Spectroscopic Study on Ultrafast Carrier Dynamics and Terahertz Amplified Stimulated Emission in...

Spectroscopic Study on Ultrafast Carrier Dynamicsand Terahertz Amplified Stimulated Emission in OpticallyPumped Graphene

Taiichi Otsuji & Stephane Boubanga-Tombet &Akira Satou & Maki Suemitsu & Victor Ryzhii

Received: 7 February 2012 /Accepted: 1 May 2012 /Published online: 3 June 2012# Springer Science+Business Media, LLC 2012

Abstract This paper reviews recent advances in spectroscopic study on ultrafast carrierdynamics and terahertz (THz) stimulated emission in optically pumped graphene. Thegapless and linear energy spectra of electrons and holes in graphene can lead to nontrivialfeatures such as negative dynamic conductivity in the THz spectral range, which may lead tothe development of new types of THz lasers. First, the non-equilibrium carrier relaxation/recombination dynamics is formulated to show how photoexcited carriers equilibrate theirenergy and temperature via carrier-carrier and carrier-phonon scatterings and in what photonenergies and in what time duration the dynamic conductivity can take negative values asfunctions of temperature, pumping photon energy/intensity, and carrier relaxation rates.Second, we conduct time-domain spectroscopic studies using an optical pump and aterahertz probe with an optical probe technique at room temperature and show that graphenesheets amplify an incoming terahertz field. Two different types of samples are prepared forthe measurement; one is an exfoliated monolayer graphene on SiO2/Si substrate and theother is a heteroepitaxially grown non-Bernal stacked multilayer graphene on a 3C-SiC/Siepi-wafer.

Keywords Graphene . Terahertz . Stimulated emission . Population inversion . Ultrafastcarrier dynamics

J Infrared Milli Terahz Waves (2012) 33:825–838DOI 10.1007/s10762-012-9908-8

T. Otsuji (*) : S. Boubanga-Tombet : A. Satou :M. SuemitsuResearch Institute of Electrical Communication, Tohoku University,2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japane-mail: [email protected]

V. RyzhiiComputational Nano-electronics Laboratory, University of Aizu, Tsuruga,Ikki-machi, Aizu-Wakamatsu 965-8580, Japan

T. Otsuji :A. Satou : V. RyzhiiJST-CREST, Chiyoda-ku, Tokyo 1020075, Japan

1 Introduction

Graphene is a one-atom-thick planar sheet of carbon atoms that are densely packed in ahoneycomb crystal lattice [1–4]. Since the discovery of the monolayer graphene byNovoselov et al. [1] in 2004 graphene has made a great impact in academic andindustry. This material has many peculiar properties and potential applications, includingthe half-integer quantum Hall effect [2], finite conductivity at zero-charge carrierconcentration [3], perfect quantum tunneling effect [4], and ultrahigh carrier mobility[5] owing to massless and gapless energy spectra. The gapless and linear energy spectraof electrons and holes lead to nontrivial features such as negative dynamic conductivityin the terahertz spectral range [6–8], which may lead to the development of new typesof terahertz lasers [8–11]. This has attracted intense interest due to the ongoing searchfor viable terahertz light sources.

To realize such terahertz graphene-based devices, understanding the nonequilibriumcarrier relaxation and recombination dynamics is crucial. Intraband and interband carrierscatterings in graphene via optical phonon modes have been extensively studied [12–15].Recently the effect of carrier-carrier scattering on carrier equilibration dynamics as well aselectron–hole generation and recombination dynamics due to interband optical phononscattering in optically excited graphene have been theoretically studied [15–17]. Thesetheoretical studies gave us an general idea of the carrier relaxation and recombinationdynamics; photoexcited carriers in graphene are firstly quasi-equilibrated via carrier-carrierscattering on ultrafast time scales of 20 to 200 fs and then cooled and thermalized mainly byintraband relaxation processes via optical phonon emission on subpicosecond to picosecondtime scales, and then by interband recombination processes via interband optical phononemission. Recently such ultrafast carrier relaxation via emissions of optical phonons hasobserved by several groups [18–24] and revealed the energy relaxation dynamics of photo-excited carriers. In particular, Breusing et al. [23] revealed that photoelectrons and photo-holes in optically pumped exfoliated graphene and graphite loose a major fraction of theirenergy within 200~300 fs, mainly by emission of optical phonons. At an earliest stage wetheoretically discovered the possibility of negative dynamic conductivity in a wide terahertzfrequency range in optically and/or electrically pumped graphene [6, 7]. Recently, wesucceeded in observation of stimulated terahertz emission from graphene under femtosecondinfrared laser pumping by using a terahertz photon echo method [25, 26].

