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Amplified Stimulated Terahertz Emission from Optically Pumped
Graphene
T. Otsuji1, 4 , S. A. Boubanga Tombet1, 4 , S. Chan2 , T. Watanabe1 ,
A. Satou1, 4 , and V. Ryzhii3, 4
1
Research Institute of Electrical Communication, Tohoku University, Japan
2
Nano-Japan Program, University of Pennsylvania, USA
3
Computational Nano-Electronics Laboratory, University of Aizu, Japan
4
JST-CREST, Japan
Abstract— The gapless and linear energy spectra of electrons and holes in graphene lead
to nontrivial features such as negative dynamic conductivity in the terahertz spectral range.
This paper reviews the recent advances in theoretical and experimental study on terahertz light
amplification by stimulated emission of radiation in optically pumped graphene.
1. INTRODUCTION
Graphene, a monolayer sheet of carbon atomic honeycomb lattice crystal, has attracted attention
owing to the massless Dirac Fermions of electrons/holes [1, 2]. The gapless and linear energy spectra
of electrons/holes lead to nontrivial features such as negative dynamic conductivity in the terahertz
(THz) spectral range under optical pumping [3], which may lead to the development of a new type
of THz lasers [4]. In this paper, we’ll review the theory and experimental results of THz amplified
stimulated emission from optically pumped graphene.
2. THEORITICAL MODEL
When graphene is pumped with the infrared (IR) photon having an energy ~Ω, electrons/holes
are photogenerated via interband transitions. When the photogenerated electrons and holes are
heated in case of room temperature environment and/or strong pumping, collective excitations due
to the carrier-carrier (CC) scattering, e.g., intraband plasmons should have a dominant play to
perform an ultrafast carrier redistribution along the energy as shown in Fig. 1 [5, 6]. Then optical
phonons (OPs) are emitted by carriers on the high-energy tail of the electron and hole distributions.
This energy relaxation process accumulates the nonequilibrium carriers around the Dirac points
as shown in Fig. 1. Due to a fast intraband relaxation (ps or less) and relatively slow interband
recombination (À 1 ps) of photoelectrons/holes, one can obtain the population inversion under a
sufficiently high pumping intensity. Due to the gapless symmetrical band structure of graphene,
photon emissions over a wide THz frequency range are expected if the pumping IR photon energy
is properly chosen.
We consider an intrinsic graphene under the optical pulse excitation in the case where the CC
scattering is dominant and carriers always take quasi-equilibrium. We take into account both the
Figure 1: Carrier relaxation/recombination dynamics in
optically pumped graphene.
Figure 2: Temporal evolution of the quasiFermi energy after impulsive pumping.
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intra and interband OPs [7, 8]. The carrier distribution (equivalent electron and hole distributions)
is governed by the following equations for the total energy and concentration of carriers:
Z
h
i
dΣ
1 X
(+)
(−)
= 2
dk (1 − fhωi −vw ~k )(1 − fvw ~k )/τiO,inter − fvw ~k fhωi −vw ~k /τiO,inter ,
dt
π
i=Γ,K
Z
h
i
dE
1 X
(+)
(−)
= 2
dkvw ~k (1 − fhωi −vw ~k )(1 − fvw ~k )/τiO,inter − fvw ~k fhωi −vw ~k /τiO,inter
dt
π
i=Γ,K
Z
h
i
1 X
(+)
(−)
+ 2
dkhωi fvw ~k (1 − fvw ~k + hωi )/τiO,intra − fvw ~k (1 − fvw ~k − hωi )/τiO,intra
π
i=Γ,K
where Σ and E are the carrier concentration and energy density, fε is the quasi-Fermi distribution,
(±)
(±)
τiO,inter and τiO,intra are the inverses of the scattering rates for inter and intraband OPs (i = Γ
for OPs near the Γ point with ωΓ = 196 meV, i = K for OPs near the zone boundary with
ωΓ = 161 meV, + for absorption, and − for emission). Time-dependent quasi-Fermi energy εF and
the carrier temperature Tc are determined by these equations. Fig. 2 shows the typical results for fs
pulsed laser pumping with photon energy 0.8 eV [9]. It is clearly seen that εF rapidly increases with
cooling the carrier and it becomes positive when the pumping intensity exceeds a certain threshold
level. This result proves the occurrence of the population inversion. After that, the recombination
process follows more slowly (∼ 10 ps).
3. EXPERIMENTAL RESULTS AND DISCUSSION
We observed the carrier relaxation and recombination dynamics in optically pumped graphene using
THz time-domain spectroscopy based on an optical pump/THz-and-optical-probe technique [10].
An exfoliated monolayer-graphene/SiO2 /Si sample is placed on the stage and a 0.12-mm-thick
(100)-oriented CdTe crystal is placed on the sample, acting as a THz probe pulse emitter as well as
an electrooptic sensor. A single 80-fs, 1550-nm fiber laser beam having 4-mW average power and
20-MHz repetition is split into two: one for optical pumping and generating the THz probe beam
in the CdTe crystal, and one for optical probing. The pumping laser, which is linearly polarized,
is simultaneously focused at normal incidence from the back surface on the graphene sample to
induce population inversion and the CdTe to induce optical rectification and emission of THz pulse
1 in Fig. 3). This THz beam reflecting back in part at the
(the primary pulse marked with “°”
CdTe top surface stimulates the THz emission in graphene, which is electrooptically detected as a
2 in Fig. 3).
THz photon echo signal (the secondary pulse marked with “°”
Figure 4 shows a typical temporal response under the maximal pumping intensity. The black/red
curve is the response when the pumping beam is focused onto the sample with/without graphene.
The second pulse, the THz photon echo signal, obtained with graphene is more intense compared
with that obtained without graphene. This indicates the graphene act as an amplifying medium.
(a)
(b)
Figure 3: (a) Experimental setup and (b) the scheme of coherent emission from graphene by an opticalpump/THz-probe technique. Time-resolved electric field intensity is electroopticaly sampled by the probe
beam throughout the CdTe sensor crystal in total reflection geometry. The CdTe also works as a THz probe
beam source.
PIERS ONLINE, VOL. 7, NO. 4, 2011
Figure 4: Measured temporal profile. The secondary
pulse is the THz photon echo transmitted and reflected through graphene.
310
Figure 5: Normalized Fourier spectra and gain profile.
Fig. 5 shows the emission spectra from graphene after normalization to the one without graphene.
The inset in Fig. 5 shows the measured gain as a function of the pumping power. A threshold
like behavior can be seen testifying the occurrence of the negative conductivity and the THz light
amplification by stimulated emission of radiation.
4. CONCLUSIONS
We have successfully observed coherent amplified stimulated THz emissions arising from the carrier
relaxation/recombination dynamics of an exfoliated graphene. The results provide evidence of the
occurrence of negative dynamic conductivity, which can potentially be applied to a new type of
THz lasers.
ACKNOWLEDGMENT
This work is financially supported in part by JST-CREST, Japan, and JSPS-BR(S), Japan.
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