Efficient Nonlinear Generation of THz Plasmons in Graphene and Topological Insulators

Abstract

Surface plasmons in graphene may provide an attractive alternative to noble-metal plasmons due to their tighter confinement, peculiar dispersion, and longer propagation distance. We present theoretical studies of the nonlinear difference frequency generation of terahertz surface plasmon modes supported by two-dimensional layers of massless Dirac electrons, which includes graphene and surface states in topological insulators. Our results demonstrate strong enhancement of the DFG efficiency near the plasmon resonance and the feasibility of phase-matched nonlinear generation of plasmons over a broad range of frequencies.PACS numbers: 81.05.ue, 42.65.-k Graphene exhibits many interesting electronic properties because of its chiral symmetry and gapless linear spectrum of free carriers near the Dirac point. In recent years, graphene has also been recognized as a promising broadband optoelectronic material in the infrared (IR) and terahertz (THz) region, especially when utilizing a surface plasmon resonance [1][2][3]. Surface plasmon is a collective mode of coupled charge-density and field oscillations at an interface between a free-carrier system and a dielectric or vacuum. Surface plasmons guided by graphene are expected to have low losses and be highly tunable by gating and doping, making graphene an attractive alternative to metal plasmonics. Surface states in certain topological insulators (TIs) have a massless Dirac-cone electron dispersion at low energies with a slope similar to that in graphene. They provide a potentially even more interesting host medium for surface plasmons due to lower scattering rates of two-dimensional (2D) surface electrons that are topologically protected from scattering on non-magnetic impurities [4]. In particular, Bi 2 Se 3 has a large bulk band gap of about 0.3 eV, suitable for THz and mid-infrared plasmonics, and a tunable Fermi level which can be put within the bulk gap [5]. The combination of highly efficient light-matter interaction, relatively long propagation distances, and tight confinement of surface plasmons in graphene and TIs promises interesting applications including compact room-temperature THz sources for imaging, spectroscopy and telecommunications; integrated photonic circuits; THz modulation of telecom signals, and compact THz sensors. Furthermore, optical methods [6] may provide a better access to characterization and manipulation of massless fermion states than transport measurements that are affected by conductivity in the bulk.Nonlinear optics of massless Dirac fermions has received little attention so far, especially in the THz range where many basic devices and components are lacking. Here we show that the difference frequency generation (DFG) in 2D layers of massless Dirac electrons, e.g. graphene and TIs, is an efficient and controllable way of generating surface plasmons over a broad range of frequencies. Second-order nonlinear processes such as DFG are usually assumed to be forbidden in an isotropic medium [14] such as the plane of a graphene layer. How...

Quantum Effects in the Nonlinear Response of Graphene Plasmons

“…Owing to its gapless, linear charge-carrier dispersion relation [3,4], graphene is capable of relatively strong, broadband coupling with light [5,6], and offers a large electrically-tunable optical response [7]. Valence and conduction electrons in this material present a uniform velocity that clearly emphasizes their anharmonic response to external fields, which has stimulated considerable interest in the graphene nonlinear optical properties [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Further motivation to study optical nonlinearities in monolayer graphene is provided by the availability of interband optical transitions within a continuous range of low photon energies, accompanied by a high electrical mobility [24,25].…”

A Simple Nanoscale Plasmonic Square-Shaped Ring Resonator Waveguide

“…Plasmonics is a rapidly growing research field [1][2][3], which covers several aspects of surface plasmons [4,5] towards realization of surface-plasmon-based devices [6][7][8][9][10]: plasmonic waveguides [11], plasmonic light-emitting devices [12], plasmonic solar cells [13] and plasma-wave THz photodetection [14,15]. Waveguide-based plasmonic structures utilizing surface plasmon polariton (SPP) are promising for their capability of high subwavelength scale confinement and low propagation loss [16,17], which could lead to a high-speed, miniaturized and integrated electrooptical technology.…”

Quantum theory of the third-order nonlinear electrodynamic effects of graphene

“…The nonlinear electrodynamic phenomena in graphene have been further studied in Refs. [22][23][24][25][26][27][28][29][30][31][32][33][34][35] (theory) and in Refs. [36][37][38][39][40][41][42][43][44][45][46][47] (experiment).…”