Here we develop a theory of bound states in the continuum (BICs) in multipolar lattices – periodic arrays of resonant multipoles. We show that off-Γ BIC can be pinned in the k-space in this multipole approximation. The developed approach set a direct relation between the topological charge of BIC and the asymptotic behavior of Q-factor of the radiative modes in its vicinity.
The most common way to enhance interaction of electromagnetic waves with matter at the nanoscale is to use microresonators and resonant optical nanoantennas. In virtue of small size their optical properties are well described in terms of multipole decomposition, namely, by first several terms in the multipole expansion. The specific multipole content of the mode is completely determined by its symmetry and shape of the resonator. Here, we classify eigenmodes in resonators of the simplest shapes depending on their symmetry group. For each type of mode, we found its multipole content. As an illustrative example, we apply the developed formalism to the analysis of dielectric triangular prism and demonstrate the formation of high-Q resonances originated due to suppression of the scattering through the main multipole channel.
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