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Observation of Amplified Stimulated Terahertz Emission from Optically Pumped Epitaxial Graphene Heterostructures

We experimentally observe the fast relaxation and relatively slow recombination dynamics of photogenerated electrons/holes in an epitaxial graphene-on-Si heterostructure under pumping with a 1550-nm, 80-fs pulsed fiber laser beam and probing with the corresponding terahertz (THz) beam generated by and synchronized with the pumping laser. The time-resolved electric-field intensity originating from the coherent terahertz photon emission is electro-optically sampled in total-reflection geometry. The Fourier spectrum from 1.8 to 5.2 THz agrees well the pumping photon spectrum. This result is attributed to amplified emission of THz radiation from the graphene sample stimulated by the THz probe beam, and provides evidence for the occurrence of negative dynamic conductivity in the terahertz spectral range.


MANUSCRIPT
Graphene, a monolayer of carbon atoms in a honeycomb lattice crystal, has attracted considerable attention due to its unique carrier transport and optical properties, including massless and gapless energy spectra [1][2][3]. The gapless and linear energy spectra of electrons and holes lead to nontrivial features such as negative dynamic conductivity in the terahertz (THz) spectral range [4], which may lead to the development of a new type of THz laser [5,6].
To realize such graphene-based devices, understanding the non-equilibrium carrier relaxation/recombination dynamics is critical. Figure 1 presents the carrier relaxation/recombination processes and the non-equilibrium energy distributions of photoelectrons/photoholes in optically pumped graphene at specific times from ~10 fs to picoseconds after pumping. It is known that photoexcited carriers are first cooled and thermalized mainly by intraband relaxation processes on femtosecond to subpicosecond time scales, and then by interband recombination processes. Recently, time-resolved measurements of fast non-equilibrium carrier relaxation dynamics have been carried out for multilayers and monolayers of graphene that were epitaxially grown on SiC [7][8][9][10][11] and exfoliated from highly oriented pyrolytic graphite (HOPG) [12,13]. Several methods for observing the relaxation processes have been reported. Dawlaty et al. [7] and Sun et al. [8] used an optical-pump/optical-probe technique and George et al. [9] used an optical-pump/THz-probe technique to evaluate the dynamics starting with the main contribution of carrier-carrier (cc) scattering in the first 150 fs, followed by observation of carrier-phonon (cp) scattering on the picosecond time scale. Ultrafast scattering of photoexcited carriers by optical phonons has been theoretically predicted by Ando [14], Suzuura [15] and Rana [16]. Kamprath et al. [12] observed strongly coupled optical phonons in the ultrafast carrier dynamics for a duration of 500 fs by optical-pump/THz-probe spectroscopy. Wang et al. [11] also observed ultrafast carrier relaxation via emissions from hot-optical phonons for a duration of ~500 fs by using an optical-pump/optical-probe technique. The measured optical phonon lifetimes found in these studies were ~7 ps [12], 2-2.5 ps [11], and ~1 ps [9], respectively, some of which agreed fairly well with theoretical calculations by Bonini et al. [17]. A recent study by Breusing et al. [13] more precisely revealed ultrafast carrier dynamics with a time resolution of 10 fs for exfoliated graphene and graphite.
It has been shown that the intraband carrier equilibration in optically excited graphene (with pumping photon energy ) Fig.   1(c)). Then, thermalization occurs via electron-hole recombination as well as intraband Fermization due to cc scattering and cp scattering (as shown with energy q   in Fig. 1(a)) on a picosecond time scale (see Fig. 1(d)), while the interband cc scattering and cp scattering are slowed by the density of states effects and Pauli blocking.
For the electron-hole recombination, radiative recombination via direct-transition to emit and non-radiative recombination via Auger processes, plasmon emissions, and phonon emissions [9,18] are considered. In the case of the radiative recombination, due to the relatively small values of  , as well as the gapless symmetrical band structure, photon emissions over a wide THz frequency range are expected if the pumping photon energy is suitably chosen and the pumping intensity is sufficiently high. The incident photon spectra are expected to be reflected in the THz photoemission spectra as evidence that such a process occurs. Previous studies on the observation of carrier recombination dynamics in graphene have been insensitive to the mechanisms of radiative/non-radiative recombination processes, and to date, the observation of such THz photoemissions has not been reported. In this work, we observed amplified stimulated THz emission from optically pumped and THz-probed heteroepitaxial graphene heterostructures and verified the occurrence of negative dynamic conductivity.
The real part of the net ac conductivity Re   (which is proportional to the absorption coefficient of photons with frequency  ) comprises the contributions of both interband and intraband transitions: The intraband term in Eq. (1) corresponds to the Drude mechanism of THz photon absorption, while the interband term corresponds to the generation/recombination rates under the Dirac-Fermion energy/momentum distribution. Let us consider a practical situation under weak pumping with infrared photons: where holes), I  is the pumping intensity, and  is the angular frequency. The intraband term takes the Drude form, decreasing monotonically and approaching 0 with increasing  , while the interband term contributes to the linear decrease (increase) in the intraband term in the low (high)  region. The breakeven frequency depends on I  and rad  . Therefore, Re   is a minimum at a specific frequency: . Assuming a device size of 100 μm 100 μm  we find that the pumping intensity required for negative dynamic conductivity is I   6 ~ 600 mW. The value of 6 mW is a feasible pumping intensity.
