Spatiotemporal Evolution of Coherent Polariton Modes in ZnO

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Cite This: Nano Lett. XXXX, XXX, XXX−XXX

Spatiotemporal Evolution of Coherent Polariton Modes in ZnO Microwire Cavities at Room Temperature Tom Michalsky,‡ Marcel Wille,‡ Marius Grundmann,‡ and Rüdiger Schmidt-Grund*,‡

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Felix-Bloch-Institut für Festkörperphysik, Universität Leipzig, Linnéstraße 5, 04103 Leipzig, Germany ABSTRACT: Tunable waveguides for propagating coherent quantum states are demanded for future applications in quantum information technology and optical data processing. We present coherent whispering gallery mode polariton states in ZnO-based hexagonal microwires at room temperature. We observed their propagation over the field of view of about 20 μm by picosecond time-resolved real space imaging using a streak camera. Spatial coherence was proven by time integrated Michelson interferometry superimposing the inverted spatial emission pattern with its original one. We furthermore show that the real and momentum space evolution of the coherent states can not only be described by the commonly used model developed for ballistically propagating Bose−Einstein condensates based on the Gross−Pitaevskii equation but equivalently by classical ray optics considering a spatially varying particle density dependent refractive index of the cavity material, not yet considered in literature so far. By changing the excitation spot size, the refractive index gradient and thus the propagation velocity is changed. KEYWORDS: ZnO, microcavity, polariton condensate, propagation, coherence the order of 10 μm.15 While the light-matter interaction is usually already in the strong coupling regime when the wires are not entirely pumped,16−18 the modes do not propagate but, due to the three-dimensional confinement, rather form standing waves. In microwires, typically lasing out of whispering gallery modes is observed,14,19 whereby only a few reports explicitly discuss the coupling regime (e.g., refs 20−24). Trichet et al. observed in ZnO microwires already coherence length of the exciton-polariton condensate of about 10 μm, but here, the excitation spot diameter was about 20 μm so that the entire system was excited coherently and no propagation could be observed.22 In ZnO microwires deposited on a silicon grating forming a one-dimensional polariton superlattice, Zhang et al. observed weak lasing from a coherent state extending over the same distance.24 Also here, the excitation laser spot size is as large as the created coherent state.20 In this letter, we present the propagation of coherent whispering gallery mode (WGM) polariton states in a ZnO microwire cavity at room temperature. We excited the system with a femtosecond-laser with spot diameters below ≈1.5 μm (fwhm) and observed temporal and spatially resolved propagation over a distance of ±10 μm. By Michelson interferometry, we proved the states to be coherent within that region. Furthermore, we estimate the charge carrier

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iniaturized sources and guides for coherent light are important for the ongoing development of optoelectronic devices. There is a wide field of possible applications regarding telecommunication, computation and quantum information technology. Coherent light-matter states are still a progressing field of research as the underlying concepts of light-matter interaction reveal fundamental physical properties such as similarities to Bose−Einstein-condensation,1 superfluidity,2,3 quantized vortex formation,4 or optical bistability.5 For possible applications in quantum information technology or optical on-chip data processing, nano- and microscale waveguides hosting propagating and manipulable coherent states are of interest.6,7 GaAs-based waveguides for excitonpolariton Bose−Einstein condensates allow for propagation distances of about 200 μm (up to millimeters in twodimensional cavities8) and manipulation in prototype device structures like interferometers and transistors.9−12 The disadvantage of this material system is its intrinsically low exciton binding energy which inhibits the existence of excitonpolaritons at elevated temperatures as well as the need of processing technologies for producing micro- and nanostructures. Therefore, for room temperature applications, wide band gap materials such as GaN and ZnO play an important role as their exciton binding energy exceeds the thermal energy. Further, these materials easily form self-organized nano- and microwires with very high structure and crystal quality. For ZnO micro- and nanostructures, various types of lasing and light-matter interaction has been observed (see, e.g., the reviews in refs 13−15). In nanowires, the lasing modes are formed by light reflection between the wires end facets, so that the resonator length and thus the modes’ extent is typically in © XXXX American Chemical Society

Received: July 3, 2018 Revised: September 19, 2018

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DOI: 10.1021/acs.nanolett.8b02705 Nano Lett. XXXX, XXX, XXX−XXX

