Anisotropic ultrafast optical response of terahertz pumped graphene

Abstract

We have measured the ultrafast anisotropic optical response of highly doped graphene to an intense single cycle terahertz pulse. The time profile of the terahertz-induced anisotropy signal at 800 nm has minima and maxima repeating those of the pump terahertz electric field modulus. It grows with increasing carrier density and demonstrates a specific nonlinear dependence on the electric field strength. To describe the signal, we have developed a theoretical model that is based on the energy and momentum balance equations and takes into account optical phonons of graphene and substrate. According to the theory, the anisotropic response is caused by the displacement of the electronic momentum distribution from zero momentum induced by the pump electric field in combination with polarization dependence of the matrix elements of interband optical transitions.Due to the peculiar electronic band structure of graphene 1,2 the field-induced motion of electrons was predicted to be strongly nonlinear in this material 3 . High nonlinearity together with the unique electronic and optical properties make graphene a prospective material for photonic and optoelectronic applications. In the light of this perspective, nonlinear optical phenomena in graphene are actively studied 4-6 . Among them are harmonic generation 7-16 , saturable absorption 17-19 , self-phase modulation 20 , and fourwave mixing 21,22 . In the optical range the frequency of light is higher than the electron-electron scattering rate, so the resulting "coherent" electronic response is determined by the properties of single-electron band structure 12-14 . In the THz range another limiting case is realized -the characteristic time of electron-electron scattering processes is shorter than the period of the light wave. The energy imparted by the electric field to electrons is quickly redistributed heating the electron gas, while the electron-phonon collisions cool and decelerate the gas. The concept of "incoherent" nonlinearity that appears due to the change of electron gas conductivity upon heating 23,24 was employed recently to explain highly effective generation of THz harmonics in graphene 16 .The routine technique used to evaluate the optical nonlinearity of graphene is the spectral analysis of light transmitted through the sample in search of harmonics of the pump frequency radiated by the nonlinear current. In the present work we employ an alternative approach by using an optical probe to detect the transient THz field-induced shift of electron momentum distribution (note that such shift can induce the optical 2-nd harmonic generation, as was recently observed 25 ). In graphene, due to the specific polarization dependence of matrix elements of interband transitions in combination with Pauli blocking, an anisotropy of electronic distribution implies an anisotropy of infrared optical conductivity, which can be measured by detecting depolarization of probe light reflected from the sample. We measure the ultrafast anisotropic optical response of graphene to inten...

Terahertz Nonlinear Optics of Graphene: From Saturable Absorption to High‐Harmonics Generation

“…This anisotropy was revealed in pump–probe FEL experiments by examining the polarization relation between the pump and probe beams, as shown in Figure d,e. It is also observable for a broad range of IR excitation photon energies and even at THz frequencies, for as long as a sufficient pump fluence is available, for both inter‐ or intraband excitations. This anisotropy vanishes via carrier relaxation by phonon emission within sub‐picoseconds or on a longer timescale, depending on the energy of the excited state relative to the optical phonon energies in graphene .…”

Plasmonic Terahertz Nonlinearity in Graphene Disks

“…A second polarizer behind the sample is used to pick the co‐ or crosspolarized component. As the linear polarization can induce an anisotropic carrier distribution in momentum space, potentially leading to a polarization dependence of the pump‐probe signal, [ 35 ] we perform additional measurements using circularly polarized light by introducing quarter‐wave plates in the pump and probe beams. In this case, anisotropic heat distribution is excluded.…”

Multifield Controlled Terahertz Modulator Based on Silicon‐Vanadium Dioxide Hybrid Metasurface

“…The optical characterization of the THz modulator was performed by the OPTP method, [44,69,70] and a schematic of the experiment is displayed in Figure 4a. Considering the energy bandgap of Si (1.1 eV), an 800 nm femtosecond optical pump with 1.55 eV photon energy was employed to generate photoinduced carriers.…”