▎ 摘　　要

We develop a novel nonlinear radiation oscillator theory, which can describe nonlinear optical responses in symmetric and anti-symmetric damping graphene coupled metamaterials. An ultra-high quality factor of induced transparency can be realized in the proposed model. The results show that the spectral response and quality factor can be effectively tuned by the resonant detuning, the phase difference, the damping factor as well as the field intensity of the pump light. Moreover, the quality factor of induced transparency is increased by more than 60 times when the field intensity of the pump light and the damping factor are changed. Especially, the single induced transparency window splits into double induced transparency windows as the damping factors of dark mode and bright mode show anti-symmetric damping case. These results may pave the way for designing the high performance of nano-optical devices in terahertz.