In this paper recent advances in spectroscopic study on ultrafast carrier dynamics andterahertz stimulated emission in optically pumped graphene are reviewed. First, the non-equilibrium carrier relaxation/recombination dynamics are formulated to show how photo-excited carriers equilibrate their energy and temperature via carrier-carrier and carrier-phonon scatterings and in what photon energies and in what time duration the dynamicconductivity can take negative values as functions of temperature, pumping photon energy/intensity, and carrier relaxation rates. Second, we conduct time-domain spectroscopic studiesusing an optical pump and a terahertz probe with an optical probe technique at roomtemperature and show that graphene sheets amply an incoming terahertz field. Two differenttypes of samples are prepared for the measurement; one is an exfoliated monolayer grapheneon SiO2/Si substrate and the other is a heteroepitaxially grown non-Bernal stacked multi-layer graphene on a 3C-SiC/Si epi-wafer. The graphene sample is first pumped by afemtosecond infrared pulsed laser. Then a terahertz probe pulse being synchronized withthe pump pulse is impinged to the sample after a few picoseconds from the pumping. Itstransmitted and reflected signal is electrooptically detected as a terahertz photon echo signal.The measured temporal response is Fourier transformed to characterize the gain spectral

826 J Infrared Milli Terahz Waves (2012) 33:825–838

profiles of the graphene samples as functions of the pumping intensity and the probe delaytiming.

2 Carrier relaxation and recombination dynamics in optically pumped graphene

Figure 1 presents the carrier relaxation/recombination processes and the non-equilibriumenergy distributions of photoelectrons/photoholes in optically pumped graphene at specifictime scales from ~10 fs to picoseconds after pumping. When the photogenerated electronsand 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 plasmonsshould have a dominant play to perform an ultrafast carrier quasi-equilibration along theenergy as shown in Fig. 1. Then optical phonons (OPs) are emitted by carriers on the high-energy tail of the electron and hole distributions. This energy relaxation process accumulatesthe nonequilibrium carriers around the Dirac points as shown in Fig. 1. Due to a fastintraband relaxation (ps or less) and relatively slow interband recombination (>>1 ps) ofphotoelectrons/holes, one can obtain the population inversion under a sufficiently highpumping intensity [6, 7, 16]. Due to the gapless symmetric band structure of graphene,photon emissions over a wide terahertz frequency range are expected if the pumping infraredphoton energy is properly chosen.

We consider an intrinsic graphene under optical pulse excitation in the case where the CCscattering is dominant and carriers always take a quasi-equilibrium distribution [16]. We takeinto account both the intra and interband OPs. The carrier distribution (equivalent electronand hole distributions) is governed by the following equations for the total energy andconcentration of carriers:

dΣdt ¼ 1

p2P

i¼Γ ;K

Rdk ð1� fhwi�nwhkÞð1� fnwhkÞ=tðþÞ

iO;inter � fnwhk fhwi�nwhk=tð�ÞiO;inter

h i;

dEdt ¼ 1

p2P

i¼Γ ;K

Rdknwℏk ð1� fhwi�nwℏkÞð1� fnwℏkÞ=tðþÞ

iO;inter � fnwℏk fhwi�nwℏk=tð�ÞiO;inter

h i

þ 1p2

P

i¼Γ ;K

Rdkhwi fnwℏkð1� fnwℏkþhwiÞ=tðþÞ

iO;intra � fnwℏkð1� fnwℏk�hwiÞ=tð�ÞiO;intra

h i;

