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Abstract
We report the momentum space dispersion pattern of strong coupling exciton-polaritons with a Rabi splitting (130 meV) in a ZnO self-construct high Q-factor whispering gallery mode (WGM) microcavity at room temperature (RT). By scanning excitations along the c-axis of a microwire (MW) using the angle-resolved spectroscopic technique (ARST) with different polarizations, the evolutions of a WGM polariton in a different coupling regime are investigated comprehensively. In addition, the more exciton-like component at a high k-value dispersion certifies the robust polariton is in SCR. The observations of polariton dispersion are well described by using the coupling wave model. Our results present a direct mapping of the exciton-polariton dispersions based on WGM, and thus supply a feasible road to realize novel polariton-type optoelectronic devices.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Microcavity polariton based on exciton-photon coupling has fascinated many researchers in the last decade because these quasiparticles exhibit half-light and half-matter properties [1]. Furthermore, polaritons can be expected to undergo a Bose-Einstein like phase transition, and a spontaneous macroscopically coherence state lasing will be established [2,3]. In the past ten years, the strong coupling exciton-polariton have been realized in series of matter, for example the CdTe quantum well, organic, two-dimensional atom materials [4–6]. These results have already brought us a significant physical understanding of polariton physics, such as Bose-Einstein condensation, [4] correlated parameter photon pair, [7] soliton propagation [8] and quantized vortex state [9]. However, low operation temperature of polariton using the conventional III-V semiconductors will be the bottleneck for its application. Similarly, the exciton electrically injection for polariton is still a critical challenging for the organic materials with high exciton binding energy (Ex). In recent years, the wide band gap materials (ZnO, GaN et. al.) with giant exciton binding energy and larger exciton oscillator strength exhibit a strong photon-exciton coupled polariton at RT [10,11]. However, the fabrication of ZnO-based vertical microcavity with a top and bottom distributed Bragg reflector is still very challenging due to the shortage of high quality single crystal substrate thus far [12,13]. Besides the artificial cavities, the above problems can be probably avoided using self-constructed microcavities of gain media itself. Although a large Rabi splitting (120 meV) of exciton polariton has been observed in single ZnO MW Fabry-Perot and WMG cavity, [14] the dispersion of polariton in momentum space is absent. The above finding strongly suggests that the self-constructed cavity may be a promising system for studying polariton physics and device.
Taking advantage of the total internal reflection near the hexagonal cross section boundaries of ZnO microwire, the resonant WGM is achievable [15]. Unlike the planar cavities, the overlap between the exciton state and cavity mode will be greatly enhanced in a WGM, because the WGM-type resonator itself is an active medium for excitons. As a result, the strength of coupled polariton will be enhanced dramatically.
In this paper, we investigate the coupling mechanism of exciton with WGM photon and the dispersion behavior of robust polariton at RT comprehensively. Detailed mapping of polariton dispersions in momentum space with differently polarized WGM is directly obtained through the ARST. Simulations for dispersion based on the coupling wave model fit excellent with the experimental observations. Our results demonstrate that the high Q-factor polygonal resonator provide a superior platform for investigating exciton-polariton and developing novel polariton-based devices.
The exploration of single-MW optical properties and exciton-polariton are carried out by a micro-photoluminescence (µ-PL) system, the schematic setup is shown Fig. 1(a). Here the adopted WGM resonator is constructed in a tapered MW structures that synthesized by a vapor-phase transport method [16]. The inset of Fig. 1(b) depicts scanning electron micrograph (SEM) of individual MW, the MW exhibits a perfect hexagonal cross-section and smooth side surfaces. The atomic force microscope (AFM) topography of the side face of bare-MW shows the RMS is small than 5.0 nm, [17,18] which indicates the high Q-factor resonance WGM can be constructed by the six side walls. In other words, the optical scattering loss due to roughness of the cavity side wall can be suppressed strongly. In addition, the longitudinal length of tapered MW is about 800 µm with diameter continuously decrease from several micrometers at the one side to a few nanometers at other side.