When graphene is strongly pumped Equation (6) shows that Re   changes from negative to positive at extremely high intensity; thus, at   , for example, Re 0    when In order to verify the proposed concept, we conduct an experimental study on the electromagnetic radiation emitted from an optically pumped graphene structure. The sample used in this experiment is heteroepitaxial graphene film grown on a SiC(110) thin film heteroepitaxially grown on a Si (110) substrate via thermal graphitization of the SiC surface [19][20][21]. In the Raman spectrum of the graphene film, the principal bands of graphene, namely, the G (1595 cm -1 ) and G' (2730 cm -1 ) bands, are observed. Furthermore, transmission electron microscopy images indicate that the film is stratified. It is thus concluded that epitaxial graphene with a planar structure can be produced by this fabrication method. Furthermore, the epitaxial graphene layer is inferred to have a non-Bernal stacking arrangement because the G' band in the Raman spectrum can be expressed as a single component related to the two-dimensionality of the graphene film [22,23]. The non-Bernal stacked epitaxial graphene layers grown by our method can be treated as a set of isolated single graphene layers, as in the case of an epitaxial graphene layer on a C-terminated SiC bulk crystal [24]. The G-band peak at 1595 cm -1 corresponds to an optical phonon energy at the zone center of 197.8 meV.
We measure the carrier relaxation and recombination dynamics in optically pumped epitaxial graphene-on-silicon (GOS) heterostructures using THz time-domain spectroscopy based on an optical pump/THz-and-optical-probe technique. The time-resolved field emission properties are measured by an electro-optic sampling method in total-reflection geometry [25]. To obtain the THz photon emissions from the above-mentioned carrier relaxation/recombination dynamics, the pumping photon energy (wavelength) is carefully selected to be around 800 meV (1550 nm). To perform intense pumping beyond the threshold, a femtosecond pulsed fiber laser with full width at half-maximum (FWHM) of 80 fs, pulse energy of 50 pJ/pulse, and frequency of 20 MHz was used as the pumping source. The setup is shown in Fig. 2. The graphene sample is placed on the stage and a 100-m-thick (101)-oriented CdTe crystal is placed onto the sample; the CdTe crystal acts as a THz probe pulse emitter as well as an electro-optic sensor. The single femtosecond fiber laser beam is split into two beams: one for optical pumping and generating the THz probe beam, and one for optical probing. The pumping laser, which is linearly polarized and mechanically chopped at ~1.2 KHz, is simultaneously focused at normal incidence onto the sample and the CdTe from below, while the probing laser, which is cross-polarized to the pumping beam, is focused from above. The incident pumping beam is defocused on the sample to satisfy the above-mentioned pumping power requirements. The resulting photoexcited carrier density is  Fig.   1(c)). On the other hand, through the Si prism attached to the CdTe crystal, the optical probing beam is totally reflected back to the lock-in detection block, and its phase information reflecting the electric field intensity is lock-in amplified. By sweeping the timing of the optical probe using an optical delay line, the whole temporal profile of the field emission properties can be obtained. The system bandwidth is estimated to be around 6 THz, which is limited mainly by the Reststrahlen band of the CdTe sensor crystal.   Fig. 4 is the photoemission spectrum predicted from the pumping laser spectrum. The emission spectrum from CdTe without graphene shows a dominant peak around 5 THz, and a weak side lobe extends to below 1 THz (blue line in Fig. 4). On the other hand, the results with graphene agree well with the THz photon spectrum predicted from the pumping photon spectrum. The results include an additional peak around 5 THz (red line in Fig. 4). It is thought that the THz emissions   Fig. 4, the results with graphene agree well with the pumping photon spectrum and include an additional peak around 1 THz from the original CdTe spectrum (red lines in Fig. 5). In order to confirm with certainty that the emissions from graphene reflect the pumping photon spectrum, the pulse compression of the pumping laser pulse was altered to broaden its spectrum as shown by the black lines in Fig. 3. Due to the pulse compression condition, the pulse energy increases ~100 pJ/pulse. As can be seen in Fig. 5(b), the emission spectrum of the graphene was broadened, corresponding to the pumping photon energy.
Furthermore, to confirm the effects of the THz probe, we replace the first CdTe crystal with another CdTe crystal having a high-reflectivity coating for IR on its bottom surface, in order to eliminate generation of the THz probe signal. In this case, no distinctive response is observed with or without graphene. Since the measurements are taken as an average, the observed response is undoubtedly a coherent process that cannot be obtained via spontaneous emission processes, providing clear evidence of stimulated emission. For all three cases of emissions from graphene in Figs. 4 and 5, the lower cutoff around 2 THz (8.3 meV) is slightly higher than the theoretical estimation (~5 meV) [5]. This may be due to a small bandgap forming due to the interlayer coupling of the existing multilayer graphene or substrate-induced asymmetric potential deformation [26].