Infinite-Q guided modes radiate in the continuum

Guided modes in photonic structures, with broadband infinite-quality factors, are inaccessible from the far field due to the momentum mismatch. They become leaky modes in the continuum when the mismatch is compensated for by introducing periodic perturbations to form photonic structures. However, the quality factors (Q factors) of such leaky modes deteriorate significantly in most regions of the $k$-space except at a few discrete high-symmetry points. It is an intriguing question as to whether guided modes can hop above the light cone and yet maintain high Q. Here, we propose a double-band-folding strategy to achieve high-Q leaky modes in compound lattices, exemplified with a one-dimensional grating and a two-dimensional zigzag array of dielectric disks. The Q factor of those leaky modes can be made ultrahigh at arbitrarily any incident angles, showing that such modes do not originate from bound states in the continuum (BICs) above the light cone. Our findings provide unique insight for elucidating the relations between guided modes, BICs, quasi-BICs, and radiation. They further provide a generalized recipe for numerous optical applications such as all-dielectric sensing, lasing, and nonlinear generation with multiple inputs.