Fig. 1. The properties of gain media for exciton polariton. (a) The schematic of micro-PL setup for the individual ZnO MW measurement. (b) The typical PL spectrum of single MW at RT. Inset, SEM photograph presents the magnified cross-section image of single MW resonator, which shows perfect side and end face quality. (c) The relation of the measured radius R and scan position xp. The solid line is fitting curve according to Eq. (1). Inset, the schematic diagram of hexagonal resonator.
We performed emission spectral measurements for detection with unpolarized TM (E//c-axis), and TE polarized (E⊥c-axis) respectively, while the electrical field of pumping laser is perpendicular to c-axis. Typical emission spectrum of the single-MW interband transitions at RT exhibits a near bandedge emission (NBE) peak nearby 390 nm that dominates in the plot [Fig. 1(b)], meanwhile, the defect related emission band is hardly detected. The NBE band is constituted by a typical exciton radiation spikes and a series of resonance spikes at its low energy shoulder [19]. The resonance fringes are known as the typical WGM interference peaks through total internal reflection. Due to the tapered structure is a varying radius WGM resonator in which the energy of cavity mode can be modulated, hence the detuning energy between the photon and exciton can be tuned flexible and controlled by choosing the radius of MW.
Figure 1(c) illustrates the relation between radius (R) of MW and scan position (xp), meanwhile the plot is fitted by Eq. (1). The schematic diagram of hexagonal WGM is also given [inset of Fig. 1(c)]. The small lateral size of polygonal resonator will separate cavity modes distinctly, which allow us to investigate the coupling between different orders WGM with exciton. By perform the scanning excitation along c-axis of MW, it can be expect that the polariton will undergo the transition from the weak coupling regime to the nearly strong coupling regime.
The valence bands (VBs) of ZnO is p-like state, which is split into three bands due to effects of crystal field and spin-orbit interactions, meanwhile the VBs can form three bright exciton as A-, B- and C-exciton [18]. Although the above three excitonic transitions are allowed in the σ polarization (E⊥c-axis and k⊥c-axis) according to optical selection rules, the C-exciton radiation is quite weak. In contrast, the C-exciton transition is allowed in π polarization excitation (E‖c-axis and k⊥c-axis), while the radiation is forbidden for A-exciton and weak for B-exciton in this configuration. Therefore, the different type excitons state can be manipulated with various polarized excitation.
In order to explore the WGM in polygonal resonator, the optical field in MW is simulated by finite-difference time-domain (FDTD) method. In view of the cross-section of MW, most of light (TE) is confined in the cavity and few leakage light from the corners of MW can be observed in six directions [ Fig. 2(a)]. Similarly, the field distribution of TM mode in the hexagonal cavity is also given [Fig. 2(b)], it is obvious that the confinement for TM is lower than TE mode. Furthermore, the cavity enhancement factor (Fp) that originally deduce by Purcell is an important parameter to evaluate the microcavity properties. Generally, the Fp factor can be deduced from the spectra as
where Δω is the spacing of adjacent modes and δω is the line-width of the cavity mode. The measured Purcell factors of TE mode versus the diameters of MW are plot [Fig. 2(c)], it is shown that our experimental data can be fitting well according to Purcell formula where the λ is the resonance wavelength, Q and Veff is the quality factor and effective volume of the microcavity respectively. As the scale of high Q-factor cavity decreasing, the Fp will be boosted. In view of the large Fp factor for WGM in MW, the coupling strength of exciton-photon will be enhanced.Fig. 2. The properties of WGM in MW. (a) The simulated result about electric-field distributions for TE polarization mode in the microcavity with diameter of 6 µm, here the photon corresponds to excitonic radiation of sample. Note, the Q-factor of WGM is high due to its optical field can be confined well in the MW. (b) The result about TM-polarization WGM field distribution in the cavity. (c) The experimental data about the dependence of Purcell factor (Fp) on the MW diameter for TE mode. The solid line indicates the fitting curve according to the Eq. (3).
