Dynamic matrix theory for resonance response of plasmonic metamaterial lattice


 In this paper, a lattice dynamics method, named M-K matrix method, is proposed to investigate the near-field resonance response of a plasmonic metamaterial lattice under an oblique incident field with an arbitrary incident angle. By considering the electric, magnetic and field-dipole interactions, we construct a dissipative many-body Lagrange model for a reference lattice. A collective forced vibration equation, with the degree of freedom equals to the number of nanoparticles in a cell, is introduced to describe the lattice resonance under a polarized field. The resonance frequencies can be conveniently obtained from the poles of transfer function matrix. Based on this elegant matrix differential equation, one can calculate the amplitude-frequency and phase-frequency responses of plasmonic lattice, and analysis the normal modes from dispersion relations. The analytical results, which are from three examples: simple square lattice, binary chain and chessboard lattice, are perfectly matched with numerical simulations in a large frequency band, proving it to be an effective tool to calculate the dynamic response of plasmonic lattice.