通过求解无限质量边界条件下石墨烯量子盘(GQDs)电子狄拉克方程，获得了电子能带结构，在此基础上理论研究了石墨烯量子盘的双光子吸收(TPA)性质，得到了任意尺寸分布函数下导带内电子跃迁引起的双光子吸收系数的解析表达式，及双光子跃迁选择定则。研究结果表明，双光子吸收系数的峰值比传统的半导体量子点的大8个数量级左右，石墨烯量子盘的能谱和双光子吸收谱可以通过石墨烯量子点的尺寸、尺寸分布函数和电子的弛豫能来调控。

The structure of electronic energy levels is obtained by solving electronic Dirac equation of graphene quantum disks (GQDs) under the infinite-mass boundary conditions. On this basis, the properties of two-photon absorption (TPA) of GQDs are studied theoretically, and the analytical expression of TPA coefficient associated with electron transitions in the conduction band under an arbitrary size-distribution as well as the two-photon transition selection rule are obtained. The research results show that the peak value of TPA coefficient is about 8 orders of magnitude greater than that of conventional semiconductor quantum dots. The energy spectra and TPA spectra can be adjusted and controlled by the GQDs size, size-distribution function and electron relaxation energy.