9>>>>>>=

>>>>>>;

ð1Þwhere Σ and E are the carrier concentration and energy density, fɛ is the quasi-Fermi

distribution at energy ɛ, tð�ÞiO;inter and tð�Þ

iO;intra are the inverses of the scattering rates for inter

and intraband OPs (i0Γ for OPs near the zone center Γ point with wΓ 0 198 meV, i0K forOPs near the zone boundary with ωK 0 161 meV, + for absorption, and – for emission). Thevalues for wΓ and ωK are typical theoretical values in the literatures [12–17]. Time evolution

Fig. 1 Carrier relaxation dynamics in optically pumped graphene.

J Infrared Milli Terahz Waves (2012) 33:825–838 827

of quasi-Fermi energy ɛF and the carrier temperature Tc are determined by these equations.Figures 2(a) and (b) show the typical calculated results for time-dependent ɛF and Tcrespectively after femtosecond-pulsed laser pumping with photon energy 0.8 eV [16]. It isclearly seen that (i) instantly after the pumping (t~0 ps) ɛF instantly falls down in negativedue to CC scattering, and then (ii) ɛF is rapidly elevated by carrier cooling due to emission ofOPs in carriers at high-energy tails, and in particular, (iii) ɛF becomes positive, i.e. thepopulation becomes inverted, when the pumping intensity exceeds a certain threshold level.This result proves the occurrence of the population inversion. After that, the recombinationprocess follows more slowly (~10 ps).

It is noted that the population inversion is a prerequisite for but does not mean the gain,because we have the Drude absorption by carriers in graphene. A quantity that determinesthe gain at frequency ω is the real part of the net dynamic conductivity Re σω; negativevalues of Re σω implies the gain. The real part of the net ac conductivity Re σω isproportional to the absorption of photons with frequency ω and comprises the contributionsof both interband and intraband contributions [6]:

Reσw ¼ Reσinterw þ Reσintraw

� e2

4ℏð1� 2fhwÞ þ ðln 2þ "F=2kBTÞe2

pℏTt

ℏð1þ w2t2Þ ;ð2Þ

where e is the elementary charge, ℏ is the reduced Planck constant, kB is the Boltzmann constant,and τ is the momentum relaxation time of carrier. The intraband contribution (the second term inEq. 2) corresponds to the Drude absorption and depends on ωτ. Typical simulated results forRe σω are shown in Fig. 3(a) and (b) as functions of time and frequency at a fixed pump intensity1×108W/cm2with different momentum relaxation times τ 01,10ps. It is clearly seen that the gainspectral bandwidth widen with longer τ value; when τ 010ps, a broad terahertz gain bandwidthfrom ~1.5 to ~10 THz is expected in picoseconds time scale after pumping [27].

Fig. 2 Simulated time evolution of (a) the quasi-Fermi level and (b) carrier temperature after impulsiveinfrared pumping for different pumping intensities.

Fig. 3 Simulated time-dependent terahertz dynamic conductivity when the pumping photon energy is800 meV and its intensity is 108 W/cm2. (a) Momentum relaxation timeτ01ps, (b) τ010ps.


