Nonlinear optical response of graphene in terahertz and near-infrared frequency regime

doi:10.1007/s12200-014-0428-0

Front. Optoelectron.

2015, Vol. 8

Issue (1) : 3-26 https://doi.org/10.1007/s12200-014-0428-0

REVIEW ARTICLE

Nonlinear optical response of graphene in terahertz and near-infrared frequency regime

Yee Sin ANG¹,Qinjun CHEN^1,²,Chao ZHANG^1,^2,^*(

)

1. School of Physics, University of Wollongong, New South Wales 2522, Australia
2. Institute of Superconducting and Electronic Materials, University of Wollongong, New South Wales 2522, Australia

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Abstract

In this review, we discuss our recent theoretical work on the nonlinear optical response of graphene and its sister structure in terahertz (THz) and near-infrared frequency regime. Due to Dirac-like linear energy-momentum dispersion, the third-order nonlinear current in graphene is much stronger than that in conventional semiconductors. The nonlinear current grows rapidly with increasing temperature and decreasing frequency. The third-order nonlinear current can be as strong as the linear current under moderate electric field strength of 10⁴ V/cm. In bilayer graphene (BLG) with low energy trigonal warping effect, not only the optical response is strongly nonlinear, the optical nonlinearity is well-preserved at elevated temperature. In the presence of a bandgap (such as semihydrogenated graphene (SHG)), there exists two well separated linear response and nonlinear response peaks. This suggests that SHG can have a unique potential as a two-color nonlinear material in the THz frequency regime where the relative intensity of the two colors can be tuned with the electric field. In a graphene superlattice structure of Kronig-Penney type periodic potential, the Dirac cone is elliptically deformed. We found that not only the optical nonlinearity is preserved in such a system, the total optical response is further enhanced by a factor proportional to the band anisotropy. This suggests that graphene superlattice is another potential candidate in THz device application.

Keywords graphene terahertz (THz) response nonlinear effect photomixing

Corresponding Author(s): Chao ZHANG

Just Accepted Date: 26 August 2014 Online First Date: 28 October 2014 Issue Date: 13 February 2015

Cite this article:

Yee Sin ANG,Qinjun CHEN,Chao ZHANG. Nonlinear optical response of graphene in terahertz and near-infrared frequency regime[J]. Front. Optoelectron., 2015, 8(1): 3-26.

URL:

https://academic.hep.com.cn/foe/EN/10.1007/s12200-014-0428-0
https://academic.hep.com.cn/foe/EN/Y2015/V8/I1/3

Fig.1 Graphene, an atomically thin layer of carbon atoms arranged in honeycomb structure, a₁ and a₂ are the lattice unit vectors. Red and green dots are atoms from two sublattices

Fig.2 (a) Reciprocal lattice of graphene, b₁ = a₂ × e_z/A, b₂ = a₁ × e_z/A, A = (a₁ × a₂) ? e_z; (b) band structure near the Dirac point

Fig.3 Temperature dependence of third order nonlinear current density for μ < 0 at f = ω/2π= 1 THz (Ref. [63])

Fig.4 Temperature dependence of third order nonlinear current density for μ > 0 at f = ω/2π= 1 THz (Ref. [63])

Fig.5 Temperature dependence of β at f = ω/2π= 1 THz. β exhibits contrasting behavior at low and high temperature regimes [68]

Fig.6 Critical field of E c ( S ) at f = ω/2π= 1 THz and μ = 0.1 eV. Weak-field critical field E_c is also shown [ 68]

Fig.7 Temperature dependence of strong-field third order nonlinear current density at f = ω/2π= 1 THz. Note that T = T_lattice if non-equilibrium heating is ignored and T = T_hot if non-equilibrium heating is considered. Since T_hot > T_lattice, the nonlinear optical response is significantly stronger if carrier heating is considered [68]

Fig.8 ? and temperature dependence of the third-order nonlinear current density [68] at f = 1.5 THz and μ = 0.12eV

Fig.9 Frequency dependence of the linear optical conductivity at different interlayer coupling strength. Dotted curve: 0.1α, dashed curve: 0.5α, solid curve: α, dash-dotted curve: 1.5α, where α = 1/(2m*) and m* = 0.33 m e [ 95]. The low frequency conductivity always approach 6σ₀ regardless the strength of the interlayer coupling [ 69]

Fig.10 Frequency dependence of the third-order nonlinear optical conductivities at zero and room temperatures [69]. The electric field strength is 1000 V/cm

Fig.11 Linear and nonlinaer conductances vs. temperature for frequency [69] of 1 THz. The electric field is 600 V/cm

Fig.12 Frequency dependent critical fields at zero and room temperatures [69]

Fig.13 Temperature dependent critical fields for frequency [69] of 1 THz

Fig.14 Frequency dependent optical conductance in the low frequency regime for two temperatures. The electric field is 3600 V/cm. The absorption edge for the frequency tripled response is shifted to Δ/3. The inset is a schematic showing different optical processes [70]

Fig.15 Frequency dependence of the critical field E(3ω) for SHG and pure (gapless) graphene [70]. The inset shows the reduction of the critical field in SHG. Note that there exists a cut-off frequency f_c =ω_c/2π = Δ/3h≈ 2.4 THz since σ₃(3ω) = 0 at frequency smaller than f_c

Fig.16 Temperature dependence of the critical field [70] at two different frequencies of 2.4 and 5 THz

Fig.17 Band structure of graphene superlattice (inset). In the p_x-p_y plan, the Dirac cone is elongated elliptically in the y-direction. L, w and U are the superlattice periodicity, potential width and potential height, respectively, of the Kronig-Penney type graphene superlattice [71]

Fig.18 Frequency dependence [71] of σ₃(3ω) at E = 1000 V/cm and T = 300 K

Fig.19 Anisotropic gapped graphene frequency-tripling conductivity [71] at T = 300 K and E = 3400 V/cm and ? = 0.03 eV

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