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Figure 1. (a) Excitation density dependent spectra at room temperature for k|| = 0 normalized to the applied pump energy density. With increasing excitation density the WGMs with mode numbers N = 50,51,52 exhibit a superlinear increase in intensity while the underlying PL signal slightly shifts to lower energies. (b) The log−log plot of PL intensity vs excitation energy density exhibits a distinct S-shape behavior. The dashed red line corresponds to the adapted multimode laser model28 with a threshold density of 27 mJ/cm2. (c) WGM broadening (HWHM; black symbols) and blue-shift (blue symbols) for the three dominating WGMs (see a) in dependence on the excitation energy density. The lines are a guide to the eye. (d) Calculated (after refs 27 and 29) refractive indices (blue) and extinction coefficients (black) for carrier densities far below (straight lines) and above (dashed lines) the Mott density. The dotted line indicates zero extinction.

imaging the spatial interference pattern, a Michelson interferometer was put in the collimated beam behind the microscope objective. One arm of the interferometer was equipped with a retro-reflector which acts as an inverter for the image of the sample surface. In this manuscript, the coordinate system is defined such that the coordinate x⃗ is along the wires cross section while z⃗ points along the wires axis, which is also the direction of k∥. In the following, we present basic optical properties and discuss the gain as well as the lasing process. After that we will discuss the spatiotemporal expansion of the coherent WGM states. Excitation energy density dependent photoluminescence (PL) spectra and a corresponding fit with a multimode laser model28 are shown in Figure 1, parts a and b. The WGMs PL intensity exhibit a nonlinear increase with increasing excitation energy density, its positions shifts to higher energies and the line width shows a minimum at the threshold excitation power (Figure 1b,c). The estimated carrier density (nth ≈ 5 × 1020 cm−3) at the threshold excitation power density of Ith = 27 mJ/ cm2 reveals that the gain process responsible for the buildup of the coherent states is connected to the (stimulated) recombination out of an electron−hole plasma.30 This is further evident by the red-shift of the broad gain profile subjacent to the WGMs emission features for increasing excitation density (Figure 1 a), reflecting the related band gap renormalization. Considering the ratio of the extend of the excited region of about ≈4 μm (sum of excitation laser spot diameter, see Figure 4 a, and two times the carrier diffusion length, see below) to the resonator length of Ltot ≡ 6Ri = 9 μm, it becomes clear that the electron−hole plasma is present in a small fraction of the cavity only. Thus, the electron−hole plasma only weakly perturbs but is a source for the coherent WGM polariton population.31 This, together with the large intrinsic coupling constant of V ≈ 300 meV,21,32 ensures that the cavities remain in the strong coupling regime. The presence of the strong coupling regime is further supported by the typical blue shift ΔE which reflects the density of the strongly coupled polaritons.33 We observed a blue shift of up to ≈10 meV (Figure 1c), being at least 1 order of magnitude lower than the coupling constant, ensuring the system not to lase out of weakly coupled WGM polariton modes. In the rayoptical picture, this blue shift can be explained by the change of

diffusion length from basic properties of the microwire system and its coherent emission. The hexagonal ZnO microwires presented in this paper were grown by a carbothermal evaporation technique.25−27 Wires grow directly on a pressed target consisting of ZnO and carbon in the mass ratio 1:1 which is placed in a heatable tube furnace. The furnace temperature was set to 1100◦C at a pressure of 120 mbar in ambient atmosphere. The growth time was 30 min. The wires typically exhibit a hexagonal cross-section and their diameters are in the micrometer range whereas their lengths can reach millimeters. After the growth process single wires are manually transferred to a SiO2 substrate. The low refractive index of the oxide guarantees the total internal reflection (TIR) conditions for WGMs confined in the hexagonal cavities. The wire presented here has an inner radius of Ri = 1.5 μm. For optical investigations, we used a home-build microphotoluminescence setup (μPL), comprising features of stateof-the-art setups presented in literature.2 We used the second harmonic of a mode-locked Ti:Sa laser oscillator (355 nm wavelength, 76 MHz repetition rate, 150 fs pulse duration) for excitation. For the reduction of sample heating, the cw-power was reduced using a pulse picker which allows only every 200th laser pulse to pass toward the sample resulting in a repetition rate of 380 kHz. A variable attenuator was used in order to vary the pump energy density. For focusing of the excitation laser light and collecting the PL signal of the sample, a microscope objective (50× magnification, 0.4 numerical aperture, corrected for the visible and near-ultraviolet) was used, allowing to image a field of view of ≈±10 μm. The pump laser spot diameter was varied between submicrometer size and ≈1.5 μm (fwhm) in order to spatially shape the excited charge carrier profile. The PL signal from the sample surface was imaged on an imaging spectrometer with a focal length of 320 mm equipped with a grating (600 grooves/mm) and connected to an array CCD camera. An additional lens between monochromator and objective allowed for the imaging of the angular and therefore the in-plane momentum (k∥) distribution of the emission. For temporal resolved measurements we combined the micro imaging setup with a streak camera. Here, a monochromator of the same type, but equipped with a 300 grooves/mm grating was used. For B

