Polariton Lasing in Micropillars With One Micrometer Diameter and Position-Dependent Spectroscopy of Polaritonic Molecules
U. Czopak, M. Prilmüller, C. Schneider, S. Höfling, G. Weihs
SSciPost Physics Submission
Polariton Lasing in Micropillars With One MicrometerDiameter and Position-Dependent Spectroscopy of PolaritonicMolecules
U. Czopak , M. Prilm¨uller , C. Schneider , S. H¨ofling , G. Weihs Institut f¨ur Experimentalphysik, Universit¨at Innsbruck, Innsbruck, Austria Technische Physik and Wilhelm-Conrad-R¨ontgen Research Center for Complex MaterialSystems, Universit¨at W¨urzburg, W¨urzburg, Germany Institute of Physics, University of Oldenburg, 26129 Oldenburg, Germany* [email protected] 9, 2021
Abstract
Microcavity polaritons are bosonic light-matter particles that can emit coherentradiation without electronic population inversion via bosonic scattering. Thisphenomenon, known as polariton lasing, strongly depends on the polaritons’ con-finement. Shrinking the polaritons’ mode volume increases the interactions me-diated by their excitonic part, and thereby the density-dependent blueshift ofthe polariton to a higher energy is enhanced. Previously, polariton lasing hasbeen demonstrated in micropillars with diameters larger than three microns, ingrating based cavities, fiber cavities and photonic crystal cavities. Here we showpolariton lasing in a micropillar with one micron diameter operating in a singletransverse mode that can be optimally coupled to a singlemode fiber. We geo-metrically decouple the excitation with an angle from the collection. From thenumber of collected photons we calculate the number of polaritons and observea blueshift large enough to qualify our device for novel schemes of quantum lightgeneration such as the unconventional photon blockade. To that end, we also ap-ply angled excitation to polaritonic molecules and show site-selective excitationand collection of modes with various symmetries.
Strong optical nonlinearities are a key component for many quantum information processingapplications [1]. Conventional lasers are nowadays widely used for linear optical commu-nication, however, the intrinsic Poissonian photon number distribution of a laser limits itsusefulness for most quantum protocols that aim to process individual quanta of light [2]. Byconfining light in tiny resonators that are comparable in size to its wavelength, the light-matterinteraction in the solid can be strongly enhanced. For example, quantum dots embedded inthe antinode of a micropillar cavity brought great advances towards perfect single photonsources [3], but scaling up to multiple indistinguishable devices is difficult because the spa-tial and spectral alignment of the quantum dots is non trivial. Excitons in two-dimensional1 a r X i v : . [ phy s i c s . op ti c s ] F e b ciPost Physics Submission quantum wells and atomically thin crystals can couple strongly to a cavity’s radiation field re-sulting in hybrid light-matter polariton modes [4–6]. In polaritonic micropillars many nonlin-ear many-body physics phenomena have been demonstrated, including polariton lasing [7, 8],and just recently, first indications of single quantum effects have been observed in highlyengineered fiber cavities [9, 10].Microcavity exciton-polaritons result from a superposition of a cavity photon and a quan-tum well exciton, i.e. a bound electron-hole pair [11, 12]. These bosonic quasi-particles ef-fectively introduce an optical nonlinearity to the radiation field inherited from the electronicinteractions of their matter part. In contrast to conventional lasers that need to be drivento an electronic population inversion, polariton lasers emit coherent light through enhancedbosonic scattering into a common state [7,13,14]. Given the light mass polaritons inherit fromtheir photonic part, this effect, which is closely related to Bose-Einstein condensation [15],already happens at moderately cryogenic temperatures in gallium arsenide, and even at roomtemperature for organic polaritons and atomically thin crystals with their much tighter boundexcitons [16–19]. The threshold for the onset of enhanced coherence is much lower withoutthe need for a population inversion, and the scattering into a common state enables measuringthe particle-density dependent blueshift.Confining polaritons to a small volume enhances the electronic interactions, alters thelight-matter coupling and thereby lowers the lasing threshold and increases the blueshift[20,21]. The ultimate goal would be a blueshift per polariton that is bigger than its linewidth,paving the way for achieving the so-called photon blockade [22] in the solid state [23], whichfilters single photons out of a conventional laser’s radiation. For the blockade to becomestrong, it was calculated that the polariton mode volume must not be larger than a cubicwavelength in the material [23,24]. An alternative approach termed the unconventional photonblockade uses the interference of two weakly nonlinear coupled modes to achieve photonnumber squeezing [25]. Strong photon antibunching is predicted even if the blueshift is twoto three orders of magnitude smaller