Nonlinear Refractive Index in Rectangular Graphene Quantum Dots

Abstract

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 m 2 /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 m 2 /W for M = 3M 0 sized RGQDs where the resonance enhancement occurred. The nonlinear refractive index could be tuned both by the edges and sizes.Graphene is comprised of a plane of carbon atoms arranged in honeycomb lattices, and has attracted intense attention due to its extraordinary physical and chemical properties [1][2][3]. The planar geometry of graphene is advantageous to the tailoring of various nanostructures, such as one-dimensional nanoribbons [4] and zero-dimensional quantum dots [5] with desired size, edge, and shape [6][7][8]. Due to the quantum size and edge effect, the tunable electronic and optical properties make the graphene-based nanostructures promising candidates for building blocks of future opto-electronic devices [9,10]. To this end, the integrability of the graphene quantum dot combined with its large refraction nonlinearity makes it ideal for use in several applications in optical communication and signal-processing [11].Numerous experimental works have been conducted on the nonlinear refractive index in the graphene and related nanostructures. H. Zhang et al. showed that graphene possesses the giant nonlinear refractive index of n 2 10 −7 cm 2 W −1 , almost nine orders of magnitude larger than bulk dielectrics, using the Z-scan technique on loosely stacked few-layer graphene [12]. The spatial self-phase modulation was observed directly by G. Wang et al. when a focused He-Ne laser beam at 633 nm went through liquid-phase-exfoliated graphene dispersions [13]. They estimated the relative change of effective nonlinear refractive index by tuning the incident intensity or the temperature of the dispersions. By means of the ultrafast optical Kerr effect method coupled to optical heterodyne detection (OHD-OKE), E. Dremetsika's group characterized the third-order nonlinear response

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