Plasmon-assisted high-harmonic generation in graphene

Cox, Joel D.; Marini, Andrea; Abajo, F. Javier García de

doi:10.1038/ncomms14380

Cited by 147 publications

(132 citation statements)

References 65 publications

(110 reference statements)

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“…Currents associated with these intraband transitions undergo a strongly anharmonic motion that reflects the linear electronic dispersion in graphene and leads to a highly nonlinear response to external electromagnetic fields [9][10][11][12][13][14][15][16][17]. However, most experimental studies on graphene nonlinear optics have dealt with interband effects, including reports of large third-order susceptibilities linked to wave mixing [18], harmonic generation [19][20][21][22][23], and the Kerr effect [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

“…Electron dynamics in graphene nanostructures is described by the single-electron density-matrix equation of motion [11,16] …”

Section: Theoretical Formalismmentioning

confidence: 99%

“…Specifically, we consider graphene nanoribbons, which are common elements in both experimental studies and envisioned applications of graphene plasmonics [31][32][33]. We simulate the optical response of the ribbons using a tight-binding model for the electronic structure combined with self-consistent-field time-domain solutions of the one-particle density-matrix equation of motion [11,16]. Results are presented for continuous-wave (cw) illumination, individual ultrashort pulses, and degenerate pump-probe irradiation.…”

Section: Introductionmentioning

confidence: 99%

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Transient nonlinear plasmonics in nanostructured graphene

Cox¹,

Abajo²

2018

Optica

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Plasmons in highly doped graphene offer the means to dramatically enhance light absorption in the atomically thin material. Ultimately the absorbed light energy induces an increase in electron temperature, accompanied by large shifts in the chemical potential. This intrinsically incoherent effect leads to strong intensity-dependent modifications of the optical response, complementing the remarkable coherent nonlinearities arising in graphene due to interband transitions and anharmonic intraband electron motion. Through rigorous time-domain quantum-mechanical simulations of graphene nanoribbons, we show that the incoherent mechanism dominates over the coherent response for the high levels of intensity required to trigger nonperturbative optical phenomena such as saturable absorption. We anticipate that these findings will elucidate the role of coherent and incoherent nonlinearities for future studies and applications of plasmon-assisted nonlinear optics.

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Section: Introductionmentioning

confidence: 99%

“…Electron dynamics in graphene nanostructures is described by the single-electron density-matrix equation of motion [11,16] …”

Section: Theoretical Formalismmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Transient nonlinear plasmonics in nanostructured graphene

Cox¹,

Abajo²

2018

Optica

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“…In hybrid graphene plasmonic waveguides, Smirnova & Solntsev [125] simultaneously phasematched the cascaded third, second and fundamental graphene plasmon harmonics to improve the third-harmonic generation by a factor of five compared with the non-cascaded regime. Finally, Cox et al [151] studied high-harmonic generation in graphene plasmons and found that harmonics as high as the 13th order could be theoretically generated with optical intensity as low as 100 MW cm −2 . Several other interesting nonlinear phenomena can be seen or enhanced in graphene plasmons.…”

Section: (D) Enhanced Second- Third-and High-harmonic Generationmentioning

confidence: 99%

Nonlinear graphene plasmonics

Ooi

Tan

2017

Proc. R. Soc. A.

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The rapid development of graphene has opened up exciting new fields in graphene plasmonics and nonlinear optics. Graphene's unique twodimensional band structure provides extraordinary linear and nonlinear optical properties, which have led to extreme optical confinement in graphene plasmonics and ultrahigh nonlinear optical coefficients, respectively. The synergy between graphene's linear and nonlinear optical properties gave rise to nonlinear graphene plasmonics, which greatly augments graphene-based nonlinear device performance beyond a billion-fold. This nascent field of research will eventually find far-reaching revolutionary technological applications that require device miniaturization, low power consumption and a broad range of operating wavelengths approaching the far-infrared, such as optical computing, medical instrumentation and security applications.

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“…This approach can be extended to the expectation values of the current density [1] and then to the calculation within the Floquet scheme of nonlinear optical properties under intense laser fields (high harmonic generation [35] and saturable absorption [36,37] ) of graphene. This will be the subject of further study.…”

mentioning

confidence: 99%

Time Evolution of Floquet States in Graphene

Manghi

Puviani

Lenzini

2018

Advances in Condensed Matter Physics

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Based on a solution of the Floquet Hamiltonian we have studied the time evolution of electronic states in graphene nanoribbons driven out of equilibrium by time-dependent electromagnetic fields in different regimes of intensity, polarization, and frequency. We show that the time-dependent band structure contains many unconventional features that are not captured by considering the Floquet eigenvalues alone. By analyzing the evolution in time of the state population we have identified regimes for the emergence of time-dependent edge states responsible for charge oscillations across the ribbon.If a time-periodic field is applied to electrons in a periodic lattice the Bloch theorem can be applied twice, both in space and in time. This is the essence of Floquet-Bloch theory [1][2][3] that has recently attracted a renewed interest for its ability to describe topological phases in driven quantum systems [4][5][6][7]. The discovery that circularly polarized light may induce nontrivial topological behaviour in materials that would be standard in static conditions [8][9][10][11] has opened the way to the realization of the so-called Floquet topological insulators, where a topological phase may be engineered and manipulated by tunable controls such as polarization, periodicity, and amplitude of the external perturbation.When the field is applied for a sufficiently long time (pulse duration much larger than the field oscillation period) electrons reach a nonequilibrium steady state characterized by a periodic time-dependence of the wave functions and, consequently, of the expectation values of any observable [12,13]. In this paper we focus on this time-dependence, looking for the time evolution of some relevant quantities such as energy and charge density. How these characteristics affect the time behaviour of these observables will be our focus. We will consider the prototypical case of graphene that under the influence of circularly polarized light exhibits in its Floquet band structure the distinctive characteristics of a 2D Chern insulator, namely, a gap in 2D and linear dispersive edge states in 1D [9,11,14,15]. These Floquet edge states are topologically protected and responsible for a quantized Hall conductance in the absence of a magnetic field [16][17][18], a remarkable realization of the so-called "quantum Hall systems without Landau levels" originally proposed by Haldane [19].Under a periodic drive, the nonequilibrium steady states, solutions of the time-dependent Schrödinger equationevolve in time aswhere 훼k (r, ) is periodic in time and 훼 (k), the Floquet quasi-energies, are the eigenvalues of an effective Hamiltonian̂퐹 ≡̂− ( / ), the so-called Floquet Hamiltonian:퐹 훼k (r, ) = 훼 (k) 훼k (r, ) .Herê(r, ) is the full Hamiltonian of the driven system (r, ) =̂0 (r) +̂(r, )

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Plasmon-assisted high-harmonic generation in graphene

Cited by 147 publications

References 65 publications

Transient nonlinear plasmonics in nanostructured graphene

Transient nonlinear plasmonics in nanostructured graphene

Nonlinear graphene plasmonics

Time Evolution of Floquet States in Graphene

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