Vortex index identification and unidirectional propagation in Kagome photonic crystals

Vortex field in photonic metamaterials has been revealed in recent years, which provides an extra degree of freedom to control the behavior of electromagnetic waves, such as the unidirectional propagation in topological metamaterials and orbital angular momentum multiplexing in optical fibers. Achieving topologically protected unidirectionality needs an external source either with a vortex index of m = ±1 (i.e. 2πm phase winding around phase singularity) or with a spin index of ±1 (i.e. right- or left-handed circular polarization). However, it is still an open question on the relationship between higher-order (|m | > 1) vortex field and topological metamaterials. Here, we study the excitation of valley bulk states by a source with a higher-order vortex index in Kagome photonic crystals. The selection rule for the excitation of valley bulk states is derived and can be applied to predict the selective excitation of valley bulk states by a source with a higher-order vortex index. Interestingly, we find that the Fourier spectrum and the averaged Fourier spectrum of the Ez component enable us to identify the vortex index of the source. Besides, it is shown that the unidirectional edge states can be excited by a source with a vortex index of 1 or 2 in a straight or 120° detour waveguide. Our work paves the way for the demonstration of the selection rule and may have potential applications in optical mode identification.