Nonlinear graphene plasmonics

Abstract

The rapid development of graphene has opened up exciting new fields in graphene plasmonics and nonlinear optics. Graphene's unique two-dimensional band structure provides extraordinary linear and nonlinear optical properties, which have led to extreme optical confinement in graphene plasmonics and ultrahigh nonlinear optical coefficients, respectively. The synergy between graphene's linear and nonlinear optical properties gave rise to nonlinear graphene plasmonics, which greatly augments graphene-based nonlinear device performance beyond a billion-fold. This nascent field of research will eventually find far-reaching revolutionary technological applications that require device miniaturization, low power consumption and a broad range of operating wavelengths approaching the far-infrared, such as optical computing, medical instrumentation and security applications.

Keywords: graphene; nonlinear optics; plasmonics.

Figure 1.

(a) Reflection image for graphene flakes in green light and (b) determination of nonlinear coefficients via four-wave mixing experiments. (Reproduced with permission from Hendry et al. [8] (Copyright © 2010 American Physical Society).) (Online version in colour.)

Figure 2.

Excitation of graphene plasmons by mid-infrared illumination mediated by scattering at atomic force microscopy tips. (Reproduced with permission from (a) Fei et al. [9] and (b) Chen et al. [10] (Copyright © 2012 Nature Publishing Group).) (Online version in colour.)

Figure 3.

Surface plasmons are the collective motion of free electrons that induces charge density oscillations. When a photon is coupled to the surface plasmon, they form surface plasmon polaritons that propagate along the metal surface. (Reproduced with permission from Zia et al. [19] (Copyright © 2006 Elsevier Ltd).) (Online version in colour.)

Figure 4.

(a) SPP dispersion of various bulk metals and graphene. (b) Rescaling of (a) for a clearer view of graphene's SPP dispersion. (Online version in colour.)

Figure 5.

Graphene's refractive indices for various Fermi levels at wavelength 1550 nm. (Online version in colour.)

Figure 6.

Effective mode area for (a) gold and (b) graphene plasmonic waveguides. The waveguides are 0.33 nm in thickness, the wavelength studied is 1.55 µm and graphene is doped to 0.7 eV. (Reproduced with permission from Ooi et al. [56] (Copyright © 2016 Authors).)

Figure 7.

Nonlinear optical processes in graphene. (a) Left: third-harmonic generation, right: parametric frequency conversion. (b) Two-photon absorption. (c) Two-colour coherent current injection. (Reproduced with permission from Cheng et al. [73] (Copyright © 2014 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft).) (Online version in colour.)

Figure 8.

(a) Nonlinear refractive index, n₂, and (b) nonlinear extinction coefficient, k₂, of graphene derived using the perturbative model from Cheng et al. [75]. (Online version in colour.)

Figure 9.

Saturable absorption in graphene. (a) Graphene saturable absorber film on a fibre pigtail. (b) Optical image of the graphene film coating on the fibre. (c) Nonlinear absorption of graphene films with the number of layers. (Reproduced with permission from Bao et al. [92] (Copyright © 2009 Wiley-VCH Verlag GmbH & Co. KGaA).) (Online version in colour.)

Figure 10.

(a) FWM of graphene laid on top of a silicon photonic crystal waveguide. (b) Soliton propagation on a graphene sheet. (Reproduced with permission from (a) Gu et al. [98] (Copyright © 2012 Nature Publishing Group) and (b) Nesterov et al. [105] (Copyright © 2013 by Wiley-VCH Verlag GmbH & Co. KGaA).) (Online version in colour.)

Figure 11.

Nonlinear optical measurement techniques for graphene. (a) The Z-scan method. (b) OHD-OKE set-up, where L is the lens, PBS is the polarizing beam splitter, GP is the Glan polarizer and λ/2 and λ/4 are the half- and quarter-wave plates, respectively. (c) SPM measurement experimental set-up for graphene cladded on a silicon-on-insulator waveguide. BS, beam splitter; D, detector; LIA, lock-in amplifier; OPO, optical parametric oscillator; OSA, optical spectrum analyser; PC, polarization controller; SMF, single mode fibre; SOI, silicon-on-insulator. (Reproduced with permission from (a) Miao et al. [97] (Copyright © 2015 Chinese Laser Press), (b) Dremetsika et al. [113] (Copyright © 2016 Optical Society of America) and (c) Vermeulen et al. [114] (Copyright © 2016 American Physical Society).) (Online version in colour.)

Figure 12.

Graphene plasmonics on a nonlinear substrate. (a) The dispersion relation changes when the Kerr nonlinear contributions of the substrate are considered. Ω is the normalized frequency in units ℏω/E_F, and the normalized momentum is in units ω/c. (b) Resonant modes of the graphene nanoribbons blue-shift with increasing intensity due to the Kerr nonlinearity of the substrate. KSPP, graphene plasmonic wavevector. (Reproduced with permission from (a) Wang et al. [115] (Copyright © 2012 Optical Society of America) and (b) Nasari et al. [119] (Copyright © 2016 Optical Society of America).) (Online version in colour.)

Figure 13.

Nonlinear parameters and SINE factors for (a) metal-based waveguides and (b) graphene plasmonic waveguides. Ω is the normalized frequency in units ℏω/E_F. (Reproduced with permission from (a) Skryabin et al. [131] (Copyright © 2010 Optical Society of America) and (b) Gorbach [122] (Copyright © 2013 American Physical Society).) (Online version in colour.)

Figure 14.

Nonlinear parameters for various graphene-based waveguides: (a) graphene-on-silicon dielectric waveguides, (b) graphene-on-metal plasmonic waveguides and (c) graphene plasmonic waveguides. (Reproduced with permission from Chatzidimitriou et al. [126] (Copyright © 2015 AIP Publishing LLC).)

Figure 15.

DFG of graphene plasmons. (a) Three wave-mixing process between two pump photons (green and blue) and a plasmon (red). (b) Calculated DFG efficiencies between phase-matched plasmons for difference scattering frequencies. (c) Experimental measurement of differential reflection, where the resonant curve appears when the difference frequency matches the energy of the graphene plasmon. (Reproduced with permission from (a) and (b) Yao et al. [135] (Copyright © 2014 American Physical Society) and (c) Constant et al. [136] (Copyright © 2015 Nature Publishing Group).) (Online version in colour.)

Figure 16.

Nonlinear response of a graphene triangular nanoisland varies with size, Fermi level ((a–d) 0.5 eV and (e–h) 1 eV) and edge structure (armchair is blue and zigzag is red). (a,e) The absorption cross-section, (b,f) the second-harmonic generation, (c,g) the third-harmonic generation and (d,f) the Kerr nonlinearity. Size of the circle indicates the absorption or nonlinear strength. (Reproduced with permission from Cox et al. [133] (Copyright © 2015 American Chemical Society).) (Online version in colour.)

Figure 17.

Nonlinear phase- and extinction-switching for graphene with various Fermi levels. Optical intensities of the order of MW cm⁻² are required for full-contrast switching. (Reproduced with permission from Ooi et al. [56] (Copyright © 2016 Authors).)

Figure 18.

Plasmonic bistability effect in graphene plasmonic waveguides. (a) Kretschmann excitation method of graphene plasmons. (b) Bistable switching of graphene plasmons due to the angle sensitivity of the excitation beam. (Reproduced with permission from Dai et al. [153] (Copyright © 2015 CC-BY 4.0).) (Online version in colour.)