DOI: 10.1021/acs.nanolett.8b02705 Nano Lett. XXXX, XXX, XXX−XXX

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Nano Letters the carrier density dependent refractive index Δn. As the WGM resonance energies are inversely proportional to the magnitude of the refractive index of the cavity material, for small changes of the refractive index the blue shift can be expressed as ΔE ≈ −E0

Δn n0 + Δn

(1)

The subscript 0 indicates the low carrier density limit for the corresponding quantities. In Figure 1 d) the modeled complex refractive index of ZnO27,29 is plotted for carrier densities below and beyond the Mott carrier density. It can be seen that in the high carrier density limit the refractive index is reduced in the spectral range of interest (energetically below the exciton groundstate resonances at ≈3.3 eV). This is a direct consequence of the screening of the excitonic oscillator strength. As mentioned above, only a small part of the microwire is pumped. Therefore, the spatial carrier density profile and thus that of the refractive index which the WGMs experience during propagating on their closed light path within the entire cavity cross section has to be considered. The carrier density profile is further governed by the charge carrier diffusion length Ld, which largely remains an unknown parameter for ZnO so far. As the resonator length Ltot and the pump spot diameter is known from modeling the WGM energies and imaging the pump laser reflection (Figure 4 a), respectively, Ld can be calculated by replacing Δn in eq 1 with ΔnLd/Ltot. The three lasing modes (N = 50, 51, 52) and their corresponding blue shifts give three different values for Ld (1.1, 2.2, and 2.3 μm), indicating that the spectral shape of the modeled complex refractive index differs from the real one as similar values for Ld are expected. Additionally, the blue shift is obtained from time integrated measurements after femtosecond excitation, introducing further uncertainties.27 But, nonetheless, for these high-quality ZnO microwires, Ld in the order of 1 to a somewhat larger 2 μm seems to be reasonable. The reduction of the WGM line width in the vicinity of the threshold is typical as the material gain (negative κ, see Figure 1d)) compensates all resonator losses, which predominantly determine the WGM line width in the low-density limit.34 The increase in line width beyond threshold is mostly guided by the pulsed excitation conditions in combination with the time integrated measurement scheme applied here. After each single excitation pulse, the carrier density changes with time resulting in a time-dependent mode blue shift over which it is integrated, becoming more pronounced for higher excitation densities.27 The energetically resolved real and k∥-space distribution (k∥: in-plane wavevector projection) of the WGM photoluminescence (PL) emission below and beyond the threshold for coherent emission are shown in Figure 2. Above threshold the emission stems from distinct points of the dispersion relation EWGM(k∥) of the WGMs in the low density limit. These points indicate the intersections of the by ΔE blue-shifted WGM ground state energies with their correspondig dispersion relation. In the framework of exciton-polariton Bose−Einstein condensation this was explained33 with the conversion of potential energy (given by ΔE) in kinetic energy ((ℏk∥)2/ (2meff)). Alternatively this can be explained under ray-optical consideration where the locally varying refractive index leads to a change of the parallel component of the wavevector (k∥) as light rays bend into the direction of higher refractive index. As

Figure 2. Energy resolved k∥- (a) and real (b) space images below (left) and above (right) threshold for a small excitation spot. The spatial direction (z) as well as k∥ are measured along the wire axis. (c) k∥-space mode distribution in dependence on the excitation spot size beyond the lasing threshold. A small (submicrometer) excitation spot size (red) results in the appearance of the coherent modes from the dispersion of the unperturbed WGMs at k∥ > 0 whereas a large (micrometer) exciton spot (black) results in coherent states distributed around k∥ = 0 with a HWHM of 0.8 μm−1.

