Multiplasmon Absorption in Graphene

Abstract

We show that graphene possesses a strong nonlinear optical response in the form of multiplasmon absorption, with exciting implications in classical and quantum nonlinear optics. Specifically, we predict that graphene nanoribbons can be used as saturable absorbers with low saturation intensity in the farinfrared and terahertz spectrum. Moreover, we predict that two-plasmon absorption and extreme localization of plasmon fields in graphene nanodisks can lead to a plasmon blockade effect, in which a single quantized plasmon strongly suppresses the possibility of exciting a second plasmon. DOI: 10.1103/PhysRevLett.114.236801 PACS numbers: 73.20.Mf, 42.50.Hz, 78.67.Wj, 79.20.Ws The field of nonlinear optics ranges from fundamental questions concerning light-matter interactions to exciting technological applications [1]. However, usually very large field intensities are required to observe nonlinear effects. One is thus always looking for systems that will exhibit nonlinear phenomena at lower powers, with the ultimate limit being strong interactions between just two quanta of light [2]. One possibility to increase nonlinear effects is to use the strong localization and enhancement of electromagnetic fields in the form of surface plasmon excitations [3]. In that regard, we note that graphene [4] has been demonstrated to support extremely localized plasmons [5][6][7][8][9][10][11][12][13][14]. While optical nonlinearities in graphene have been studied by several authors [15][16][17][18][19][20][21][22][23][24][25][26], here we predict a novel nonlinear effect in the form of multiplasmon absorption. We also show how this effect leads to saturable absorption in graphene nanoribbons at low input powers in the farinfrared and terahertz spectrum. Moreover, we predict that the extreme localization of plasmon fields in graphene nanodisks leads to such a strong two-plasmon absorption that it becomes nearly impossible to excite a second quantized plasmon in the system. This plasmon blockade effect would cause the nanodisk to behave essentially like a quantum two-level system, which is observable in its resonance fluorescence spectrum.Graphene is a two-dimensional hexagonal lattice of carbon atoms [4]. The low-energy band structure of graphene is described by Dirac cones with the electron dispersion E nk ¼ nℏv F jkj, where v F ¼ 10 6 m=s and n ¼ AE1 stands for the conduction (valence) band [27]. In its intrinsic form graphene is a zero-gap semiconductor; however, it can also be easily doped with free carriers and as such it supports plasmon modes [5][6][7]. At low frequencies, one can get a rather accurate description of these modes by using a simple Drude conductivitywhere E F is the Fermi energy of graphene and γ is a phenomenological damping rate that takes into account various decay channels like impurity or phonon scattering [7]. The resulting plasmon dispersion is given byand we assume the average dielectric permittivityε r ≈ 2.5, which roughly corresponds to the case of graphene on a SiO 2 substrate and air on top. This...

Transient nonlinear plasmonics in nanostructured graphene

“…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].…”

Padé resummation of many-body perturbation theories

“…Even at rather low electronic density, such as found in graphene, the modification of the spectral function compared to the n b  = 0 state is substantial and can be experimentally observed. However, for confined systems 69 , direct optical excitation of plasmons is inefficient 70, 71 . Therefore, we argue, by exciting the system using a beam of free electrons, the appearance of extra satellites in the electronic density of states can be probed by the time-resolved photoemission 22, 72, 73 .…”

Quantum Nonlinear Optical Interactions between Graphene Plasmons

“…1a. A similar argument reveals that two-plasmon absorption can take place in the green shaded region, and three-plasmon absorption in the yellow region [8]. To understand the fields required to observe strong multi-plasmon absorption, we note that one can define a characteristic field E e = e/(4π 0 r 2 e ), where r e ∝ λ F is the typical distance between carriers in graphene.…”

“…The nonlinear optical properties of graphene have been discussed in greater detail in a number of works [4][5][6][7][8], and here our goal is to provide an intuitive understanding and discuss briefly the potential consequences. There are qualitatively two different mechanisms that can be responsible for the nonlinear response.…”