3 Experiments

3.1 Experimental setup

In order to verify the above mentioned scenario to obtaining the terahertz gain we conducttime-domain spectroscopic experiments based on an optical pump/terahertz-and-optical-probe technique [25, 26]. Figure 4 shows the experimental setup and the pump/probegeometry. The time-resolved field emission properties are measured by an electroopticsampling (EOS) method in total-reflection geometry. The pumping photon energy (wave-length) is selected to be around 800 meV (1550 nm), much higher than the optical phononenergy (∼198 meV). A 2-mm-long, 0.5-mm-wide CdTe crystal with a Si prism is used forreflective electrooptic probing and placed directly onto the sample. The CdTe crystal acts asan electrooptic sensor as well as a terahertz probe pulse generator. A femtosecond-pulsedfiber laser with a full width at half-maximum (FWHM) of 80 fs, repetition rate of 20 MHzwas used as the optical pump and probe source. The maximal available average power andfluence are about 4 mW and 0.2 nJ/pulse, respectively. The laser is split into two paths usedfor pump and probe. The pumping laser beam, being linearly polarized, is mechanicallychopped at∼1.2 kHz (for lock-in detection) and focused with a beam diameter of about40 μm onto the sample and the CdTe from the back side, while the probing beam is cross-polarized with respect to the pump beam and focused from the top side. The CdTe, anonlinear optical crystal, can rectify the pump laser pulse to emit terahertz enveloperadiation. The magnitude of the emitted terahertz envelope pulse grows along the Cherenkovangle, preserving the phase-matching condition between the infrared and the terahertzradiations [28]. Its forward-propagating pulse is first electrooptically detected by the opticalprobe beam. The terahertz pulse is partially reflected at the top surface of the CdTe, thensubjects back to the graphene, serving as a terahertz probe pulse [arrowed blue line in Fig. 4]to stimulate terahertz photon emission. The terahertz probe pulse including stimulatedemission reflects in most part at the interface between the SiO2 (or SiC) layer and the Sisubstrate and travels back to the Si prism, which is detected as a terahertz photon echosignal, as shown in Fig. 4. Therefore, the original data of the experimental temporal responseconsists of the first forward-propagating terahertz pulsation (no interaction with graphene)followed by a photon echo signal (probing the graphene). The delay between these twopulsations is given by the total round-trip propagation time of the terahertz probe pulse

Fig. 4 Experimental setup (left) and the pump/probe geometry.


through the CdTe. The system bandwidth is estimated to be around 6 THz, mainly limited bythe Reststrahlen band of the CdTe sensor crystal.

3.2 Samples and characterizations

A. Exfoliated graphene on SiO2/Si

The first sample used is an exfoliated monolayer graphene on SiO2/Si substrate. Thesample consists of (i) a 560-μm-thick highly doped Si (100) substrate having a resistivity of0.005 Ω-cm, used as the back gate, (ii) a thermally oxidized 300-nm-thick SiO2 layer on topsurface of the Si substrate, and (iii) some islets of exfoliated monolayer, bilayer, and few-layers-thick graphene that are transferred onto the SiO2 layer. The flake size of the mono-layer graphene under measurement is about 7000 μm2. The defect-free quality of themonolayer graphene flake was confirmed by Raman spectroscopy as shown in Fig. 5.Almost no peak is seen at D band whereas G peak stays at 1576 cm-1 with a sharp linewidth9.8 cm-1, resulting in a high G-peak-to-D-peak intensity ratio, IG/ID, greater than 35. As isexperimentally examined in Ref. [18], the graphene crystal quality characterized by IG/IDstrongly correlates to the carrier momentum relaxation time τ. The obtained IG/ID value(> 35) suggests that the assumption on the τ value of 10 ps in Section 2 is feasible even atroom temperature. To see the G’ (2D) band it stays at 2670 cm-1 with mono but asymmetricpeak and with a line width 18.6 cm-1. Compared to the results for free-standing suspendedmonolayer graphene in Ref. [29], no degradation is seen in its crystal quality. Also very lessdoping effect is confirmed from the G’ peak position with no blue-shifting from the idealposition.

In order to characterize the electrical quality of our sample, we conduct back-gatecurrent–voltage transfer characterization, as well as atomic and Kelvin force microscopyto the surface of the SiO2/Si substrate and that of graphene on SiO2/Si substrate.Atomic Force Microscopy (AFM) proved a flat surface morphology of the monolayergraphene flake with a variances σ of 0.142 nm. Figure 6 shows the measured transfercharacteristics with a Dirac voltage close to 0 V, showing that the level of intrinsicdoping is very low in this sample. The Kelvin Force Microscopy (KFM) measurementshows a very smooth surface potential distribution on 10×10 μm2 area with a variance

Fig. 5 Raman spectrum of the monolayer exfoliated graphene on SiO2/Si substrate, showing G and G’ (2D)peaks and excellent G-peak-to-D-peak ratio greater than 35.


of 4.05 meV as shown in Fig. 7. We therefore carefully selected this high-qualitysample, which has less substrate effect [30], for the experiments.

