High-harmonic generation in
graphene enhanced by elliptically
polarized light excitation
Naotaka Yoshikawa,1,2 Tomohiro Tamaya,1† Koichiro Tanaka1,2*
The electronic properties of graphene can give rise to a range of nonlinear optical
responses. One of the most desirable nonlinear optical processes is high-harmonic
generation (HHG) originating from coherent electron motion induced by an intense light
field. Here, we report on the observation of up to ninth-order harmonics in graphene
excited by mid-infrared laser pulses at room temperature. The HHG in graphene is enhanced
by an elliptically polarized laser excitation, and the resultant harmonic radiation has a
particular polarization. The observed ellipticity dependence is reproduced by a fully
quantum mechanical treatment of HHG in solids. The zero-gap nature causes the unique
properties of HHG in graphene, and our findings open up the possibility of investigating
strong-field and ultrafast dynamics and nonlinear behavior of massless Dirac fermions.
High-harmonic generation (HHG) has been intensely investigated in atomic gases for its application to the generation of coher- ent attosecond radiation in the extreme ultraviolet and soft x-ray regions (1, 2).
HHG has been reported in various crystalline
solids (3–11) and described as a probing method
of the electronic properties of solids. The mechanism of HHG in solids is fundamentally different from that in atomic gases because of the
higher density of the atoms and their periodic
structure. In particular, recent reports have revealed that HHG is sensitive to the orientation of
the electric field relative to the crystal axis (9–11).
HHG has been demonstrated as a good tool for
exploring the nature of the electron systems in
crystals in terms of the symmetry of the electronic band structure (9), interatomic bonding
(10), and the material’s Berry curvature (11).
Although this property of HHG clearly reflects
the diversity of solids, the diversity it affords may
obscure the universal nature of HHG in solids.
Several theoretical models have been proposed
for solid-state HHG (3–14), such as interband
polarization combined with dynamical Bloch
oscillations (4, 7, 9), intraband electron dynamics
(10, 11), and time-dependent diabatic process
(12); however, a unified predictive theory that
captures the essential feature of HHG in solids
In bulk crystals, the essential feature of solid-state HHG may be swept out due to the propagation effects, such as phase matching conditions.
It is therefore important to gain an understand-
ing of HHG in simple, two-dimensional material.
Graphene is a monolayer of carbon atoms packed
in a two-dimensional honeycomb lattice, and it
exhibits a unique band structure with a zero energy gap and linear energy dispersion, the Dirac
cone (15, 16). The important characteristic here is
that the band structure of graphene relevant to
HHG is isotropic even in the visible region. An
HHG experiment in graphene should capture the
universal properties of HHG in solids independently of the crystal angle and provide a standard
test case for checking the validity of proposed
The band structure of graphene gives rise to
several remarkable properties, including universal conductivity (17–19). Linear energy dispersion
also gives a fixed group velocity that is only dependent on the direction of the k vector, leading
to a strongly nonlinear electromagnetic response.
Although the semiclassical model (20) and quan-
tum mechanical theory (21) each predict HHG,
there has been no report of observation of HHG
(23). The low efficiency should come from the ex-
traordinarily fast relaxation of electrons (24–28)
that prohibits coherent optical processes in the
THz frequency region. Because of this problem,
attention has shifted to devising an HHG exper-
iment with mid-infrared light.
A typical high-harmonic (HH) spectrum is
shown (Fig. 1B) of monolayer graphene excited
by linearly polarized mid-infrared (0.26 eV) pulses
(Fig. 1A) (29). The peak power of the pump pulse
was 1.7 TW/cm2, which corresponds to an electric
field 30 MV/cm inside the graphene, taking into
account the reflectivity of the substrate. All experiments were performed at room temperature.
Odd-order harmonics can be seen up to ninth order. We subtracted the background broad luminescence from impurities or defects insensitive to
the photon energy and polarization of the excitation light (fig. S4) (29). The intensity of fifth-harmonic
radiation as a function of the peak power of the
excitation pulse Iexc (red circles, Fig. 1C) shows a
saturation-like behavior, whereas it should show
an I5 dependence (dashed red line) in the perturbative limit. It scales as I2 exc (gray line) at the
highest pump intensity in this study. The power
dependence clearly shows the nonperturbative
nature of the HHG process in graphene (4, 11).
Figure 2 shows HH spectra for various polarizations of the pump laser as characterized by
ellipticity, defined as e = Ey/Ex . The peak power of
the laser was 0.8 TW/cm2. The orientation of the
variable retarder was fixed, and we controlled the
laser ellipticity by changing the retardance in order
to keep the major axis of the elliptical polarization
fixed. All harmonics vanish when the graphene
is pumped by circular polarized light (e = 1).
However, with the elliptically polarized pump
(e = 0.32), the seventh and ninth harmonics are
enhanced compared with those having a linearly
polarized pump (e = 0). This is notably different
from gas-phase HHG, where the yield of HHG
736 19 MAY 2017 • VOL 356 ISSUE 6339 sciencemag.org SCIENCE
1Department of Physics, Graduate School of Science, Kyoto
University, Sakyo-ku, Kyoto 606-8502, Japan. 2Institute for
Integrated Cell-Material Sciences (WPI-iCeMS), Kyoto
University, Sakyo-ku, Kyoto 606-8501, Japan.
*Corresponding author. Email: firstname.lastname@example.org
(N. Y.); email@example.com (K. T.)
†Present address: Nanoelectronics Research Institute (NeRI),
National Institute of Advanced Industrial Science and Technology
(AIST), Tsukuba, Ibaraki 305-8568, Japan.
Fig. 1. HHG from graphene. (A) The spectrum of the excitation pulse. The full width at half maximum is
~60 meV. (B) HH radiation spectrum of graphene (red curve) and spectrum of excitation pulse (blue
dotted curve). (C) Pump power dependence of intensity of fifth-harmonic radiation.