Dual optical bistabilities in Octonacci photonic multilayers doped by graphene

We theoretically investigate the optical bistability in a compound structure which is composed by graphene and photonic multilayers. The photonic multilayers are stacked by different dielectrics and of which the arrangement order is submitted to the Octonacci sequence. The Octonacci lattices are aperiodic and support optical fractal resonance states. These fractal modes split exponentially as the generation number of sequence increases. Especially, the optical fractal states have strong electric field localization, which could be utilized to enhance the nonlinearity of graphene. Consequently, low-threshold dual optical bistabilities are achieved as graphene is embedded around the strongest intensity site of electric field. The two optical bistabilities are separated and of which the upper and lower thresholds of bistability can be modulated by the chemical potential of graphene and the incident wavelength flexibly. This study may be helpful in designing all-optical multivalued switches, optical memory and optical logic devices.