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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 25 — Dec. 7, 2009
  • pp: 22452–22461
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Epitaxial quantum dots in stretchable optical microcavities

Tim Zander, Andreas Herklotz, Suwit Kiravittaya, Mohamed Benyoucef, Fei Ding, Paola Atkinson, Santosh Kumar, Johannes D. Plumhof, Kathrin Dörr, Armando Rastelli, and Oliver G. Schmidt  »View Author Affiliations


Optics Express, Vol. 17, Issue 25, pp. 22452-22461 (2009)
http://dx.doi.org/10.1364/OE.17.022452


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Abstract

Arrays of GaAs microring optical resonators with embedded InGaAs quantum dots (QDs) are placed on top of Pb(Mg1/3Nb2/3)O3-PbTiO3 piezoelectric actuators, which allow the microcavities to be reversibly “stretched” or “squeezed” by applying relatively large biaxial stresses at low temperatures. The emission energy of both QDs and optical modes red- or blue- shift depending on the strain sign, with the QD emission shifting more rapidly than the optical mode with applied strain. The QD energy shifts are used to estimate the strain in the structures based on linear deformation potential theory and the finite element method. The shift of the modes is attributed to both the physical deformation and the change in refractive index due to the photoelastic effect. Remarkably, excitonic emissions from different QDs are observed to shift at different rates, implying that this technique can be used to bring spatially separated excitons into resonance.

© 2009 OSA

1. Introduction

One of the basic requirements for studying and possibly making use of coupling phenomena between exciton and cavity mode, is the capability to tune the emission energy EX of an exciton into/out of resonance with the energy EM of an optical mode confined in the microcavity. For this reason, several approaches have been developed to shift EX relative to EM. Tuning methods are either irreversible or reversible. The former include the fabrication of cavities with EM closely matching a particular EX [11

11. A. Dousse, L. Lanco, J. Suffczyński, E. Semenova, A. Miard, A. Lemaître, I. Sagnes, C. Roblin, J. Bloch, and P. Senellart, “Controlled light-matter coupling for a single quantum dot embedded in a pillar microcavity using far-field optical lithography,” Phys. Rev. Lett. 101(26), 267404 ( 2008). [CrossRef] [PubMed]

,12

12. A. Badolato, K. Hennessy, M. Atatüre, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoglu, “Deterministic coupling of single quantum dots to single nanocavity modes,” Science 308(5725), 1158–1161 ( 2005). [CrossRef] [PubMed]

] or post-fabrication tuning of EM by digital etching [7

7. K. Srinivasan and O. Painter, “Linear and nonlinear optical spectroscopy of a strongly coupled microdisk-quantum dot system,” Nature 450(7171), 862–865 ( 2007). [CrossRef] [PubMed]

,13

13. K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atatüre, J. Dreiser, and A. Imamoğlu, “Tuning photonic crystal nanocavity modes by wet chemical digital etching,” Appl. Phys. Lett. 87(2), 021108 ( 2005). [CrossRef]

], dielectric deposition [14

14. X. D. Yang, C. J. Chen, C. A. Husko, and C. W. Wong, “Digital resonance tuning of high-Q/Vm silicon photonic crystal nanocavities by atomic layer deposition,” Appl. Phys. Lett. 91, 161114–1-3 ( 2007). [CrossRef]

], modification of the microcavity dielectric environment [15

15. A. Faraon, D. Englund, D. Bulla, B. Luther-Davies, B. J. Eggleton, N. Stoltz, P. Petroff, and J. Vučković, “Local tuning of photonic crystal cavities using chalcogenide glasses,” Appl. Phys. Lett. 92(4), 043123 ( 2008). [CrossRef]

], or local oxidation [16

16. K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoğlu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett. 89(4), 041118 ( 2006). [CrossRef]

]. Reversible and fine tuning techniques are required for detailed studies of the coupling [17

17. A. Laucht, F. Hofbauer, N. Hauke, J. Angele, S. Stobbe, M. Kaniber, G. Boehm, P. Lodahl, M.-C. Amann, and J. J. Finley, “Electrical control of spontaneous emission and strong coupling for a single quantum dot,” N. J. Phys. 11(2), 023034 ( 2009). [CrossRef]

] or/and to switch on/off the exciton-cavity interaction. The traditional method to reversibly tune EX into resonance with a mode with EX>EM consists in increasing the temperature T either of the full sample (see e.g. Ref. 2

