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Abstract
Room-temperature polariton lasing is achieved in GaN microrods grown by metal-organic vapor phase epitaxy. We demonstrate a large Rabi splitting (Ω = 2g0) up to 162 meV, exceeding the results from both the state-of-the-art nitride-based planar microcavities and previously reported GaN microrods. An ultra-low threshold of 1.8 kW/cm2 is observed by power-dependent photoluminescence spectra, with the linewidth down to 1.31 meV and the blue shift up to 17.8 meV. This large Rabi splitting distinguishes our coherent light emission from a conventional photon lasing, which strongly supports the preparation of coherent light sources in integrated optical circuits and the study of exciting phenomena in macroscopic quantum states.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Exciton polaritons are quasi-particles formed by the strong coupling [1] between excitons and photons in a microcavity. Due to the extremely light effective mass (10−4 −10−5 me) and bosonic nature, exciton-polaritons are not only an excellent platform for studying the macroscopic quantum states such as BEC [2–5], superfluidity [6], quantum vortices [7], and solitons [8]; but also hold great promise for in optoelectronics and electronic application like single-photon sources [9], photodetectors [10], and switches [11]. Among them, one of the most attractive phenomena is polariton lasing, which originates from coherent photons leaking out of condensed polaritons. Since no population inversion is required, the threshold of polariton lasing is much lower (2-3 orders of magnitude lower than conventional lasers) or even zero threshold [12–15].
Polariton lasing was first demonstrated in the GaAs and CdTe microcavities at cryogenic temperatures, and many signatures of polariton lasing, such as peak blueshift and Bose-Einstein (BE) distribution in momentum space, were observed [3,4]. Recently, as a representative of wide-bandgap semiconductors, GaN has gained more and more attention in the field of polariton lasing. Because it has higher exciton binding energy and oscillator strength [16,17] to work at room temperature. Moreover, GaN can be easily doped with both n- and p-type [18,19] and is therefore capable of electrical injection. Both optically and electrically pumped polariton lasers have been realized in GaN-based two-dimensional planar microcavities, where the active region is sandwiched by two distributed Bragg reflectors (DBRs) [20,21]. However, it is difficult to grow high-quality DBRs directly in III-N devices due to the lack of suitable DBR materials, while another solution of bonding dielectric DBRs with epitaxial layers requires a complex process [22].
Therefore, a whispering gallery (WGM) mode within GaN microrod could be a perfect alternative. The WGM in GaN microrod is formed by its total internal reflection at the six semiconductor/air interfaces [23–25]. Using WGM instead of the F-P mode in GaN microrods could increase the cavity quality factor by at least one order, resulting in higher Rabi splitting and ultralow threshold polariton laser. Additionally, GaN microrods with low crystal defects and stresses can be easily grown by self-organized and selective growth methods [13,26]. Trichlet et al. [27] and Gong et al. [28] have reported the strong coupling within a GaN microwire with Rabi splitting of 115 meV and 130 meV, as well as a quality factor of 800 and 130, respectively. However, no polariton lasing was observed due to the relatively poor cavity quality.
This paper shows a large Rabi splitting of ∼162 meV and a high quality-factor of ∼2405 for GaN microrods. The Rabi splitting exceeds the state-of-the-art nitride-based planar microcavities and previously reported GaN microrods [21,29–31]. We also observed ultra-low threshold single-mode polariton lasing in GaN microrod at room temperature. A large number of polaritons condense toward the ground state in momentum space when the excitation power density reaches 1.8 kW/cm2, and the maximum peak blue shift is ∼17.8 meV.
2. Experiment
The high crystalline quality GaN microrods in this study were grown on c-plane sapphire substrates by metal−organic chemical vapor deposition (MOCVD) via a self-assembly method without using any catalysts or masks. Before growth, the sapphire substrate was heated to 1100 °C for 20 min in an atmosphere of ammonia. Then GaN microrods were grown at 1040 °C and a pressure of 200 Torr, with Trimethylgallium (TMGa) and ammonia (NH3) as precursors. The TMGa flow rate was maintained at 30 sccm, and the NH3 flow rate was kept at 240 sccm, with pure hydrogen (H2) used as the carrier gas. The same fabrication method was also described in a previous report [26]. The diameter and length of the obtained microrods [see Figs. 1(a) and (b)] is ∼3 µm and ∼200 µm, respectively, which is the typical size to obtain both high crystalline quality and high cavity quality factor. Regular hexagonal cross-sections and smooth sidewall surface morphology are observed, ensuring high-quality WGM formation. Clear WGMs were also seen from Cathodoluminescence (CL) spectrum (not shown).
