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Nonlinear metasurfaces offer new paradigm for boosting optical effect beyond limitations of conventional materials. In this work, we present an alternative way to produce pronounced third-harmonic generation (THG) based on nonlinear field resonances rather than linear field enhancement, which is a typical strategy for achieving a strong nonlinear response. By designing and studying a nonlinear plasmonic-graphene metasurface at terahertz regime with hybrid-guided modes and bound states in the continuum modes, it is found that a THG with a narrow bandwidth can be observed, thanks to the strong resonance generated between a weak THG field and these modes. Such strong nonlinear field resonance greatly enhances the photon-photon interactions, thus resulting in a large effective nonlinear coefficient of the whole system. This finding provides new opportunity for studying nonlinear optical metasurfaces.

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.

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