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Frontiers of Optoelectronics

Front. Optoelectron.    2015, Vol. 8 Issue (1) : 3-26     DOI: 10.1007/s12200-014-0428-0
REVIEW ARTICLE |
Nonlinear optical response of graphene in terahertz and near-infrared frequency regime
Yee Sin ANG1,Qinjun CHEN1,2,Chao ZHANG1,2,*()
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 Authors: 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.
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http://journal.hep.com.cn/foe/EN/10.1007/s12200-014-0428-0
http://journal.hep.com.cn/foe/EN/Y2015/V8/I1/3
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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 × ez/A, b2 = a1 × ez/A, A = (a1 × a2) ? ez; (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 Ec 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 = Tlattice if non-equilibrium heating is ignored and T = Thot if non-equilibrium heating is considered. Since Thot > Tlattice, 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 fc =ωc/2π = Δ/3h≈ 2.4 THz since σ3(3ω) = 0 at frequency smaller than fc
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 px-py 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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