Third-harmonic Generation In Graphene Research Articles

Enhanced terahertz third-harmonic generation in graphene–metal metasurface with bound states in the continuum

We propose a graphene–metal metasurface with bound states in the continuum (BICs) for the enhancement of terahertz (THz) third-harmonic generation (THG). With the adjustment of graphene Fermi level, the parameter-tuned BICs produced by the graphene–metal metasurface can make the transition to distinct quasi-BICs. It enables strong confinement of the localized field in monolayer graphene. By exploiting the large third-order nonlinearity of graphene, the efficient THG process at the quasi-BICs can be boosted under low pump threshold. With the 50 kW/cm2 of fundamental THz incidence, a THG conversion efficiency as high as ∼3% is achievable at the quasi-BICs regime. This renders the BIC metasurfaces very attractive for THz nonlinear photonics.

Highly anisotropic microwave third-harmonic generation due to mobile carriers in a graphene superlattice

We use a microscopic semiclassical approach based on the Boltzmann transport equation to explore the microwave third-harmonic generation (THG) due to mobile carriers in a one-dimensional graphene superlattice on a SiC substrate. As a model of the periodic potential of the superlattice, we adopt the piecewise constant Kronig–Penney potential. For the case of microwave radiation normally incident on the graphene superlattice, we calculate the THG conductivity of the superlattice both in the direction of its periodicity and in the perpendicular direction, and then evaluate the corresponding output THG powers from the superlattice in the reflected direction. The results obtained testify to a very strong dependence of this power on the polarization direction of the incident radiation (along or across the superlattice period) and, in addition, show that the superlattice potential applied to graphene can significantly enhance the microwave THG in graphene, which offers additional technological potentials for the design of graphene-based microwave frequency multipliers and up-converters needed for high data rate communication links.

Impact of nitrogen doping on the linear and nonlinear terahertz response of graphene

It is well known that impurities play a central role in the linear and nonlinear response of graphene at optical and terahertz frequencies. In this work, we calculate the bands and intraband dipole connection elements for nitrogen-doped monolayer graphene using a density functional tight-binding approach. Employing these results, we calculate the linear and nonlinear response of the doped graphene to terahertz pulses using a density-matrix approach in the length gauge. We present the results for the linear and nonlinear mobility as well as third-harmonic generation in graphene for adsorbed and substitutional nitrogen doping for a variety of doping densities. We show that the conduction bands are more parabolic in graphene structures with substitutional nitrogen doping than for those with adsorbed nitrogen. As a result, substitutional doping has a greater impact on the terahertz mobility and nonlinear response of graphene than adsorbed nitrogen does.

Giant enhancement of third-harmonic generation in graphene-metal heterostructures.

Nonlinear nanophotonics leverages engineered nanostructures to funnel light into small volumes and intensify nonlinear optical processes with spectral and spatial control. Owing to its intrinsically large and electrically tunable nonlinear optical response, graphene is an especially promising nanomaterial for nonlinear optoelectronic applications. Here we report on exceptionally strong optical nonlinearities in graphene-insulator-metal heterostructures, which demonstrate an enhancement by three orders of magnitude in the third-harmonic signal compared with that of bare graphene. Furthermore, by increasing the graphene Fermi energy through an external gate voltage, we find that graphene plasmons mediate the optical nonlinearity and modify the third-harmonic signal. Our findings show that graphene-insulator-metal is a promising heterostructure for optically controlled and electrically tunable nano-optoelectronic components.

Hot Electrons Modulation of Third-Harmonic Generation in Graphene

Hot electrons dominate the ultrafast ($\sim$fs-ps) optical and electronic properties of metals and semiconductors and they are exploited in a variety of applications including photovoltaics and photodetection. We perform power-dependent third harmonic generation measurements on gated single-layer graphene and detect a significant deviation from the cubic power-law expected for a third harmonic generation process. We assign this to the presence of hot electrons. Our results indicate that the performance of nonlinear photonics devices based on graphene, such as optical modulators and frequency converters, can be affected by changes in the electronic temperature, which might occur due to increase of absorbed optical power or Joule heating.

