  Chiroptical responses of helical superstructures are determined by collective
behaviors of the individual building blocks. In this paper, we present a full
theoretical description of the collective resonance in superstructures. We use
the gold nanorods as individual building blocks and arrange them helically
along an axis in an end-to-end fashion. Numerical simulations on single-unit
cells reveal that the plasmonic coupling between the nanorods produces
hybridized resonances, whose intensity is strongly dependent on the excitation
light with left- or right-handed circular polarizations (LCP or RCP). A
node-mode criterion is proposed on the basis of the microscopic mechanism,
which successfully explains the difference between LCP and RCP. We further
demonstrate, by repeating the unit cell from 1 to infinity along the helical
axis, the multiple hybridized resonances gradually evolve and merge into a
single collective resonance, whose energy is also dependent on LCP and RCP. An
analytical description is provided for the collective resonance of the helical
superstructure on the basis of the coupled dipole approximation method. Our
theory shows that n collective resonance modes are present in the helical
superstructure with the unit cell consisting of $n$ nanorods. Strikingly, only
one resonance can be excited by the incident light with certain circular
polarization. We propose a universal selection rule for such selective
excitation of the collective resonances by analyzing the symmetry of the
helical superstructures. The new insights provided in this work may shed light
on future designs and fabrications of helical superstructures using plasmonic
building blocks.
