Here, an optical pulse controlled 2 × 2 surface–plasmon–polariton (SPP) mode interference coupler based on graphene clad is designed for the operation of optical fundamental gates. Exploiting the light–matter interactions on graphene–silicon interface and nonlinear optical property of graphene, coupling characteristics are obtained as a function of extra phase change between the excited SPP modes (fundamental and first order) modes with incidence of optical pulse. The device with a very small coupling length of ∼4.3 μm shows optical NOT, AND, and OR gate operation. Our compact design with high fabrication tolerance opens an avenue for the development of a complex optical processor.