Erratum: “Cavity enhanced third harmonic generation in graphene” [Appl. Phys. Lett. 112, 011102 (2018)

In the paper Cavity enhanced third harmonic generation in graphene, we reported third harmonic generation from a graphene-dielectric-metal cavity. Since the original publication, it has come to light that a rather severe error was made in the calibration of the detector used in the experiments. Correcting this error (see corrected Figs. 1 and 2) leads to significantly lower absolute powers than previously reported, and power conversion efficiencies approaching ∼10-8 (for the largest powers used in the experiment) when resonant with the cavity and ∼10-10 when off resonance. The off resonance conversion efficiency is in line with previously reported values for planar graphene measured with comparable pulse fluence.1 Note that, due to a miscommunication between the authors, this error did not propagate into the numerical modeling results from the paper, i.e., our pW output powers are in line with v3 of order 10-17 m2=V2, as found in the analytical modeling of Ref. 2. It should also be noted that the main conclusion of our original paper, i.e., a two orders of magnitude enhancement in the harmonic generation due to the cavity, is unaffected by this error. (Figure Presented).

Broadband, electrically tunable third-harmonic generation in graphene.

Optical harmonic generation occurs when high intensity light (>1010 W m-2) interacts with a nonlinear material. Electrical control of the nonlinear optical response enables applications such as gate-tunable switches and frequency converters. Graphene displays exceptionally strong light-matter interaction and electrically and broadband tunable third-order nonlinear susceptibility. Here, we show that the third-harmonic generation efficiency in graphene can be increased by almost two orders of magnitude by controlling the Fermi energy and the incident photon energy. This enhancement is due to logarithmic resonances in the imaginary part of the nonlinear conductivity arising from resonant multiphoton transitions. Thanks to the linear dispersion of the massless Dirac fermions, gate controllable third-harmonic enhancement can be achieved over an ultrabroad bandwidth, paving the way for electrically tunable broadband frequency converters for applications in optical communications and signal processing.

Cavity enhanced third harmonic generation in graphene

Graphene displays a surprisingly large third order nonlinearity. Here, we report that conversion efficiencies approaching 10–4 are possible for third harmonic generation (THG). Moreover, the atomically thin nature of graphene allows for simple integration in cavity designs to increase this even further. We demonstrate a 117-fold enhancement, of resonant vs non-resonant wavelengths in the THG from graphene due to the integration of a graphene layer with a resonant cavity. This large enhancement occurs as the cavity is resonant for both the fundamental field and the third harmonic. We model this effect using the finite difference time domain approach. By comparing our model with experiment, we are able to deduce the value of a bulk third order susceptibility of graphene of |χ(3)|=4×10−17(m/V)2.

Theory of third-harmonic generation in graphene: A diagrammatic approach

We present a finite-temperature diagrammatic perturbation theory of third harmonic generation (THG) in doped graphene. We carry out calculations of the third-order conductivity in the scalar potential gauge, highlighting a subtle cancellation between a Fermi surface contribution, which contains only power laws, and power-law contributions of inter-band nature. Only logarithms survive in the final result. We conclude by presenting quantitative results for the up-conversion efficiency at zero and finite temperature. Our results shed light on the on-going dispute over the dependence of THG on carrier concentration in graphene.

Erratum: Quantum theory of third-harmonic generation in graphene [Phys. Rev. B90, 241301(R) (2014)

Received 21 December 2014DOI:https://doi.org/10.1103/PhysRevB.91.039904©2015 American Physical Society

Quantum theory of third-harmonic generation in graphene

A quantum theory of the third-harmonic generation in graphene is presented. An analytical formula for the nonlinear conductivity tensor $\sigma^{(3)}_{\alpha\beta\gamma\delta}(\omega,\omega,\omega)$ is derived. Resonant maxima of the third harmonic are shown to exist at low frequencies $\omega\ll E_F/\hbar$, as well as around the frequency $\omega=2E_F/\hbar$, where $E_F$ is the Fermi energy in graphene. At the input power of a CO$_2$ laser ($\lambda\approx 10$ $\mu$m) of about 1 MW/cm$^2$ the output power of the third-harmonic ($\lambda\approx 3.3$ $\mu$m) is expected to be $\simeq 50$ W/cm$^2$.

Optical Third-Harmonic Generation in Graphene

The optical properties of graphene previously used to probe its electronic structure are its optical dispersion and absorption coefficients. Now, scientists report the third-harmonic generation of light in graphene and demonstrate the promise of this nonlinear optical response as a technically versatile microscopic imaging approach of the physical structure of graphene.