Fig. 1. (a) SEM image of GaN microrod grown on c-plane sapphire and (b) enlarged image of a regular hexagonal facet. R is the radius of a circumcircle of microrod. (c) Schematic of GaN microrod transferred to fused silica. (d) Schematic of an angle-resolved micro-photoluminescence measurement setup. k⊥represents the wave vector component perpendicular to the c-axis, kz (k||) represents the component parallel to the c-axis, and θ represents the angle between k and k⊥.
The sample microrod was harvested from its substrate and transferred onto a fused silica substrate [see Fig. 1(c)]. One of the facets was shattered on purpose to eliminate F-P modes between the two facets, giving its way to the strong coupling of exciton and WGM photon. To demonstrate the strong coupling, we measured the angular dispersion (i.e., the energy E versus the emission angle θ) of the emission from several WGM polariton modes of single GaN microrods by angle-resolved photoluminescence (ARPL) spectrometer at room temperature. As described in Fig. 1(d), the ARPL system consists of three confocal Fourier lenses, a sample stage, and a spectrometer. During the measurement, the GaN microrod is placed at the focus of the objective lens and turned parallel to the slit of the spectrometer. The reciprocal PL image of GaN microrod is constructed on the Fourier plane behind the objective lens, which is then projected onto the spectrometer through the two confocal lenses. The angle and energy of PL emission are resolved by the slit and grating respectively, thus giving the E−θ dispersion curve of the polariton. Optical excitation of the single microrod was realized with a 325 nm continuous wave He−Cd laser and a 355 nm pulsed Nd:YAG laser (1.1 ns pulse duration, 10 kHz repetition rate), which are used to investigate the strong coupling and the polariton lasing characteristics, respectively. The laser was focused into a 1 µm spot by the objective microscope lens to selectively excite a short part of the microrod with constant diameter. The photoluminescence image in k space is formed with emission angle θ varying from −30° to +30° (objective N.A. 0.5). The photoluminescence passes through a linear polarizer in order to select TE (electric field perpendicular to the c-axis) or TM (magnetic field perpendicular to the c-axis) polarization emission.
3. Results and discussion
3.1 Dispersion curves of exciton-polaritons
For wurtzite GaN, there are three possible transitions of electrons from the conduction band to the valence band, which results in A B and C excitons. According to the selection rules, the emission of A exciton and B exciton are TE polarization ($\vec{\boldsymbol{\varepsilon}} \bot \vec{\textbf{c}}$), and the emission of B exciton and C exciton are TM polarization ($\vec{\boldsymbol{\varepsilon}}\mathrm{\parallel }\vec{\textbf{c}}$) [32]. Considering that the possibility of C excitonic transition is very small, the intensity of TM mode is too weak to be distinguished so that the PL spectra discussed below are all TE polarized.
Figure 2(a) shows the room temperature ARPL spectrum under TE polarization. The white dashed line indicates the exciton resonance (3.412 eV read from the PL spectrum in Fig. S1 in Supplement 1). Additionally, nine parabolic-like dispersion curves, named LP1 to LP9, are observed below the exciton resonance. The curvature of these dispersion curves increases gradually as the energy decreases, and the energy spacing between adjacent dispersion curves becomes larger as the energy becomes smaller, which is the typical characteristic of the strong coupling between excitons and photons to form polaritons. Since upper polaritons (UP) are hard to be detected due to thermal relaxation, these dispersion curves should be fitted by coupled Hamiltonian of lower polaritons (LP) [33]:
Fig. 2. (a) The angle-resolved photoluminescence spectrum with 325nm cw laser pumping is detected under TE polarization. The white and green dash lines labeled EX and C3 correspond to exciton and the third whispering gallery mode dispersions before strong coupling, and lines LP1 to LP9 are the fitted results for low-polariton branches (LPB) dispersion with different WGM numbers. The color-bars represent the polariton emission intensity. (b) The energy of UP and LP is simulated as a function of exciton-photon energy detuning using experiment data, where the Rabi splitting Ω = 2g0 is exacted to be about 162.5 meV. (c) The Hopfield coefficient of the exciton (red lines) and photon (black lines) for LP branches 2 and 5.
