedom for tailoring the optical directionality compared to the conventional sources. The results may open new possibilities for directional light manipulation and can find applications in on-chip optical routing, waveguiding, and nanophotonic communications.