discussed above, the spatial refractive index profile is caused by charge carrier density dependent screening of the excitonic polarization27,29 and thus reflects approximately the excitation laser spot profile. The maximum achievable in-plane wavevector component k∥max for a mode generated at k∥ = 0 in dependence on the refractive index change Δn is given by35 2π k max ≃ 2n0|Δn| λ0 (2) with λ0 being the vacuum wavelength of the corresponding mode. Independent of the picture which is chosen (interacting particles with effective mass meff or light rays in a polarizable medium), the spatially narrow excitation leads to an acceleration of the coherent states, corresponding to lower polariton branches, away from the excitation center. This is directly reflected in the real space emission pattern as shown in Figure 2 where below threshold the contribution of low k∥ states results in effectively lower spatial expansion compared to the lasing case. There, the high k∥ states dominate the emission resulting in an effectively larger spatial expansion. A principle sketch of propagating WGM is shown in Figure 3a). The spatiotemporal expansion of the coherent WGMs was observed with a streak camera. In order to alter the expansion velocity distribution, the diameter of the excitation laser spot C

DOI: 10.1021/acs.nanolett.8b02705 Nano Lett. XXXX, XXX, XXX−XXX

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0.4 μm−1. This value is smaller than expected from the HWHM in the k∥-space distibution and may be a result of the fact that WGMs accelerate in the spatially varying potential, whose size is given by the carrier diffusion length here. Due to the restricted time resolution of the streak camera system and the diffraction limit this acceleration process appears to be hidden for observation. Spatial coherence as measured by Michelson interferometry of the propagating WGM states over the entire observed region of the microwire is demonstrated. The spatial shape of the excitation spot was determined by imaging the spatial resolved reflection of the excitation laser light on the CCD using only one arm of the interferometer (Figure 4a). Below the threshold

Figure 4. Spatial coherence: (a) Pump laser beam reflection from the wire surface yielding a spot size of 0.38 μm × 0.70 μm, resulting in an excited area of approximately 0.2 μm2. Interferogram of the PL signal from the wire surface (b) below the threshold and (c) beyond the threshold. (d) Normalized intensity of the interferogram depicted in part c. Note that in parts c and d, fringes due to autocorrelation appear at the position of the excitation spot. The dashed lines in part a mark the outer edges of the wire. The top facet has a width of about 1.5 μm

Figure 3. (a) Sketch of WGM-polariton propagation in the hexagonal ZnO microwire (purple lines), the laser excitation is indicated. (b) Spectrally resolved spatiotemporal evolution of coherent WGMs after femtosecond-excitation with a large (micrometer) excitation spot. The time steps are given in the corresponding image. The absolute value of the time scale does not represent the time difference to the excitation laser pulse. (c) Same for a single coherent WGM (E = 3.188 eV). The log-spectra are normalized to their corresponding maximum and shifted with a constant offset corresponding to a spatial separation of 0.5 μm.

(see interferogram in Figure 4b), the spontaneous PL emission from the wire surface and edges is observed with a spatial extension of about 4 μm (fwhm), exceeding the actually excited area already due to carrier diffusion and propagating uncondensed states with a broad momentum distribution (see also Figure 2a). The interferogram shows no fringes as the emission is dominated by spontaneous excitonic recombination which is spectrally broad (fwhm ≈100 meV) at room temperature. The situation changes if the excitation energy density is beyond the threshold (see Figure 4c). Here, the wire emission is dominated by WGMs coupling out of the wire edges and clear interference fringes appear. In Figure 4d, the normalized intensity Inorm(x⃗) calculated after the equation36

was changed. For a submicrometer excitation spot (about 500 nm fwhm diameter), high-momentum WGMs are created (k∥ ≈ ±7 μm−1, Figure 2a,c). For such states, the propagation time within the field of view is shorter than the temporal resolution of the streak camera of about 4 ps and thus the signal appeared distributed within the entire imaged region immediately. For the larger excitation spot of ≈1.5 μm diameter (fwhm), a wider, less steep carrier density profile is created causing coherent states distributed around k∥ = 0 with a HWHM of 0.8 μm−1 (Figure 2c) and thus a lower propagation velocity. The reconstructed spectrally resolved real space images for different time steps are shown in Figure 3b), revealing the spatial expansion of the lasing modes in time. Investigating a single mode (see Figure 3c), a velocity vmeas ≈ 1.5 μm/ps was measured which corresponds to a wavenumber of k||,meas ≈