By sampling the multiple curves in the ARPL spectrum and fitting them simultaneously using the above model, we can get the optimal parameters as shown in Table 1. In our sample, the extracted Rabi splitting energy (Ω = 2g0) is up to 162.5 ± 14.4 meV, which is much larger than the typical value in nitride planar cavity (∼50 meV) and previously reported Rabi splitting in GaN microrods [21,29–31]. The simulated dispersion of the low-polariton branches (LPB) in Fig. 2(a) (indicated by the pink dashed line with a slightly larger angular range) is in good agreement with the experimental data. Notably, LP3 is highlighted by a solid green line due to the smallest bandwidth among nine LPs. The measured bandwidth of LP3 is ∼1.3 meV, and the Q-factor (defined as Q= λ/Δλ) is derived to be 2405. Meanwhile, the uncoupled cavity mode C3 is also calculated, as shown by the green dash line. The curvature of C3 is much smaller than that of LP3, and the energy at kz = 0 of C3 and LP3 can be read as 3.411 eV and 3.331 eV, respectively. It is the relatively high Rabi splitting energy and Q-factor that ensures the polariton lasing occurs at the ultra-low threshold.
Table 1. Fitting parameters and results of polariton dispersions.a
Figure 2(b) plots the energy of exciton-polaritons as a function of detuning (defined as $\Delta = {E_{cav}} - {E_{exc}}$). The scatter points represent the energies of different LPs at θ = 0 extracted from Fig. 2(a), the blue and red lines are the modes of UP and LP calculated according to Eq. (1) and parameters in Table 1. As shown in Fig. 2(b), the energy of UP is always above the higher one of the uncoupled Ecav and Eexc, while the energy of LP is always below the lower one of the two. In other words, UP and LP exhibit an anti-crossing feature. Moreover, as the detuning value shifts from positive to negative, the lower exciton-polaritons change from more exciton-like to more photon-like.
The exciton and photon fractions of polaritons are usually quantified by Hopfield coefficients. Figure 2(c) shows the Hopfield coefficients versus sinθ for LP2 and LP5 as an example. When the detuning is positive (42.32 meV), as in the case of LP2, the exciton component dominates at kz = 0. While for LP5, whose detuning is negative (−88.96 meV), the photon component is larger at kz = 0. The detuning controls the component of photon and exciton and thus the condensation behavior. On the one hand, the photon component of LPs allows them to have a very small effective mass so that the system can have a very high critical temperature, according to Bose statistics. On the other hand, the exciton component of LPs means they cool faster down to kz = 0 by scattering with each other and scattering with phonons hence the critical density can be reached more easily [33]. The multiple WGMs in the GaN microrod provide adjustable detunings from positive to negative. So that we can always find an optimal detuning for polariton lasing, which is determined by the competition of two mechanisms.
3.2 Polariton lasing at room temperature
For further investigation of polariton lasing, the sample was excited non-resonantly by a pulsed Nd:YAG laser with an output wavelength of 355 nm and a pulse repetition rate of 10 kHz to generate high carrier densities. The angle-resolved emission spectra measured at different pump power are shown in Fig. 3. We focus on the energy range of 3.33ev to 3.38ev. The polariton dispersion curves of LP2 and LP3 shown in the black (white) and red lines are detectable, despite the degradation of the signal-to-noise ratio caused by the pulsed pump.
Fig. 3. (a)-(g) The angle-resolved photoluminescence spectra pumped by 355 nm pulsed laser at different power show polariton lasing and blueshift behavior. The dash lines are the simulation results of LP branches 2 and 3. The color-bars represent the polariton emission intensity.