than the linewidth [26]. However, as the required meaninput power versus the resulting antibunching strength scales with the nonlinearity, increasingthe nonlinearity is still desirable. We show here that the nonlinear blueshift is indeed muchenhanced by confining polaritons in small micropillars. In addition the expected weak signalcan be optimally coupled to single mode fibers and fast and sensitive single photon detectors,as micropillars have an excellent mode overlap with singlemode fibers [3].In this article we study polaritonic micropillars with diameters ranging from 3 µ m downto 1 µ m and analyze their nonlinear optical properties. To do so, we employ excitation underan angle to the sample plane. This technique was originally developed to excite quantumdot nanowires [27]. We show here that this in principle filter-free excitation technique alsoworks for micropillar cavities with diameters down to 1 µ m, making our approach attractivefor experiments with quantum dots in micropillars as well. The angled excitation allowsus to directly address the quantum wells of any pillar on the sample while collecting allthe light they emit perpendicular to the sample plane. This approach makes it easier tooptically address tiny structures close to the optical diffraction limit, which is otherwisechallenging in cryogenic environments. We observe polariton lasing accompanied by a blueshiftof 28 µ eV per polariton in a 1 µ m-sized pillar with a minimal linewidth of 149(5) µ eV. Inaddition, we also apply the angled excitation to study so-called polaritonic molecules. Weshow that we can selectively excite symmetric and antisymmetric polaritonic modes that occurin such overlapping micropillars [28]. In similar systems fascinating nonlinear many-bodyphysics has been shown, including polariton condensation [29], Josephson oscillations and2 ciPost Physics Submission self-trapping [30], bistability [31] and periodic squeezing [32]. Studying polaritonic moleculeswith geometrically decoupled excitation and collection demonstrates a promising avenue toinvestigate single-particle nonlinearities mediated by the unconventional polariton blockade.The structure of the paper is as follows: After an introduction to microcavity polaritonswe describe our experimental setup and semiconductor sample. Subsequently, we present ourresults for lasing in single pillars, and our results for the position-dependent excitation ofpolaritonic molecules. Polaritons are bosonic mixed light-matter particles resulting from the strong coupling be-tween a quantum well exciton (creation operator b † ) at energy E X and a microcavity photon(creation operator a † ) with energy E C . The effective Hamiltonian reads [23]: H eff = E X b † b + E C a † a + ¯ h Ω R ( ba † + b † a ) + V XX b † b † bb − V S ( b † b † ab + a † b † bb ) (1)with Ω R being the vacuum Rabi frequency, i. e. the rate at which exciton and photon arestrongly coupled and exchange energy. This rate depends on the exciton’s dipole moment,which is a function of the design of the quantum wells, its’ material and dimensions, andthe electric field strength which depends on the cavity’s dimensions. A measurement on anunetched part of our cavity yields a value of Ω R ≈ V XX from its exciton part, mainly due to the exchange ofcarriers [34, 35], and an additional, weaker nonlinearity is caused by the saturation of theexciton’s oscillator strength V S [36]. For a two-dimensional exciton with binding energy E B and Bohr radius a B the interaction constants read V XX A ≈ E B a B ; V S A = 8 π h Ω R a (2)for a system area A [33]. The binding energy E B and the Bohr radius a B are in generala function of the quantum well’s material and dimensions [37]. In (In)GaAs quantum wellsthe Bohr radius is about 5 nm to 15 nm and the binding energy between 4 meV to 30 meV,depending on the well’s thickness and material composition. If we take the values from[37] for a 3 nm thick quantum well we have E B = 30 meV and a B = 5 nm which yields V XX = 4 . µ eV µ m and V S = 2 . µ eV µ m . The resulting polariton-polariton interaction forthe here considered lower polariton in one spin configuration depending on the exciton fraction X (0.8) and photon fraction C (0.2) is [12] V LP = | X | V XX + 2 | X | XCV S = 2 . µ eV µ m . InReference [23] a factor of 2 . / (2 R ) was suggested for a cylindrically confining potential, with R being the radius of the cylinder. This yields blueshifts of 6 . µ eV, 1 . µ eV and 0 . µ eV perpolariton for micropillars with diameters of 1 µ m, 2 µ m, and 3 µ m, respectively. In addition,an incoherent blueshift from excitons created by the pump that do not couple to the lightfield can be significant [38]. Details about the dynamics behind polariton lasing can be foundin [12, 13, 39]. 3 ciPost Physics Submission In order to realize decoupled excitation and collection, the Janis ST-500 flow cryostat ismounted on a horizontal translation stage and so allows moving the sample with respect tothe fixed aspheric collection lens with a numerical aperture of 0.68 mounted above (see figure1). In this way, all the radiation emitted from the pillar can be collected.
