Giant Optical Nonlinearity of Graphene in a Strong Magnetic Field

Abstract

We present quantum-mechanical density-matrix formalism for calculating the nonlinear optical response of magnetized graphene, valid for arbitrarily strong magnetic and optical fields. We show that magnetized graphene possesses by far the highest third-order optical nonlinearity among all known materials. The giant nonlinearity originates from unique electronic properties and selection rules near the Dirac point. As a result, even one monolayer of graphene gives rise to appreciable nonlinear frequency conversion efficiency for incident infrared radiation.PACS numbers: 81.05.ue, 42.65.-k Graphene, a two-dimensional monolayer of carbon atoms arranged in a hexagonal lattice, holds many records as far as its mechanical, thermal, electrical, and optical properties are concerned; see. e.g. [1] for the review. With this Letter we would like to add yet another distinction to this list of superlatives: we show that graphene in a strong magnetic field has the highest infrared optical nonlinearity of all materials we know.Strong optical nonlinearity of graphene, like most of its unique electrical and optical properties, stems from linear dispersion of carriers near the K,K' points of the Brillouin zone. As a result, the electron velocity induced by an incident electromagnetic wave is a nonlinear function of induced electron momentum. Nonlinear electromagnetic response of classical charges with linear energy dispersion has been studied theoretically in [2]. Recently, fourwave mixing in mechanically exfoliated graphene flakes without magnetic field has been observed at near-infrared wavelengths [3]. Effective bulk third-order susceptibility was estimated to have a very large value, χ (3) ∼ 10esu. This is comparable in magnitude to the resonant intersubband χ (3) nonlinearity observed in the mid-infrared range for low-doped quantum cascade laser structures [4], which are essentially asymmetric coupled quantum well heterostructures.Nonlinear cyclotron resonance in graphene was considered theoretically in [5], again in the classical limit, by solving the equation of motion F = dp/dt for a massless charge. Classical approximation can be applied to electrons in low magnetic field that are occupying highly excited Landau levels n 1, when energy and momentum quantization are neglected. Here we present rigorous quantum mechanical description of the nonlinear optical response of magnetized graphene, which is valid for arbitrary magnetic fields and electron distributions over Landau levels (LLs). After finding matrix elements of the optical transitions between LLs, we calculate the thirdorder nonlinear susceptibility using the density-matrix formalism and then evaluate the efficiency of the fourwave mixing process. The magnitude of χ (3) turns out * Electronic address: belyanin@tamu.edu to be astonishingly large, of the order of 10 −1 esu at mid/far-infrared wavelengths in the field of several Tesla. This leads to a surprisingly high four-wave mixing efficiency of the order of 10 −4 W/W 3 per monolayer.Linear (one-photon) absorption...

Multiplasmon Absorption in Graphene

“…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.…”

Polarized dependence of nonlinear susceptibility in a single layer graphene system in infrared region

“…Moreover, due to growing high quality epitaxial graphene and combination of uncommon electronic features with extraordinary optical properties, they are very favoraitable for applications in infrared and terahertz optics [51][52][53]. Some optical properties of graphene [54][55][56][57][58][59][60][61][62][63] based on the nonlinear optical interaction in the presence of strong magnetic field have been analyzed. For example, generation of polarization entangled photons [54], generation and propagation of ultraslow optical solitons [57,58], controlling the optical bistability and multistability [61][62][63] have been reported very recently.…”

“…Some optical properties of graphene [54][55][56][57][58][59][60][61][62][63] based on the nonlinear optical interaction in the presence of strong magnetic field have been analyzed. For example, generation of polarization entangled photons [54], generation and propagation of ultraslow optical solitons [57,58], controlling the optical bistability and multistability [61][62][63] have been reported very recently. However, to the best of our knowledge, no theoretical or experimental work has been reported for observing enhanced Kerr nonlinearity of monolayer graphene system which causes the present work.…”

Laser Induced Multiphoton Effects in Nano-Graphene Molecules

“…Distinct symmetries between graphene and graphite are observed in the anisotropy of SHG [14]. Recently, the nonlinearity is examined under a strong magnetic field up to 3 Tesla [18].…”

“…It is interesting to see the multiphoton processes in this system under a high intensity laser field. Some efforts have been made to explore the nonlinear effects in graphene [11][12][13][14][15][16][17][18]. With an electron-hole model, Mikhailov theoretically predicted the strongly nonlinear response to the external electric field in graphene [11].…”