Photonic BICs originating from various mechanisms have been found in a number of optical systems, such as photonic crystal slabs 3, 14, dielectric gratings 15, 16, spheres/rod arrays 17, 18, waveguides 19, 20, and others 21. BICs also features a resonance with an infinite quality ( Q) factor in a spectrum, i.e., they are dark modes. BICs are unique waves that lie in the continuum but remain entirely confined without any radiation. Recently, bound states in the continuum (BICs) have attracted a growing interest in the optics community 1– 7, owing to their fundamental properties and their practical applications, such as strong resonances 8– 10 and high-quality optical lasing 11– 13. Our findings provide a way of realizing higher-order BICs and link their properties to the disorder of photonic systems. By practically designing a structural ZIM waveguide, the existence of BICs is numerically confirmed, as well as their independence on the presence of geometrical symmetry. We further show theoretically and numerically that the existence of those higher-order BICs depends only on the number of objects. The geometric-symmetry-free BICs are robust, regardless of the objects’ external shapes and material parameters in the ZIM host. We find that robust BICs exist and are protected from the disordered distribution of multiple objects inside the ZIM host by its physical symmetries rather than geometrical ones. Here we propose an approach by introducing the concept of geometrical-symmetry-free but symmetry-protected BICs, realized using the static-like environment induced by a zero-index metamaterial (ZIM).

However, this benefit is only theoretical in many cases since fabricated samples’ unavoidable imperfections may easily break the stringent geometrical requirements.

Geometrical symmetry plays a significant role in implementing robust, symmetry-protected, bound states in the continuum (BICs).

Epsilon geometry dash background