Pulsed LaserSpectrometerCCD Piezoactuator
Figure 1: The setup allows moving the micropillar sample in both transverse directions,coarsely by fine adjustment screws and by computer-controlled piezo actuators for fine ad-justments. The excitation can be aligned independently by a single mode fiber with a focuserat the output mounted on translation stages next to the cryostat. A fixed asphere collimatesthe radiation from the micropillars and sends it to a spectrometer where the emission isrecorded. For the position dependent spectroscopy in section 4.3 an automated measurementsets the piezo position and takes a spectrum for each position.A long-distance micro-focuser delivers the beam for the angled excitation (Sch¨after undKirchhoff 5M) from an attached polarization-maintaining optical fiber. A Titanium::Sapphirelaser with a repetition rate of 80 MHz at a wavelength of 820 nm (1 .
512 eV) and a pulse lengthof 10 ps is used for above-band excitation. Because the focal length of the focusing lens f focus is smaller than that of the collimating lens f coll the resulting spot size is smaller than the modefield diameter MFD of the singlemode fiber (Φ Spot = f focus f coll MFD). In our case this correspondsto ≈ µ m, if we do not consider distortions due to the cryostat window. The whole excitationoptics is mounted on a five-axis stage designed in a way to control the excitation in all threetranslational dimensions plus two angles (see figure 1). A spectrometer (Acton SP 2750) isused to measure the spectrum of the light emitted by the nanostructures on a nitrogen-cooledCCD camera. This allows us to measure the number of photons resolved in spectral photonenergy and consequently to estimate the nonlinear interaction strength of the polaritons andthe resulting blueshift.In order to estimate the number of polaritons that contribute to one measured spectrumwe calculate the spectrometer efficiency to be 9 . ciPost Physics Submission Component Efficiency3x Al+MgF Mirror 0.87(3)1500 Grooves/mm Grating 0.62(5)Aperture Loss / Mode Match 0.75(25)CCD Quantum Efficiency 0.65(5)Electronic Gain 0.50(5)Total 0.099(36)Table 1: Factors contributing to the spectrometer efficiencyThus ≈ . Our cavities consist of two GaAs/AlGaAs DBR mirrors grown by molecular beam epitaxy(MBE). A λ -cavity between the two DBR mirrors hosts six 3 . R ≈ µ m to 5 µ m, and for each diameter so-called photonic molecules consistingof two overlapping pillars with center-to-center distances ranging from 50 % to 100 % of thepillar diameter are defined. Because the MBE growth rate decreases from the center of thewafer to its edge, we achieve a wide range of cavity lengths and thus different exciton-photondetunings. 5 ciPost Physics Submission λ -Cavity with 6 Quantum WellsExcitation + - + - + - + - + - + - + - + - Figure 2: An SEM picture of a polaritonic molecule with a pillar diameter of 3 µ m and acenter-to-center distance of 2 . µ m (see scale bar). The λ/ To investigate the nonlinear effects in single polaritonic micropillars we start our investigationby scanning the power of the excitation laser (described in Section 3) and analyze the recordedspectra. We rotate a half-wave plate in front of a polarizer to control the laser power andrecord spectra for a series of excitation powers. The maximum laser power measured directlyafter the excitation lens is approximately 4 mW. The actual power injected into the quantumwells, however, is a function of the excitation spot size relative to the pillar diameter and thesize of the quantum wells and is thus significantly smaller. The coupling is further reducedby wavefront abberations caused by the convergent laser beam passing through the cryostat’swindow and the small effective cross section of the quantum wells when projected onto thelaser beam axis. In Figure 3 a), c), and e) we show a representative selection of spectratogether with a Gaussian fit to the polariton mode with the lowest energy. Although the cavityline should have a Lorentzian shape, the observed peaks show better overlap with Gaussianfunctions. In the low power spectra the onset of lasing is visible, while in the high powerones the shape of the peaks with maximum blueshift can be seen. From the Gaussian fits weextract the peak emission intensity (normalization constant) and the linewidth (FWHM) andplot these against a linearized excitation power axis in figure 3 b), d), and f). The blueshiftis analyzed in the next chapter (Section 4.2). 6 ciPost Physics Submission
Excitation Power (P/P Th ) P ea k E m i ss i on I n t en s i t y ( a . U . ) Emission Intensity L i ne w i d t h F W H M ( m e V ) b) Linewidth and Intensity 3µm Linewidth
Excitation Power (P/P Th ) P ea k E m i ss i on I n t en s i t y ( a . U . ) Emission Intensity L i ne w i d t h F W H M ( m e V ) d) Linewidth and Intensity 2µm Linewidth
Excitation Power (P/P Th ) P ea k E m i ss i on I n t en s i t y ( a . U . ) Emission Intensity L i ne w i d t h F W H M ( m e V ) f) Linewidth and Intensity 1µm Linewidth
