Abstract
Geometrical symmetry plays a significant role in implementing robust, symmetry-protected, bound states in the continuum (BICs). However, this benefit is only theoretical in many cases since fabricated samples’ unavoidable imperfections may easily break the stringent geometrical requirements. 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). 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. The geometric-symmetry-free BICs are robust, regardless of the objects’ external shapes and material parameters in the ZIM host. We further show theoretically and numerically that the existence of those higher-order BICs depends only on the number of objects. 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. Our findings provide a way of realizing higher-order BICs and link their properties to the disorder of photonic systems.
Highlights
Geometrical symmetry plays a significant role in implementing robust, symmetry-protected, bound states in the continuum (BICs)
We introduce the concept of geometric-symmetryfree but physical-symmetry-protected BICs, i.e., a zero-index metamaterial (ZIM) host embedded with N ≥ 2 objects, which support radiative monopole modes with non-zero magnetic flux
If we introduce two identical objects with reflection symmetry, we obtain two bound modes localized near the objects, showing even and odd symmetry, respectively
Summary
Geometrical symmetry plays a significant role in implementing robust, symmetry-protected, bound states in the continuum (BICs). This benefit is only theoretical in many cases since fabricated samples’ unavoidable imperfections may break the stringent geometrical requirements. The coupling of the discrete bound state of one symmetry class (i.e., odd symmetry) to the other symmetry class’s continuous spectrum (i.e., even symmetry) is forbidden, leading to the existence of symmetry-protected BICs. Physically, electromagnetic (EM) guide modes supported by the waveguide may be described by the st1icoωanl2ma:r=H^cw2ψamviseðxtf;huyenÞcH1⁄4tioaðmnωi2mψlt=mocðn2xiÞa;ψnymÞ,,ðnxw;ðhxyi;Þc,yhÞwohisbeertyehseH^ths1⁄4peaHt∇iae2lllmþy h1⁄2donel2tpðzexne; qydÞuenaþ-t refractive index profile, ω is the frequency and c is the light speed. Topological photonic crystals have been previously proposed to realize topological Fano resonances (i.e., quasi-BICs) robust to geometrical imperfections[23], the topological photonic crystals themselves are governed by the symmetry of geometric lattice, leading to similar control problems on the system’s geometry
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