Graphene electrically tuneable third harmonic generation

Abstract

Optical harmonic generation occurs when high intensity light (> 10 10 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 tuned by over two orders of magnitude by controlling the Fermi energy and the incident photon energy. This is due to logarithmic resonances in the imaginary part of the nonlinear conductivity arising from multi-photon transitions. Thanks to the linear dispersion of the massless Dirac fermions, ultrabroadband electrical tunability can be achieved, paving the way to electrically-tuneable broadband frequency converters for applications in optical communications and signal processing.The response of a material to interaction with an optical field can be described by its polarization[1]:where E is the incident electric field and ǫ 0 is the permittivity of free space. χ (1) (dimensionless) is the linear susceptibility, while the tensorsare the second-and third-order nonlinear susceptibilities [2]. Thanks to the nonlinear terms of P , new frequencies can be generated inside a material due to harmonic generation[3] and frequency mixing[4]. E.g., in Second Harmonic Generation (SHG) an incident electromagnetic wave with angular frequency ω 0 = 2πν, with ν the photon frequency, generates via χ (2) a new electromagnetic wave with frequency 2ω 0 [3]. The SHG efficiency (SHGE) is defined as the ratio between the SH intensity and the intensity of the incoming light. Analogously, Third Harmonic Generation (THG) is the emission of a photon with energy triple that of the incident one. The THG efficiency (THGE) is defined as the ratio between the TH intensity and the intensity of the incoming light. Second-order nonlinear processes are also known as three-wave-mixing, as they mix two optical fields to produce a third one [5]. Third-order nonlinear processes are known as four-wave-mixing (FWM)[5], as they mix three fields to produce a fourth one. Nonlinear optical effects are exploited in a variety of applications, including laser technology[6], material processing[7] and telecommunications [8]. E.g., to generate new photon frequencies (532nm from SHG in a Nd:YAG laser at 1.06µm) [9] or broadly tuneable ultrashort pulses (fs-ps) by optical parametric amplifiers (OPAs)[10] and optical parametric oscillators (OPOs) [11]. High harmonic generation is also used for extreme UV light [12] and attosecond pulse generation [13], while difference frequency generation is used to create photons in the THz range [14].Second order nonlinear effects can only occur in materials without inversion symmetry, while third order ones occur in any system independent of symmetry[15], and they thus represent the main intrinsic nonlinear response for most materials. THG intensity enhancement was achieved...

2D Layered Materials: Synthesis, Nonlinear Optical Properties, and Device Applications

“…Meanwhile, other optical properties, including third‐harmonic generation, parametric process, and stimulated Brillouin scattering, have been also explored, which promotes the development of layered materials‐based nonlinear optics.…”

Strong Light–Matter Interactions Enabled by Polaritons in Atomically Thin Materials

“…Fortuitously, the unique linear electronic dispersion relation of graphene, giving rise to its universal 2.3% broadband light absorption and facile electrical tunability, also endows this 2D material with an intrinsically anharmonic response to external electromagnetic fields: low‐energy charge carriers within a single Dirac cone have energies ε k = ℏ v F | k |, where k is the electron wavevector and v F ≈ c /300 is the Fermi velocity, endowing them with a velocity of fixed magnitude that instantaneously changes sign when crossing the Dirac point; an applied ac electric field E ( t ) = E 0 cos( ωt ) thus leads to a square‐wave surface current density J ( t ) = − env F sign{sin ( ωt )} in the E 0 → ∞ limit that is weighted by the charge carrier density n and contains significant contributions from all odd harmonics in its Fourier decomposition (see Figure a) . However, despite a large optical nonlinearity associated with intraband charge carrier motion near the Dirac point, most experiments in graphene nonlinear optics have only probed the interband response linking vertical transitions between Dirac cones, presumably due to the availability of interband transitions at all photon energies that could potentially enhance nonlinear processes involving multiple light frequencies, and the wider abundance of high‐powered lasers operating in the near‐IR and visible regimes that are routinely employed in nonlinear optical experiments. The initial report of a large optical nonlinearity in graphene was demonstrated in a four‐wave‐mixing experiment using intense near‐IR/visible light pulses, followed by explorations of harmonic generation, the optical Kerr effect, and other four‐wave‐mixing schemes, with reported values of the third‐order nonlinear susceptibility χ (3) ranging from ≈10 −15 –10 −19 m 2 V −2 (≈10 −7 –10 −11 esu in Gaussian units) .…”

“…The initial report of a large optical nonlinearity in graphene was demonstrated in a four‐wave‐mixing experiment using intense near‐IR/visible light pulses, followed by explorations of harmonic generation, the optical Kerr effect, and other four‐wave‐mixing schemes, with reported values of the third‐order nonlinear susceptibility χ (3) ranging from ≈10 −15 –10 −19 m 2 V −2 (≈10 −7 –10 −11 esu in Gaussian units) . The ability to electrically modulate the nonlinear optical response in graphene has recently been demonstrated, along with high‐harmonic generation (HHG) by the carbon monolayer when driven by intense terahertz and mid‐IR light pulses.…”

Theory of the strongly nonlinear electrodynamic response of graphene: A hot electron model

“…[28][29][30] respectively. Experimentally the higher harmonics generation [36][37][38][39][40] , the four-wave mixing [41][42][43][44][45] , the radiation induced absorption changes [46][47][48][49][50] , Kerr effect [51][52][53][54][55] , the photoconductivity 56 and other nonlinear phenomena have been observed. All of them demonstrated very large absolute values of the nonlinear optical parameters of graphene.…”