Figure 3: In a), c), and e) we show spectra recorded for different excitation powers frommicropillars ranging from 3 µ m to 1 µ m in diameter. The grey layer indicates the center of theemission at the lowest excitation power to serve as a guide to the eye for the relative blueshiftat higher powers. While for the 3 µ m pillar there are still three lower polariton modes present,single mode operation becomes evident in the 1 µ m pillar. Due to the photonic confinementthe lowest energy mode is at higher energy for smaller pillars. At about 1 .
468 eV a broadpeak from excitons that do not couple to the cavity is visible. For the lowest power this is thedominant emission feature, then higher order polariton modes get populated and at highestexcitation powers most of the population is in the fundamental mode. The linewidth and peakheight of the Gaussian fits to the fundamental mode are shown in b), d), and f). Above acertain threshold excitation power P Th the peak height grows in a nonlinear way accompaniedby a decline in linewidth. Both are evidence for polariton lasing. The linewidth broadeningat higher powers is caused by temporal integration over the ringdown from higher to lowerblueshifts as the population decays after the excitation pulse.7 ciPost Physics Submission The effect of shrinking pillar sizes on the nonlinear emission properties can be clearly seenin Figure 3. For smaller pillars fewer modes are present and the fundamental photonic modegets blueshifted. This effect makes the polaritons more exciton-like, which in addition to thehigher exciton-exciton interaction energy in a smaller reservoir enhances the blueshift. Thehigh and low power emission peaks overlap at the low energy side of the spectrum becausewe integrate over the ringdown from high to low occupation. Therefore, one would expectan asymmetric peak shape that shows the actual linewidth on its high energy side. This canbe seen to some extent for the high power spectrum of the 2 µ m pillar (purple line in Figure3 c). This effect also seemingly broadens the linewidth for higher excitation powers and toextract more meaningful values of the linewidth we fit Gaussian functions to the high energyside of the peaks. For the two bigger pillars we see a decline in linewidth while approachingthe lasing threshold, which is characteristic for polariton lasing, and a broadening thereaftercaused by the blueshift and the ringdown to lower energies. In the 1 µ m pillar the lasingthreshold is so low that the linewidth already starts at a minimal value. The lowest value forthe linewidth we measure here is 73 µ eV (FWHM) corresponding to a Q -factor of 20000(1570).In the 2 µ m pillar however the linewidth seems to decrease again for powers over 1.5 times thethreshold. This could be related to some mode competition as the fundamental mode here ismuch more enhanced at higher powers than in the 3 µ m pillar, while no higher modes existat all in the 1 µ m pillar. In addition, in the fit to the highest power spectrum the asymmetricpeak shape is even less compatible with a Gaussian than for the other data. The singlemodenature of the 1 µ m pillar lowers its lasing threshold in comparison to its bigger counterparts,and also increases the interaction-related blueshift. Due to this extreme blueshift the peakbroadens more in width than it grows in height. This also explains the bigger linewidththat we observe in this structure, as the particle number fluctuation is expected to obeyPoissonian statistics [40]. The fact that we see lasing in such a tiny structure demonstratesthe high quality of our semiconductor sample and optical setup. To the best of our knowledgeour device is among the smallest polariton lasers reported in the literature so far [21, 41, 42].The extreme blueshift that we observe motivates an estimate of the number of contributingpolaritons, which we perform in the following section. In order to determine the absolute magnitude of the blueshift it is crucial to know how manypolaritons contributed to it. To this end we follow references [20, 43] and count the photonsthat are recorded by the spectrometer. As outlined in Section 3 we can roughly estimate thenumber of photons in front of the spectrometer if we multiply the total counts that contributedto a peak by 10(4). We calculate the total counts by summing over all the CCD photoelectroncounts in a peak corrected for the background level. To obtain the number of photons per pulsewe have to divide the total counts by the number of laser pulses during one CCD exposuretime 12 . ·