B. Heteroepitaxial graphene on 3C-SiC/Si

The second sample used in this experiment is a heteroepitaxial graphene film grown on a3C-SiC(110) thin film heteroepitaxially grown on a 300-μm thick Si(110) substrate viathermal graphitization of the SiC surface [31, 32]. In the Raman spectrum of the graphenefilm, the principal bands of graphene, the G (1595 cm-1) and G’ (2730 cm-1) bands, areobserved, as shown in Fig. 8. Furthermore, transmission electron microscopy imagesindicate that the film is stratified. It is thus concluded that epitaxial graphene with a planarstructure can be produced by this fabrication method. Furthermore, the epitaxial graphenelayer is inferred to have a non-Bernal stacking arrangement because the G’ band in theRaman spectrum can be expressed as a single component related to the two-dimensionalityof the graphene film [32]. The non-Bernal stacked epitaxial graphene layers grown by ourmethod can be treated as a set of isolated single graphene layers, as in the case of an epitaxialgraphene layer on a C-terminated SiC bulk crystal [33]. The G-band peak at 1595 cm-1

corresponds to an optical phonon energy at the zone center of 197.8 meV.

3.3 Results and discussions

A. Exfoliated graphene on SiO2/Si

The experiments were done with two CdTe sensor crystals (A and B), having orientations(100) and (101) and thicknesses of 120 and 80 μm, respectively. Figure 9 shows temporalresponses measured on monolayer graphene with the thinner (black line) and the thicker (redline) CdTe crystals for the pumping pulse intensity of 3×107 W/cm (almost one order ofmagnitude below the level of Pauli blocking). These curves are plotted with the same originfor comparison. One can notice that, as predicted, each temporal profile is composed of twopeaks from optical rectification (OR) in CdTe and the terahertz photon echo signal. Themeasured time delays between these two pulsations with crystal A (thinner) and crystal B(thicker) of around 2 and 3.5 ps respectively are in good agreements with the round-trippropagation times of the terahertz pulse through the CdTe crystals. The refractive index of

Fig. 6 Measured ambipolar characteristics of the monolayer graphene flake sample on SiO2/Si substrate.


CdTe is obtained from Ref. [34]. The OR pulse is found to be narrower in crystal A than incrystal B, owing to better phase-matching conditions in the thinner crystal. Indeed, thecoherent length in CdTe is estimated to be around 100 μm at a photon energy 0.8 eV [35].The inset of Fig. 9 presents the echo signal peak intensity measured with crystal B on

Fig. 8 Raman spectra of heteroepitaxial graphene on 3 C-SiC/Si(110) with the D (1365 cm-1), G (1595 cm-1)and G’ (2730 cm-1) peaks. (after Ref. [25].) The right panel is a transferred electron microscopic image of thecross section of the part of multilayer graphene on 3 C-SiC.

Fig. 7 KFM topographic images and the corresponding histograms of (a) monolayer exfoliated graphene onSiO2/Si substrate and (b) SiO2/Si substrate. The data shown in panels (a) and (b) are described by Gaussiandistributions (black solid lines) with variances of 4.05 meV and 4.84 mV respectively. (after Ref. [26].)


graphene as well as the reference curve (grey line) measured on the area without graphene. Itis clearly seen that the peak obtained on graphene is more intense than that one obtained onthe substrate without graphene. This suggests that graphene amplifies the terahertz echo(terahertz probe) signal. The possible origins of the observed amplification could be (i) theterahertz pulse that stimulates the emission from graphene by electron–hole radiativerecombination whose energy falls in the range of the negative dynamic conductivity or (ii)the increase in reflectivity under pumping due to the increase in photocarrier-dependentDrude conductivity.

