Dynamical centrosymmetry breaking — A novel mechanism for second harmonic generation in graphene

  • a School of Engineering and Physical Sciences, Heriot-Watt University, EH14 4AS Edinburgh, UK
  • b ICFO-Institut de Ciencies Fotoniques, 08860 Castelldefels (Barcelona), Spain

Abstract

We discover an unusual phenomenon that occurs when a graphene monolayer is illuminated by a short and intense pulse at normal incidence. Due to the pulse-induced oscillations of the Dirac cones, a dynamical breaking of the layer’s centrosymmetry takes place, leading to the generation of second harmonic waves. We prove that this result can only be found by using the full Dirac equation and show that the widely used semiconductor Bloch equations fail to reproduce this and some other important physics of graphene. Our results open new windows in the understanding of nonlinear light-matter interactions in a wide variety of new 2D materials with a gapped or ungapped Dirac-like dispersion.

Keywords

  • Nonlinear optics;
  • Frequency conversion;
  • Harmonic generation, including higher-order harmonic generation;
  • Dynamics of nonlinear optical systems;
  • Optical instabilities, optical chaos and complexity, and optical spatio-temporal dynamics;
  • Nonlinear waveguides

1. Introduction

The physics of graphene and related materials has attracted a broad interest since the initial experimental realisation of graphene monolayers  [1]. At relative low energies, graphene shows a unique Dirac-like band structure and this implies that quasielectrons behave as if they were massless Dirac fermions  [2]. Due to this special property, graphene electronics is quite different from conventional semiconductor electronics, and holds the promise of revolutionising the technological landscape in many different ways  [2]. Apart from its noteworthy electronic properties, graphene also shows extraordinary optical properties  [3] which have already been employed in photonics for ultrafast photodetectors  [4], optical modulation  [5], molecular sensing  [6], and several nonlinear applications  [7] and [8].

Graphene’s optical response is characterized by a highly-saturated absorption at rather modest light intensities  [9], a remarkable property which has already been exploited for mode-locking in ultrafast fiber-lasers  [10]. The high nonlinear response of graphene leads to the efficient generation of higher harmonics  [11] and [12]. Theoretical approaches to model the nonlinear dynamics of graphene typically rely on the Boltzmann transport equation, accounting only for intraband electron dynamics  [13], and on the popular semiconductor Bloch equations (SBEs), which account only for the interband dynamics adapted to the conical dispersion  [14].

In this paper we show the existence of a previously unknown nonlinear optical phenomenon that occurs when a graphene monolayer is illuminated by a short and intense pulse at normal incidence. Due to the pulse-induced oscillations of the Dirac cone, a dynamical breaking of the layer’s centrosymmetry takes place, leading to the generation of second harmonics. The importance of this novel nonlinear effect is that it can only be found by using the full Dirac equation, while the SBEs completely fail to describe it, and we explain the deep motivations behind this failure in the latter equations.

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