Surface lattice resonance (SLR) relies on both the lattice structure and its unit cell, which usually contains metallic nanoparticles. Since the full width half maximum of the lattice resonance is much narrower than that of localized surface plasmon resonance of a single particle, it is receiving attention increasingly. Based on the modified long-wavelength approximation, in this paper we derive an analytical expression for the extinction cross section of the dimer array of metallic nanoparticles.

Comparing with the single particle array, good tunability can be achieved by the lattice resonance of the dimer array, which is influenced by more factors, including the arrangement of the array, the structural parameter and the rotation of the dimer, the shape and size of the particles, etc. First, the polarizabilities of the two kinds of particles in the dimer array are adjusted by introducing a matrix of the array factors, which take into account the influence of dipole fields of every particle. Then a simple expression of the resonance condition for the SLR of the dimmer array is obtained. The proposed model can be applied to a wide variety of dimer arrays of ellipsoid particles, and the applied method can be generalized to more complicated structure like polymer arrays. In this paper we further discuss the polarization dependence and ability to modulate the lattice resonance, by changing the excitation condition and the structural parameters of the dimer array. It is found that the resonances of the dimmer array can be classified as three main categories. The resonance related to the particles is independent of the variation of the dimmer arrangement or the array structure. On the other hand, the resonances corresponding to the dimmer and the array rely crucially on the structural parameters. By carefully adjusting the structural parameters, we can modulate the specific resonance effectively. This research is of theoretical importance for studying the SLR for more complicated structures and may find potential applications in the design of new photoelectric chip via nanoparticle array.