▎ 摘　　要

We investigate the optical bistability, tristability and multistability in a complex structure which composed by graphene and dielectric multilayers submitted to the Thue-Morse (TM) sequence. Dielectric multilayers pattern spatially to meet the TM sequence rules and graphene is embedded at the interfaces of dielectrics. The TM lattices support discrete resonant modes and strong field localization which can greatly enhance the nonlinear effect of graphene, and sequentially render low-threshold double bistability. The thresholds of bistability and the intervals between the upper thresholds and lower thresholds increase as the chemical potential of graphene is increasing. Furthermore, tristability and multistability are also induced by modulating the incident wavelength with a large red-detuning. This study paves a new way towards all-optical multivalues switches, optical logic elements and optical storage.