Lattice resonances in nanoparticle arrays recently have gained a lot of attention because of the possibility to produce spectrally narrow resonant features in transmission and reflection as well as significantly increase absorption in the structures. Most of the efforts so far have been put to study these lattice resonances in dipole approximation. However, the recent research shows that higher multipoles not only produce resonant feature but are also involved in cross-coupling, affect each other, and induce a magnetoelectric response. In this Prospective, we review the recent achievements in studying of interplay and coupling of different multipoles in periodic nanoparticle arrays and share our vision on further progress of the field.
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