80 MHz = 984000. Assuming equal photon and exciton contributions we expecthalf the polaritons to decay non-radiatively as excitons and the other half to exit the cavityas photons and enter the spectrometer. Plotting the blueshift from the fits of the powerseries against the number of polaritons we infer an estimate of the nonlinearity per particle.A possible caveat here is our off-resonant excitation that creates an excitonic background,which also blueshifts the polaritons. Another possible problem are potential dark backgroundstates, which could in principle live much longer than the 12 . ciPost Physics Submission Estimated Mean Polariton Number B l ue s h i ft ( e V ) -3 Blueshifts
Figure 4: Plotting the center energy shift as a function of the extimated occupation numbershows that smaller pillars exhibit a much bigger blueshift than larger ones. The solid linesare linear fits to a subset of data points at high occupation number to extract the asymptoticbehavior.The blueshifts in Figure 4 seem to show a logarithmic dependence on the occupationnumber, as it was also seen in Reference [8]. However, for very low powers the majority of theexcitations in the quantum well are bare excitons, as can be seen in the low power spectra inFigure 3. The absolute amount of these uncoupled excitons is difficult to estimate because theyare not expected to decay into the cavity mode that is coupled into the spectrometer. Fromthe slope of the linear fits we get a blueshift of 28 µ eV, 18 µ eV and 13 µ eV per polariton, forthe 1 µ m, 2 µ m and 3 µ m pillar respectively. Our measurements agree well with the theoreticalpredictions for interaction constants of exciton-polaritons and are within the broad range ofresults reported in the literature so far. The inverse proportionality between the nonlinearityand the transverse confinement, as discussed in the theory section (2), is clearly demonstrated.A recent overview of comparable measurements can be found in [43]. In comparison to thatreference our results are an order of magnitude higher, but significantly higher nonlinearitieshave been reportet for InGaAs quantum wells. We emphasize that we use a structure witha quite exotic arrangement of InGaAs quantum wells. They are much thinner and closer toeach other than what is commonly used, and the changes of the exciton’s properties and lightcoupling are difficult to estimate theoretically, especially given the tight spatial confinementin our micropillars. Polariton lasing was mostly studied using GaAs quantum wells, althoughInGaAs offers certain advantages for polariton lasing [45]. Therefore, observing such a strongblueshift here is surprising and encouraging.In previous works it was assumed that the threshold for lasing occurs at a mean occupationof one. This matches our findings, as we find a occupation of around one between the third9 ciPost Physics Submission and the fourth measurement point for the 1 µ m pillar and between the seventh and the eigthfor the 2 µ m and 3 µ m pillars, exactly at the lasing threshold indicated in figure 3 b, d, e.Although it would be interesting to determine the absolute threshold excitation power this isnot possible here due to limitations discussed in section 4.1. The results obtained motivatefurther, more sophisticated measurements. Suggested improvements include to resonantlyexcite polaritons with a repetition cycle lower than the lifetime of any dark states in thesystem and to precisely calibrate the intensity measurement. Resonant excitation under anangle from the side is a big advantage towards that goal because then all the radiation leavingthe pillar can be collected.In summary in this section we used our angled excitation to show lasing in single pillarswith diameters ranging from 1 µ m to 3 µ m. Features of lasing were shown for each and thedependence of the magnitude of the blueshift on the pillar size was clearly demonstrated. Inaddition it could be interesting to study the dynamics of the power-dependent emission in themultimode pillars for various exciton-photon detunings and excitation locations, but this isbeyond the scope of this paper. In addition we perform position-dependent spectroscopy on polaritonic molecules such as theone in Figure 2. This is similar to what was shown in [29], however we continuously changethe excitation location, and in addition our approach makes it possible to excite one pillarand collect from the other. The excitation and collection lenses are kept stable and thepolaritonic molecule is moved along its main axis by a piezo actuator in the translation stagesbelow the cryostat. Depending on the individual mode’s field strength at the excitationlocation different modes are excited. For example, if the molecule is excited at the centerbetween the two pillars, no antisymmetric modes are excited and detected because they havea node there. We demonstrate this effect by showing two different spectra of a molecule witha pillar diameter of 3 µ m and center-to-center separation of 2 . µ m. One spectrum is recordedfor excitation at the center between the two pillars and the other at the center of one pillar(Figure 5a). The big advantage of this approach is demonstrated by scanning the cryostat’sposition along the molecules axis, thereby collecting spectra for each position. The recordedspectra assembled together in a two dimensional density plot clearly show the mode structureof the polaritonic molecule under investigation. As in a simple double well potential, thefundamental mode is symmetric, followed by an anti-symmetric mode with one node in thecenter, then another symmetric mode with two nodes symmetric around the center and soon. Thus, modes with similar symmetry appear at similar excitation locations (see figure 6).10 ciPost Physics Submission Emission Energy (eV)