The graphene transfer function H(ω) is defined as H(ω)0G(ω)/S(ω), where G(ω) and S(ω) are the Fourier transforms of the photon echo signals measured on graphene andsubstrate (without graphene) respectively. Figure 10(a) shows the transfer function ofmonolayer graphene for different values of pumping pulse intensity Ipump. One can see fromthese results that decreasing Ipump drastically reduces the gain spectra, and below 107 W/cmthe gain disappears and only attenuation can be seen. The phase data [Fig. 10(b)] show clearLorentzian-like normal dispersion around the gain peak when the pumping pulse intensity isbeyond the threshold, demonstrating amplification originated from stimulated emission ofphotocarriers in the inverted states. Comparing the phase data for the pumping intensitiesbeyond the threshold, with an increase in the pumping intensity, the gain peak frequency(given by the zero point of the phase data) shows a blue shift and the upper cutoff frequencyincreases, whereas the lower cutoff frequency barely changes. These tendencies well reflectthe dependence of the gain spectral profile on pumping intensity as shown in Fig. 3 [6, 36].We also present in the inset of Fig. 10(a) (lower panel) the corresponding ratio AG/AS,where AG and AS are the amplitudes of echo signal peaks measured on graphene andsubstrate (without graphene) respectively. The graphene transfer function and AG/AS showa clear threshold-like behavior, demonstrating population inversion and negative dynamicconductivity in optically pumped graphene. The threshold intensity is found to be around107 W/cm2. The inset of Fig. 10(a) (upper panel) presents the normalized EOS signalamplitude of the first peak (see Fig. 9) for different values of the pumping pulse intensities.This EOS signal is proportional to the terahertz electric field generated by OR in CdTecrystal. The terahertz emitted intensity is quadratically dependent of the infrared intensity

Fig. 9 Measured temporal responses for monolayer exfoliated graphene on SiO2/Si with thick (redline) andthin (black line) CdTe crystals for the pumping pulse intensity of about 3×10 7W/cm2. Inset: Temporalresponses of photon echo signals measured on graphene (red line) and the area without graphene (grey line)for the measurement with thick CdTe crystal. (after Ref. [26].)


(ITHz ∝ IIR2). Since ITHz ∝ ETHz

2, the linear dependency of the EOS signal amplitude with thepumping pulse intensity is a clear evidence of its OR source [26].

The obtained AG/AS value of the gain is larger than the theoretical limit of∼1.01 for asingle process of stimulated emission estimated from Ref. [6], taking into account theabsorbance of monolayer graphene and the permittivity’s of CdTe and SiO2. In the exper-imental setup, a multipath reflection effect is considered as a factor that increases the gain.The forward-propagating terahertz probe pulse is amplified, its large fraction is transmitted,and∼70 % is reflected back at the SiO2/Si interface. This reflected part will also interact withgraphene and be amplified. Since the round-trip delay in the 300-nm-thick SiO2 layer is∼4 fs, almost no distortion is seen in the temporal response. This multipath reflection effectmay double the gain at most but cannot fully explain the obtained AG/AS.

We also considered an effect of photocarrier-dependent Drude conductivity on reflectiv-ity. In case of our graphene/SiO2/Si sample whose Si substrate has a low resistivity of 0.005Ω-cm and whose carrier momentum relaxation time is long and close to 10 ps, the increase inreflectivity under pumping due to the increase in photocarrier-dependent Drude conductivityis as small as 1–2 % and quite monotonic over the entire terahertz spectral range of interest.A few percentages of such increase in the reflectivity should be de-embedded from theobtained photon-echo signal but barely affect the gain spectral profile. We need further studyto give a perfect quantitative interpretation for the observed results.