To observe the polariton emission, the µ-PL scanning with polarized detection is performed, which will explore the interaction of cavity modes with exciton directly through scanning the excitation spot along the c-axis of tapered MW. The results about PL mapping of single-MW with σ excitation and TE polarized detection are shown in Fig. 3. Due to the optical selection rules, the A- and B-exciton radiation dominate in the spatially resolved PL spectra [Fig. 3(a)]. It displays a blue-shift behavior with the gradual reduce of the MW diameter. The solid line is fitting curve according to Eq. (4) and the numbers indicate the order of cavity mode. The plots represent the detailed evolution of A-/B-excitonic polariton as a function of cavity size [Fig. 3(b)]. As the focus spot scanning, excitons couple with the different orders WGM one by one, giving rise to the observed series polariton branches. The bending of spectra curves in the energy range of 3.2-3.3 eV indicate a transition from photon-like to exciton-like state. Above results indicate polariton is more WGM-like at the low energy side, while it is more exciton-like at high energy side.
Fig. 3. PL mapping of the single tapered MW with σ excitation (E and k ⊥ c-axis). (a) Spatially resolved PL along the c-axis of MW with TE polarized detection. Here, the color balls indicate the peak of spectra. The solid line is fitting curve and the numbers indicate the mode order. (b) The detailed µ-PL mapping along the c-axis with the σ excitation configuration. The white dash line indicates the isolated A-/B-exciton state, meanwhile, the theoretical fittings of polariton branches are shown with red lines. (c) Calculated results about the whole dispersion of polariton. The energy of A-/B-exciton are shown with a unified black dotted lines and the lower (yellow), upper polariton branch (green), pure WGM (blue) are also given. The sign of UPB and LPB denote the UP and LP branches, respectively.
Based on plane wave model, theoretical calculated results about the dispersion of WGM polariton are plot [Fig. 3(c)]. The energy of A-and B-exciton are shown with a unified dotted lines, meanwhile the low-polariton (LP), upper-polariton (UP) branch and bare cavity mode are also given. Here, the resonant WGM energy (E) versus the radius of MW can be written as [20]
Our theoretical calculations for the LP branches give an accurate fit to the experiments, which indicates that the observed polaritons in the tapered hexagonal cavity are the hybridized states of A-/B-excitons with WGM of number N=23, 24, 25, respectively. It is remarkable that the different order WGM can be coupled with excitons strongly and the polariton are clearly resolved even upon RT. Due to the modulated behavior that transited from more WGM-like to more exciton-like along with the different order cavity mode, the intensity of each polariton emission decreases and eventually disappears. It means that one may manipulate the polariton state via tailoring the MW diameter.
As mentioned above, the observed emission is from the LP branch and the UP is absent. One reasonable explanation for the absence of UP is that the interaction between polariton and phonon via the exciton component is very strong at RT, therefore the polaritons at UPB will be quickly relaxed to the lower energy state. As a result, the emission from UPB cannot be observed. To further illustrate the WGM polariton behavior, the evolution of LPB properties versus radius with different mode orders is explored (Fig. 4). As described by Hopfield, [22] the respective weights of excition or photon in the polariton is proportional to Ck and Xk coefficients respectively. To obtain the relative excitonic and photonic fractions of LPB for k// vector, the following formulas are used:
Fig. 4. The characteristics of WGM polaritons at RT. The A-/B-exciton and photon fraction (Hopfield coefficient) of the LP branch versus radius of MW with different WGM orders of 23, 24 and 24 for a, b and c respectively.
By taking the WGM resonance condition and the polariton dispersion into account, an exact expression for the polariton dispersion is given as [23]
Fig. 5. The RT angle-resolve PL spectra for the dispersion characteristics of WGM polariton with the σ excitation. (a) The schematic diagram of wavevector in MW for the ARST measurement. (b) The pattern presents the dispersion behavior of TE and TM mode polariton in the MW respectvely, which is obtained at certain diameter of the tapered MW. The blue shift of TM polariton can be visible remarkable, which is resulted from the high energy C-exciton coupling polariton.
