Second harmonic enhancement effect in the double U split-ring resonators

Frequency multiplication plays an important role in spectrum research; therefore, in order to achieve enhancement of the second harmonic, the internal structure of nonlinear plasma metamaterial cells becomes more and more complex. The original harmonic oscillator model only regards the cell as a single harmonic oscillator, and a complete understanding of the physical processes involved in harmonic generation experiments in plasmonics is still lacking. In the case in which the plasma structure in a single cell becomes more and more complex, it is not reasonable to regard the entire cell as a single nonlinear oscillator. So expanding the harmonic oscillator model becomes more significant. In this paper, the internal structure of the proposed double U split-ring resonators (DU-SRRs) is regarded as two harmonic oscillators with different resonant frequencies, and the generation process of the enhanced second harmonic is explained by the resonance theorem. The second and third order nonlinear coefficients of the metamaterial are calculated, and the theoretical second harmonic conversion efficiency is obtained by using the second order nonlinear coefficients. Compared with the simulation results of the DU-SRR based on the split-ring resonator, we validate this classical theory as well as the associated numerical algorithm. The ability of the DU-SRR to enhance the second harmonic is proved, and the physical changes inside the cell and the reasons for the enhancement are explained in detail. This method can be used to analyze the nonlinear phenomena in metamaterials with complex cell structures.