Inorm(x ⃗) =

Iinterf (x ⃗) − I1(x ⃗) − I2( −x ⃗) 2 I1(x ⃗)I2( −x ⃗)

⃗ x ⃗ + ϕ) = g 1(x ⃗ , −x ⃗) cos(k interf

(3)

is plotted, where I1, I2, and Iinterf describe the intensity patterns of the single arms and their combined image, respectively. The ⃗ quantities kinterf and ϕ describe the setup-defined interference wavevector and phase. The amplitude of the interference D

DOI: 10.1021/acs.nanolett.8b02705 Nano Lett. XXXX, XXX, XXX−XXX

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charge carrier diffusion length within the high-quality ZnO microwires to be in the range of one to somewhat larger than 2 μm. The results pave the way further for achieving tunable waveguides for propagating coherent quantum states operating at room temperature. As the velocity easily can be tuned by the excitation laser spot shape, those structures are promising for switching applications in transistor-like devices.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Telephone: +49 (0)341 9732619. Fax: +49 (0)341 9732668. ORCID

Figure 5. Spatial coherence g1(x⃗,−x⃗) extracted from the x = −2 μm line (wire-edge) as presented in the normalized intensity pattern in Figure 4d). The symbols represent a local fit for g1((−2 μm,z),− (−2 μm,z)) over one period of the interference pattern. The red line is a smoothed plot (Savitzky−Golay) of the data as guide to the eye. The minimum of the spatial coherence in the observable range can be found close to the excitation center around z = 0 μm.

Rüdiger Schmidt-Grund: 0000-0002-9655-9479 Author Contributions ‡

T.M. and M.W. carried out photoluminescence measurements, M.W. grew the microwire, T.M. analyzed the data, and R.S.-G. supervised the work. The manuscript was written by T.M. and R.S.-G. with contributions from all coauthors. Notes

The authors declare no competing financial interest.

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and 5 that the coherence is highest at the wire edges, away from the excitation center. This is because at the excitation center a nonvanishing population of uncoherent states is present, lowering the total coherence. Contrarily, away from the excitation center, only the emission from the highly coherent strongly coupled propagating WGM-polariton states is detectable, which preferentially couple out at the wire edges via their photonic component.34 The reason for g1 being always noticeably below unity can be found mainly in the fact that during the measurements vibrations of the sample were unavoidable, introducing intensity fluctuations in the emission on the one hand and a smearing of the interference fringes on the other hand. Furthermore, the single (interferometer-) arm measurements had to be performed separately, which together with the intensity fluctuations result in an uncertainty in the normalized intensity. In conclusion, coherent strongly coupled WGM polariton states propagating at room temperature in a ZnO microwire cavity over a distance of ≈±10 μm were demonstrated, where the observed extend of the coherent states was only restricted by the actual field of view of our setup. By changing the excitation spot size and thus the spatial shape of the complex refractive index profile we manipulated their wavevector and thus their propagation velocity from being higher than the temporal resolution of the used streak camera down to slow values of ≈1.5 μm/ps (≈0.5% of free space light velocity). By Michelson interferometry, we proved the spatial coherence g1(x⃗,−x⃗) of the entire system. We showed, that such propagating states, which are usually being described using the Gross−Pitaevskii formalism in the framework of exciton− polariton Bose−Einstein condensation,33 can be equivalently explained by ray-optical considerations taking into account the excitation laser-induced spatial refractive index profile. Further, we identified the gain mechanism to be recombination in an inverted electron−hole-plasma being present only in a small region of our cavity and thus only weakly perturbing but feeding the coherent WGM states, which represent strongly coupled exciton-polaritons in a noninverted system. From the modes’ energy blueshift above condensation threshold and by calculating the charge carrier density dependent complex refractive index, we estimated the

ACKNOWLEDGMENTS The authors thank S. Richter and C. Sturm for fruitful discussions. This work was funded by the Deutsche Forschungsgemeinschaft within Forschergruppe 1616 (SCHM2710/2) and Gr 1011/26-1.

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REFERENCES

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DOI: 10.1021/acs.nanolett.8b02705 Nano Lett. XXXX, XXX, XXX−XXX