CCD C oun t s () Exication on one Pillar at 1.3µmExcitation between the Pillars at 0µm Figure 5: The orange line in the left plot shows a spectrum taken when we excite a polaritonicmolecule in its center between the two pillars. The symmetric fundamental mode is stronger inthis case. The blue line, in contrast, shows a spectrum recorded when we excite the moleculecentral on one pillar. In this case antisymmetric modes are stronger. On the right side weassemble 98 spectra in a density plot and interpolate between them. The colorbar shows therespective CCD counts.In this way we can study the mode structure of polaritonic molecules and measure thetunneling constant. From the data above we exctract a value of J=340 µ eV.To validate our experimental results and understand the physical mechanisms we per-formed simulations in Lumerical FDTD Solutions. Dipoles that excite a purely photonicmolecule with same dimensions as in our experiment are swept along 99 positions on themolecule axis and for each position a spectrum is computed. This corresponds to our mea-surement where we excite excitons site-selectively along the molecule’s axis. -4 -2 0 2 4 Dipole Position (µm) M ode E ne r g y ( e V ) Figure 6: The FDTD Simulation shows qualitative similar results as the measurements whenwe move the dipoles that excite the modes on the molecules axis and assemble the spectratogether as before. For illustration, on the right side we show the field amplitude of lowestorder modes computed in the eigenmode solver.Both individual and the assembled spectra one clearly sees the first two branches of sym-11 ciPost Physics Submission metric and antisymmetric modes, separated by an energy splitting that depends on the pillarseparation and is equal to two times the tunnel constant J . An important difference betweenmeasurement and simulation is that the dipoles in the simulations are point like emitters,whereas in the measurement we create excitons over the whole spot size. Additionally, in apolaritonic molecule the exciton-photon detuning plays a big role in the dynamics that deter-mine which mode gets populated most strongly. Our technique can be used to routinely scanentire samples, facilitated by independent control over excitation and collection. By furtherimproving the optical performance, for example by positioning the lens inside the cryostat, itshould be feasible to selectively drive desired modes at one location on the molecule resonantlyand collect from the other one. This could pave the way to more sophisticated experimentssuch as the unconventional polariton blockade. We used angled excitiation of polaritonic micropillars and observed their nonlinear behavior inpolariton lasing. In the 1 µ m sized pillar we observed an extremely strong blueshift of 28 µ eVper polariton, witness to high nonlinearities and a promising result towards the unconventionalphoton blockade. In addition, we applied our excitation technique to polaritonic moleculesand compared the results to simulations. Further improving the optical performance, forexample by placing the lenses inside the cryostat, angled excitation could also work for theresonant case. That is also interesting for micropillars hosting quantum dots as there is noneed to filter the pump light then. We hope that the presented techniques and experimentsopen the way to studies with strongly interacting polaritons in the single particle regime. Acknowledgements
We acknowledge help in setting up the FDTD Simulations by S. Betzold. Support by K.Winkler, M. Emmerling and A. Wolf in sample fabrication is acknowledged. We thank R.Keil, R. Chapman and S. Frick for helpful comments to the manuscript. N. Gulde form RoperScientific we thank for informations about the spectrometer.
Author contributions
UC performed the measurements, analyzed the data, wrote themanuscript and evaluated the simulation. MP helped to set up the measurement. CS andSH designed and fabricated the micropillar sample. GW supervised the project. All authorscontributed comments to the manuscript.
Funding information
We thank the Austrian Science Fund FWF for supporting this workthrough project I2199. UC and MP received funding from the Austrian Science Fund (FWF),Grant No. W1259, “DK-AL” 12 ciPost Physics Submission
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