DC current induced second order optical nonlinearity in graphene

Cheng, Jinluo; Vermeulen, Nathalie; Sipe, J. E.

doi:10.1364/oe.22.015868

Cited by 77 publications

(86 citation statements)

References 48 publications

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“…These relaxation times can depend on the electron state energy, momentum, band index, doping level, and the external fields. However, at optical frequencies the largest effect of relaxation processes is to remove physical divergences associated with resonances [29,[35][36][37][38], and so they can be described by relaxation time constants, which in some cases can be extracted from experiments. In such a phenomenological way we model the intraband (interband) relaxation process by a parameter i ( e ), and then…”

Section: Modelmentioning

confidence: 99%

“…However, the dependence of the nonlinearity on chemical potential, temperature, and the excitation frequency have not been systematically measured. Of the theoretical studies reported, most are still at the level of single particle approximations within different approaches, which include perturbative treatments based on Fermi's golden rule [25,26], the quasiclassical Boltzmann kinetic approach [1,2,27,28], and quantum treatments based on semiconductor Bloch equations (SBE) or equivalent strategies [3,[29][30][31][32][33][34][35][36][37][38]. When optical transitions around the Dirac points dominate, analytic expressions for the third order conductivities can be obtained perturbatively by employing the linear dispersion approximation [3,[35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

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Numerical study of the optical nonlinearity of doped and gapped graphene: From weak to strong field excitation

2015

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Numerically solving the semiconductor Bloch equations within a phenomenological relaxation time approximation, we extract both the linear and nonlinear optical conductivities of doped graphene and gapped graphene under excitation by a laser pulse. We discuss in detail the dependence of second harmonic generation, third harmonic generation, and the Kerr effects on the doping level, the gap, and the electric field amplitude. The numerical results for weak electric fields agree with those calculated from available analytic perturbation formulas. For strong electric fields when saturation effects are important, all the effective third order nonlinear response coefficients show a strong field dependence.

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Section: Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical study of the optical nonlinearity of doped and gapped graphene: From weak to strong field excitation

2015

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“…More general, quantum theories, which take into account both contributions, have been recently proposed in Refs. [19][20][21][22][23][24]. It was shown that, apart from a strong resonance at low (hω ≪ 2E F ) frequencies, the third-order nonlinear conductivity σ αβγδ (ω 1 , ω 2 , ω 3 ) demonstrates a number of resonances at the frequencies corresponding to the one-, two-and three-photon interband absorption.…”

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confidence: 99%

Giant enhancement of the third harmonic in graphene integrated in a layered structure

Savostianova

Mikhaǐlov

2015

Applied Physics Letters

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Graphene was shown to have strongly nonlinear electrodynamic properties. In particular, being irradiated by an electromagnetic wave with the frequency ω, it can efficiently generate higher frequency harmonics. Here we predict that in a specially designed structure "graphene -dielectricmetal" the third-harmonic (3ω) intensity can be increased by more than two orders of magnitude as compared to an isolated graphene layer.PACS numbers: 78.67. Wj, 42.65.Ky, 73.50.Fq It was theoretically predicted [1] that, due to the "ultra-relativistic", massless energy dispersion of graphene electrons,it should demonstrate a strongly nonlinear electrodynamic response; here v F ≈ 10 8 cm/s is the Fermi velocity of graphene and k is the electron wave-vector. Physically, this is due to the absence of inertia of graphene electrons: According to (1), electrons can move only with the velocity v F in any directions, therefore, being placed in the oscillating external electric field they have to "instantaneously" change their velocity from +v F to −v F in the return points. This leads to the emission of radiation at higher (multiple) frequencies as well as to other nonlinear phenomena. The efficiency of the nonlinear effects in graphene was predicted to be many orders of magnitude larger than in many other nonlinear materials [1].Experimentally, a strong nonlinearity of the graphene response has been confirmed at microwave [2] and optical [3] frequencies. Further experimental studies of different nonlinear electrodynamic effects in graphene can be found in Refs. [4][5][6][7][8][9][10][11]. A quasi-classical theory of the nonlinear electrodynamic response of graphene, which is valid at relatively low (microwave, terahertz) frequencies hω ≪ 2E F , has been developed in Refs. [1,[12][13][14][15][16][17][18]; here E F is the Fermi energy. This theory takes into account only the intra-band electronic transitions and ignores the inter-band ones. More general, quantum theories, which take into account both contributions, have been recently proposed in Refs. [19][20][21][22][23][24]. It was shown that, apart from a strong resonance at low (hω ≪ 2E F ) frequencies, the third-order nonlinear conductivity σ αβγδ (ω 1 , ω 2 , ω 3 ) demonstrates a number of resonances at the frequencies corresponding to the one-, two-and three-photon interband absorption.In Refs. [19][20][21][22][23][24] the third-order nonlinear response functions of graphene have been calculated for a single, freely hanging in vacuum (or in air) mono-atomic graphene layer. In reality graphene lies of a dielectric substrate (of thickness d). In this Letter we study the influence of the dielectric environment on the efficiency of the third harmonic generation and show that, depending on the ratio d/λ ω , as well as on physical properties of layers supporting graphene, the output third harmonic intensity can be both several orders of magnitude smaller and several orders of magnitude larger than in the isolated graphene layer. A proper choice of the geometrical parameters and physica...

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“…0.147 J/cm 2 ( Fig. 2), was a factor 2 higher for graphene on silicon than for graphene on SiO 2 (0.076 J/cm 2 ), while the damage threshold for bare SOI was 0.546 J/cm 2 (Fig. 2).…”

Section: Femtosecond Laser Ablationmentioning

confidence: 96%

“…In recent years graphene, a two-dimensional hexagonal lattice of carbon atoms, has been shown to exhibit unique optical properties that can strongly improve the functioning of photonic devices and even of entire photonic circuits [1,2]. When depositing graphene on chip-scale photonic circuits consisting of silicon waveguides, a high-resolution patterning method to locally remove the graphene layer without affecting the underlying silicon waveguide is desired for most applications.…”

Section: Introductionmentioning

confidence: 99%

Laser ablation- and plasma etching-based patterning of graphene on silicon-on-insulator waveguides

Erps¹,

Ciuk²,

Pasternak³

et al. 2015

Opt. Express

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Abstract:We present a new approach to remove monolayer graphene transferred on top of a silicon-on-insulator (SOI) photonic integrated chip. Femtosecond laser ablation is used for the first time to remove graphene from SOI waveguides, whereas oxygen plasma etching through a metal mask is employed to peel off graphene from the grating couplers attached to the waveguides. We show by means of Raman spectroscopy and atomic force microscopy that the removal of graphene is successful with minimal damage to the underlying SOI waveguides. Finally, we employ both removal techniques to measure the contribution of graphene to the loss of grating-coupled graphene-covered SOI waveguides using the cut-back method.

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DC current induced second order optical nonlinearity in graphene

Cited by 77 publications

References 48 publications

Numerical study of the optical nonlinearity of doped and gapped graphene: From weak to strong field excitation

Numerical study of the optical nonlinearity of doped and gapped graphene: From weak to strong field excitation

Giant enhancement of the third harmonic in graphene integrated in a layered structure

Laser ablation- and plasma etching-based patterning of graphene on silicon-on-insulator waveguides

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