The TE polarized polaritons emission pattern in k-space indicates the interaction between exciton and photon is operating in the SCR [left panel of Fig. 5(b)]. Meanwhile, the bottleneck of relaxation for LP that hindered in GaAs, CdTe at low-temperature can be overcome directly by increasing the temperature to favor polariton-phonon interactions or polariton-polariton scattering in ZnO [25]. The fitting of LP branch dispersion indicates the detuning (δ) between A-/B-exciton and photon is in the range of 80-120 meV, and the bottom of UP is deduced to be at 3.31 eV. In contrast, the C-excitonic polariton is allowed while A-/B-excitonic transitions are weakly allowed in TM configuration [right panel of Fig. 5(b)]. The remarkable blue shift of LP branch can be attributed to the high energy C-exciton, which is about 40 meV larger than A-/B-exciton [26]. Moreover, the intensity of LP branch at k//=0 is about five times smaller than the TE polarization.
Under the σ excitation at RT, the polariton emission from rotated MW is collected with the TE polarization detection (left panel of Fig. 6). As shown in image, the low polariton branches are fitting by black lines. Remarkable, the dispersion in the high longitudinal wave vector region depicts a flat behavior and approaches to the finite energy in the short wavelength limit. Considering the A-/B-exciton dominate the coupling polariton with the TE mode, hence, the intrinsic exciton relative fractions of LP branch at large k// vector will be enhanced dramatically. In order to elaborate the strong coupling mechanism of polariton via WGM, the coupling wave equation based on Lorenz oscillated dipole is adopt to perform the simulation. The simulated result about the dispersion of polariton with TE polarization (right panel of Fig. 6) is in agreement excellent with the measurement results. According to the fitting curve, the Rabi splitting of polariton (N=85) is deduced to be about 130 meV. The variation of the curvature of LP branch confirms our robust polariton is operating in SCR.
Fig. 6. The dispersion properties of WGM polaritons at large k// vector. The experimental TE polarization (Exp. TE) dispersion of polariton at large angle is given (left panel). Note that the detected angle has been enhanced to 50°, which can be used to observe the exciton component at high k-value. The dash lines indicate the fitting curves for different order LPB. For comparison, the simulated results (Sim. TE) about WGM polaritons in MW is also given (right panel). Here, the value of δ between photon and exciton is about −110 meV for m=85.
In summary, we report a direct dispersion pattern of the WGM polariton in k-space with different polarization. It is demonstrated that the cavity modes with high Fp factor in hexagonal MW couple with free excitons in SCR. Moreover, the coupling mechanism for distinct polarized cavity mode (TE and TM) is investigated. The dispersion behavior of polariton at high k-value confirm its more exciton-like component in SCR. The observations of polariton dispersion at RT are well described by using the coupling wave model. Our results certificate that high Q-factor WGM is an ideal platform for the investigation of polariton condensation lasing and the developing of novel polariton-type devices.
2 Experimental section
2.1 Microwire fabrication and characterization
In the experiment, a quartz boat with zinc powder (Alfa Aesar, 99% purity) is used as the source, and a gold film served as the catalyst for the growth of the MW. During the growth process, a mixed gas of Ar and O2 is injected into the furnace. The morphology of the MW is characterized by field-emission scanning electron microscopy (SEM, Hitachi S4800). The PL spectra of single-MW are measured with a He-Cd laser (325 nm) through a µ-PL system. The laser spot focused on the sample is scanning along its c-axis with the step of 0.3 µm. The dispersion features from the single-MW is nonresonant continue wave excited and collected by the angle-resolved µ-PL system, then is analyzed by a spectrometer equipped with a silicon charge-coupled device.
2.2 Simulation of the polariton
FDTD simulations are carried out to provide numerical calculation results. The excited source in MW is selected as dipole, and the refractive index of media (n) is 2.2. The dispersion characteristics of WGM polaritons are calculated through coupling wave equation.
Funding
Natural Science Foundation of Shanghai (19ZR1420100); Guangzhou Science and Technology Program key projects (201707020014); National Science Fund for Distinguished Young Scholars (2016A030306044); National Natural Science Foundation of China (NO. 11974122, NO. 11974433, NO. 91833301).
Disclosures
The authors declare no conflicts of interest.
Supplementary materials
See Supplement 1 for supporting content.
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