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We study behavior of resonant modes with a distance between two identical dielectric cylinders and disks. We reveal two basic scenarios of evolution of resonances with the distance between the cylinders. For larger distances and respectively weaker interaction of particles the resonances are bound around the Mie resonances and evolve by spiral way. For shorter distances and respectively stronger interaction the resonances bypass the Mie resonances. Both scenarios demonstrate considerable enhancement of the Q factor compared to the case of isolated particle.
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