As the pumping power increases [see Figs. 3(a)–(c)], the intensities of both LP2 and LP3 become larger, accompanied by a striking blue shift, while the intensity of LP3 grows faster and gradually dominates. The blue shift is believed to arise from the polariton-polariton Coulomb repulsive interactions and thus grows monotonically with the polariton densities. Once the power (density) exceeds the threshold of 58 µW (1.8 kW/cm2) [see Figs. 3(d)–(f)], the polaritons collapsed to the bottom of the LP3 at kz = 0 (i.e., the ground-state), and the emission of LP2 was competed away. Increasing the power (density) further to 353 µW (11.2 kW/cm2) [see Fig. 3(g)], the polaritons in LP3 start to discrete occupy the ground and high-energy states. This indicates the system remains in the strongly coupled regime despite the large density of polaritons [34]. Therefore, we can attribute it to the formation of polariton lasing from the proofs of progressive blue shift and dramatic polaritons condensation in k-space. Or, in more detail, massive polaritons occupy the ground quantum state via stimulated relaxation of polariton-polariton or polariton-phonon scattering, when the polaritons density reaches the threshold. The as-formed condensate of polaritons generates coherent light emission with ultra-low threshold, namely “polariton lasing”.
For quantitative analysis of the nonlinear optical behavior, we extracted the PL spectrum [see the inset of Fig. 4(b)] around kz = 0 from the ARPL spectrum. The integrated intensity and half-width of the LP3 are plotted in log−log scale as a function of pump power in Fig. 4(a). As shown by the s-shape feature of the black curve, the integrated intensity of LP3 increases sharply by 2 orders of magnitudes around the threshold of 58 µW (1.8 kW/cm2). At the same time, the half-width of the emission peak (red curve) undergoes a sudden narrowing from 20.1 meV to 1.31 meV. These nonlinear optical behaviors represent a spontaneous coherent phase transition in the system, which shares the common characteristics with conventional photon laser. [26] What makes it different is Fig. 4(b), the continuous peak blue shifts with increasing pump power density for both LP2 and LP3.
Fig. 4. (a) Integrated PL intensity and linewidth of the LP3 emission as a function of pump power. (b) The emission peak of LP2 and LP3 as a function of pump power, the inset is the PL spectrum around zero detection angle under different pump powers.
The blue shift of LP2 above the threshold was not recorded due to mode competition, and the maximum blueshift of LP2 is ∼15.4 meV. For LP3, two regions with distinctly different blue shift behavior can be clearly distinguished. The first region is below the threshold where LP3 peaks are blue shifted faster from 3.330 eV to 3.346 eV. The second region is above the threshold, the blue shift of LP3 increases slightly with the increase of excitation power. This is because the coherent state is being established before the threshold, so that the k-space and real space of the polaritons contract sharply, leading to a rapid increase in the polariton density. While above the threshold, the coherent state of the system has been established, thus the polariton density of the system increases slowly. The maximum blue shift of LP3 is ∼17.8 meV, and the corresponding polariton density can be estimated from the theoretical equation: $\mathrm{\Delta }{E_{LP}} = 6.6\pi {|{{X_0}} |^2}E_x^Ba_B^3{N_{3D}}$ [35]. By putting the binding energy of the exciton $E_x^B = 28meV$, the effective Bohr radius of the exciton ${a_B} = 3.5nm$, and the exciton fraction ${|{{X_0}} |^2} = 0.456$ (see the detailed calculation Supplement 1), we can get the density of LP3 polariton ${N_{3D}} \sim 1.5 \times {10^{18}}c{m^{ - 3}}$ which is one order lower than the Mott density of $3 \times {10^{19}}c{m^{ - 3}}$ [36]. Moreover, although the blue shift of LP3 is as large as 17.8 meV in our experiment, the final nonlinear emission peak (3.347 eV) is still far below the pure WG mode C3 (3.411 eV). Therefore, we have good reason to believe that the coherent emission originates from the condensation of massive polaritons in the ground state rather than from conventional photon lasing.
4. Conclusion
In summary, room temperature ultra-low threshold polariton laser is achieved in GaN microrod with Rabi splitting up to 162.5 ± 14.4 meV and quality factor of 2405. It takes a little step further towards high-efficiency electrically driven polariton devices and on-chip integration for photonics devices. Based on this structure, high-quality GaN/InGaN core-shell microrods could be fabricated, and more macroscopic quantum phenomena within them could be investigated soon.
Funding
National Natural Science Foundation of China (61334005); Key Technologies Research and Development Program (2017YFB0405000); Science Challenge Project (JCKY2016212A503); Beijing Municipal Science and Technology Project (Z161100002116037); Beijing Nova Program (Z201100006820081, Z201100006820137).
Acknowledgments
H. Chen and J. Li contribute equally to this work. The authors would like to thank all the staff during the measurements at the beamline 1W1A at BSRF.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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