Figure 11 shows the Fourier transform of the photon echo signal measured on the areawithout graphene (reference) with crystal A (black line) and crystal B (red line). Thenormalized dynamic conductivity for the pumping pulse intensity three times higher than thethreshold pumping pulse intensity at 300 K is also presented (see Ref. [6]). The photon echo

Fig. 10 (a) Transfer functions of monolayer exfoliated graphene on SiO2/Si for different values of pumpingpulse intensities. Inset: normalized EOS signal amplitude of the first peak (upper panel) and AG/AS ratio(lower panel) for different values of the pumping pulse intensities. (b) Variation of the phase of the measuredterahertz electric field for different values of pumping pulse intensities. (after Ref. [26].)


pulse interacts with graphene during the recombination process and induces emission ofterahertz photon in graphene within the negative dynamic conductivity area (blue shadedarea). The expected graphene emission spectral bandwidth is limited at lower frequenciesby the Drude mechanism of terahertz absorption, and the higher frequency limit is given bythe system bandwidth, which is estimated to be around 6 THz (see the horizontal solid linesin Fig. 11). The black and red shaded areas show the expected graphene emission band-width, from∼1.5 to∼5 THz using the thicker crystal and from∼1.5 to∼6 THz using thethinner crystal.

The inset of Fig. 11 presents the transfer functions of monolayer graphene obtained withcrystal A (black line) and crystal B (red line). The obtained spectra are in good agreementwith the above mentioned expectations. It is possible to compare these spectra within thesmallest bandwidth (from∼1.5 to∼5 THz). The graphene emission spectrum obtained withthe thinner CdTe crystal is broader than that one obtained with the thicker crystal. In thethinner crystal, the graphene excitation with the terahertz probe is done earlier (2 ps) after theoptical pump than in the thicker crystal (3.5 ps). This spectral narrowing at longer terahertzprobe delay time is a clear trace of the progress of equilibration process from 2 to 3.5 ps asshown in Figs. 2 and 3. Indeed, at 3.5 ps, the quasi-Fermi energy is closer to the equilibriumcompared to that at 2 ps. It is worth noting that this broadening may not be observed in thecase of amplification due to an increase in reflectivity.

Such a temporal dependency of the gain profile is theoretically testified [16]. As is shownin Fig. 2, temporal evolutions of the quasi-Fermi energy of impulsively pumped graphenerapidly recovers its level and exceeds the equilibrium level when pumping intensity exceedsa threshold and resumes to the equilibrium state. Figure 12 shows the dynamic conductivitycalculated as a function of the pumping intensity at a fixed time (3.5 ps) and a fixedfrequency (3 THz). Compared with the experimentally observed threshold behavior, themeasured results qualitatively agree with the simulated ones. The threshold intensity is onthe same order. It is thought that the quantitative difference comes from the fact that weassume the complete quasi-equilibration by the CC scattering, raising the threshold pumpingintensity to the highest level, and this leads to excessively high threshold intensity.

Fig. 11 Terahertz emission spectra of the photon echo signal measured on the area without graphene(reference) with thick CdTe (red line) and thin CdTe (black line) crystals and the normalized dynamicconductivity (blue line). Inset: transfer functions of monolayer graphene obtained with thick CdTe (red line)and thin CdTe (black line) crystals. (after Ref. [26].)


Furthermore, to confirm the effects of the terahertz probe that stimulates the emission ingraphene, the CdTe crystal was replaced by a CdTe crystal having a high-reflectivity coatingfor Infrared on its bottom surface in order to eliminate generation of the terahertz probesignal. In this case, no distinctive response was observed. Since the measurements are takenas an average, the observed response is undoubtedly a coherent process that cannot beobtained via spontaneous emission processes, which also supports the occurrence of thestimulated emission.

B. Heteroepitaxial graphene on 3C-SiC/Si

As mentioned above we focus to observe the secondary terahertz photon echo pulse thatreflects the response of graphene. Typical raw data of observed temporal response is shownin Fig. 13(a). As is mentioned in IV, we extracted the temporal response of the secondaryterahertz pulsation from the measured raw data to identify the frequency response of thegraphene. Figure 13(a) shows the measured temporal responses, in which repetitivelymeasured results are overlaid, showing the measurement reproducibility. Figure 13(b) showsthe Fourier spectra corresponding to the typical traces plotted with thick lines in Fig. 13(a).

