Abstract
Recent studies have employed perturbation techniques to derive amplitude-dependent band structures in nonlinear periodic materials. The associated applications include amplitude-dependent filters, waveguides, and diodes. However, for a range of frequencies and wavenumbers, perturbation-based dispersion corrections for a single wave break-down due to internal resonance between the primary wave and its nonlinearity-induced higher-harmonics. This work presents a perturbation analysis of one-dimensional plane waves in lattices with internal resonances. The exchange of energy between propagating modes within the same branch of the lattice’s band structure is considered, and the stability of the energy exchange is assessed through a local analysis. Direct numerical integration of the lattice equations of motion validates the analytical expressions for energy exchange. These findings can be used to resolve discontinuities in band diagrams that do not account for internal resonances and may inspire new technology that enables long-range coherent signal transmission in nonlinear media.
