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We study the effect of structural disorder on the transition from the bound states in the continuum (BICs) to quasi-BICs by the example of the periodic photonic structure composed of two layers of parallel dielectric rods. We uncover the specificity in the robustness of the symmetry-protected and accidental BICs against various types of structural disorder. We analyze how the spatial mode localization induced by the structural disorder results in an effective reduction of the system length and limits the Q factor of quasi-BICs. Our results are essential for the practical implementation of BICs especially in natural and self-assembled photonic structures, where the structural disorder plays a crucial role.

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Three types of quasicrystal lattices based on the Penrose tiling are considered. We analyze the maximum filling fraction of these structures and find a design with the filling fraction corresponding to the case of periodic lattices. By using simulations of a Gaussian beam propagation through the quasicrystal structure we obtain a homogeneous field distribution that is a hallmark of near-zero regimes in metamaterials.