Fig. 12 Numerically simulated dynamic conductivity as a function of the pumping intensity at a fixed time of3.5 ps and a fixed frequency of 3 THz. (after Ref. [26].)

Fig. 13 (a) Measured temporal profiles for heteroepitaxial graphene on 3 C-SiC/Si (GOS) and (b) theirFourier spectra when the terahertz probe beam is generated by the optical rectification in the CdTe crystal.Dashed line in (b) is the photoemission spectrum predicted from the pumping laser spectrum and the negativedynamic conductivity. (after Ref. [25].)


Owing to the second-order nonlinear optical effects, the emission from “CdTe only”without the GOS sample exhibits a temporal response similar to optical rectificationwith a single peak at around 1 THz and an upper weak side lobe extending to around5 THz as shown by the green lines in Fig. 13(b). On the other hand, the temporalprofile of the result from “CdTe and GOS” intensifies the pulsed response with higherfrequency components so that its Fourier spectrum exhibits the growth of the mainlobe around 2 to 4 THz and the lower side lobe around 1 THz. The main lobe fairlycorresponds to the expected gain spectral region which is shown with the dashed linein Fig. 13(b), while the side lobe fairly corresponds to the component of terahertzprobe signal generated from the CdTe. It is inferred that the terahertz emissions fromgraphene are stimulated by the coherent terahertz probe radiation from the CdTe.Furthermore, the terahertz emissions are amplified via photoelectron/hole recombina-tion in the range of the negative dynamic conductivity. Compared to the results fromthe exfoliated monolayer garaphene on SiO2/Si, the measured responses show poor S/N and reproducibility, which is presumably attributed to poor crystal quality of theheteroepitaxial graphene sample. Further study is expected for more accuratemeasurements.

4 Conclusion

Recent advances in spectroscopic study on ultrafast carrier dynamics and terahertzstimulated emission in optically pumped graphene were reviewed. When we considerthe ultrafast carrier relaxation and relatively slow recombination dynamics in opticallypumped graphene, one dramatic feature of negative dynamic conductivity in theterahertz range is derived. We have successfully observed amplification of an incom-ing terahertz pulse during the relaxation-recombination process in graphene. Westudied the pump-power-dependent measurements and showed the existence of acritical pumping intensity at which the amplification regime starts. We investigatedthe amplitude and the phase of the measured terahertz field. The amplitude measuredon graphene is larger than that measured on the area without graphene, while thephase shows clear inverted behavior with normal dispersion around the gain peakfrom that for the loss cases, demonstrating that the amplification can be attributed tostimulated emission of photo-carriers in the inverted states. We also confirmed thedependence of the emission spectra on terahertz-probe timing. The gain spectra shownon-monotonic frequency dependence with a clear narrowing when the terahertz probetiming is set at longer delay time (3.5 ps). A possible interpretation is that weobserved coherent amplified stimulated terahertz emissions and its threshold behavioragainst the pumping intensity arising from the fast relaxation and relatively slowrecombination dynamics of photogenerated electrons or holes in exfoliated grapheneon SiO2/Si as well as in heteroepitaxial graphene on 3C-SiC/Si. The obtained resultssupport the occurrence of negative dynamic conductivity, which can be applied to newtypes of terahertz lasers.

Acknowledgements The authors thank H. Karasawa, T. Watanabe, S. Chan, and T. Fukushima at TohokuUniversity, Japan, for their contribution on the experimental works. They also thank M. Ryzhii at Universityof Aizu, Japan, and V. Mitin at University at Buffalo, SUNY, USA, for their theoretical support, and J. Kono atRice University, USA, for his valuable discussion. This work is financially supported by JST-CREST, Japan,JSPS Grant-in-Aid for Specially Promoting Research, JSPS Core-to-Core Programs, Japan, and the NSF-PIRE Teranano Nano-Japan Program, USA.


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