In order to study the excitation and evolution of rogue waves in the periodic background, the excitation and evolution of rogue waves in the case of two kinds of periodic potentials (real potential and complex potential) are discussed by using the split-step fast Fourier transform, according to the self-focusing nonlinear Schrodinger equation model with periodic external potential. The results show that rogue waves can be excited by plane waves with a little perturbation in both kinds of periodic potential backgrounds. In the case of only real periodic potential, different optical phenomena can be generated by changing the amplitude and period of the period potential. In the parity-time symmetry periodic potential, a very large rogue wave can be excited, and the real part amplitude has energy dissipation and deceleration effect on the rogue wave, while the imaginary part amplitude has energy gain and acceleration effect on the rogue wave. Therefore, choosing appropriate real part amplitude and imaginary part amplitude can generate large rogue wave with different intensity. The study can help to capture and adjust the strange wave in the optical lattice, and get high power waves.