A low-loss zero-index photonic crystal slab based on toroidal dipole mode

Zero-index medium has profound application for light manipulation. Certain types of dielectric photonic crystals (PCs) may have zero effective index since they form Dirac cone at the Γ point of their band structure. Although zero index photonic crystals provide a solution to impedance mismatch in photonic integrated circuits, its propagation modes strongly radiate to the surrounding environment, which hampers their application for high-density integration. In this paper, by an appropriate design of PC's unit cell, toroidal dipole mode is excited at Dirac-point frequency through coupled Mie resonance to suppress radiative losses of other multipoles. The PCs with the Dirac-like dispersion at the Γ point can be mapped to an effective zero-index medium. The physical mechanism was utterly investigated by means of multipole decomposition and band structure analysis. Due to the non-radiation property of the toroidal dipole mode, the proposed photonic crystal slab process is low-loss based on numerical simulation. Moreover, its relatively simple design facilitates integration with future quantum photonic devices.