Nonlinear Refractive Index in Rectangular Graphene Quantum Dots

Alongside its other favorable properties, the large refraction nonlinearity of graphene-related material makes it ideal for use in optoelectronics applications. Numerous experimental studies about nonlinear optical refraction have been conducted, but theoretical verification is lacking. In this paper the nonlinear refractive index for rectangular graphene quantum dots (RGQDs) was calculated using the relationship between nonlinear refractive index and the third-order nonlinear optical susceptibility. The third-order nonlinear optical susceptibility for third harmonic generation was derived employing the electronic states obtained from the Dirac equation around K point in RGQDs under hard wall boundary conditions. Results revealed that the calculated nonlinear refractive index, n 2 , was in the magnitude of 10−14 m2/W in the visible region, which is nearly five orders larger than conventional semiconductor quantum dots, while in the infrared region the nonlinear refractive index reached up to the magnitude of 10−11 m2/W for M = 3M0 sized RGQDs where the resonance enhancement occurred. The nonlinear refractive index could be tuned both by the edges and sizes.