LAUSR

Usually, on-chip beam splitting can be achieved by manipulating the in-plane iso-frequency curves (IFCs) of the structure, where the confinement of light along the out-of-plane direction is governed by total internal reflection. In this Letter, without needing a high-index dielectric background material for total internal reflection, we achieve on-chip beam splitting in a linear-crossing metamaterial (LCMM) mimicked by a two-dimensional photonic crystal (PhC) slab where the vertical confinement is enabled by a bound state in the continuum (BIC) and totally beyond the light cone. Particularly, the light propagating inside the LCMM can be flexibly controlled by the rotation angle of the rectangular silicon pillars in the PhC slab. On-chip triple beam splitting can further be designed by combining two kinds of LCMM with opposite rotation angles. Such light beam splitting beyond the light cone originates from the combined manipulation of the BIC and the spatial dispersion of LCMMs. Our work promotes the development of optical devices in integrated optics, such as on-chip focusing, switching, and (de)multiplexing.