2. J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 ( 2004). [CrossRef] [PubMed]

) or locally [18

18. A. Faraon, D. Englund, I. Fushman, J. Vučković, N. Stoltz, and P. M. Petroff, “Local quantum dot tuning on photonic crystal chips,” Appl. Phys. Lett. 90(21), 213110 ( 2007). [CrossRef]

], from the typical measurement temperatures of <10 K up to ~50 K. For higher T values the QD emission tends to quench and is affected by significant dephasing due to interaction with phonons, limiting the tuning range to less than ~1 meV. Other techniques have thus been developed, which allow EM and/or EX to be tuned while keeping T<10 K. Cavity modes can be smoothly red- or blue-shifted by gas condensation on the cavity surface [19

19. S. Mosor, J. Hendrickson, B. C. Richards, J. Sweet, G. Khitrova, H. M. Gibbs, T. Yoshie, A. Scherer, O. B. Shchekin, and D. G. Deppe, “Scanning a photonic crystal slab nanocavity by condensation of xenon,” Appl. Phys. Lett. 87(14), 141105 ( 2005). [CrossRef]

] or by laser-assisted gas desorption [20

20. A. Rastelli, A. Ulhaq, S. Kiravittaya, L. Wang, A. Zrenner, and O. G. Schmidt, “In situ laser microprocessing of single self-assembled quantum dots and optical microcavities,” Appl. Phys. Lett. 90(7), 073120 ( 2007). [CrossRef]

], without appreciably affecting EX. EM can also be modified by approaching a dielectric tip in the near-field of the cavity [21

21. F. Intonti, S. Vignolini, F. Riboli, A. Vinattieri, D. S. Wiersma, M. Colocci, L. Balet, C. Monat, C. Zinoni, L. H. Li, R. Houdre, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Spectral tuning and near-field imaging of photonic crystal microcavities,” Phys. Rev. B78,041401(R) ( 2008). [CrossRef]

]. Alternatively, a tip can be used to locally modify the strain of the structure [22

22. S. Mendach, S. Kiravittaya, A. Rastelli, M. Benyoucef, R. Songmuang, and O. G. Schmidt, “Bidirectional wavelength tuning of individual semiconductor quantum dots in a flexible rolled-up microtube,” Phys. Rev. B 78(3), 035317 ( 2008). [CrossRef]

]. EX can also be tuned independently from EM via the quantum confined Stark effect, as recently demonstrated for InGaAs/GaAs QDs embedded in the intrinsic region of microcavities containing a p-i-n structure [17

17. A. Laucht, F. Hofbauer, N. Hauke, J. Angele, S. Stobbe, M. Kaniber, G. Boehm, P. Lodahl, M.-C. Amann, and J. J. Finley, “Electrical control of spontaneous emission and strong coupling for a single quantum dot,” N. J. Phys. 11(2), 023034 ( 2009). [CrossRef]

,23

23. C. Kistner, T. Heindel, C. Schneider, A. Rahimi-Iman, S. Reitzenstein, S. Höfling, and A. Forchel, “Demonstration of strong coupling via electro-optical tuning in high-quality QD-micropillar systems,” Opt. Express 16(19), 15006–15012 ( 2008). [CrossRef] [PubMed]

]. This method is probably the most appealing for applications based on single-QD cQED, because of its integration with photonic devices, and the potentially high tuning rates (~GHz). The method requires however elaborate sample growth and processing, and the maximum tuning range is limited to a few meV by carrier tunneling at large electric fields.

In this Letter we report a simple fabrication method and optical investigation of GaAs optical microcavities containing InGaAs QDs, where EX and EM can be reversibly tuned by applying an external biaxial stress. To this aim, arrays of resonators are transferred on top of a Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT) piezoelectric actuator. From the practical point of view, the desired energy shift (here up to about ± 2 meV for EX) is achieved by simply applying a voltage bias V to the device (see Fig. 1(a)
Fig. 1 (a) Sketch of the experimental configuration including GaAs microrings with embedded InGaAs QDs, placed on top of a PMN-PT actuator. V and F are the applied voltage and electric field respectively. F produces an out-of plane expansion (contraction) and consequently and in-plane contraction (expansion) of the resonators (see arrows). (b), (c) SEM images of a GaAs microring before (b) and after (c) removal of the AlGaAs sacrificial layer. (d) Top-view optical microscopy image of an array of microrings after transfer onto the piezoelectric actuator via PMMA. (e) RT in-plane strain vs. electrical field F (see (a)).
). To demonstrate the flexibility of the approach, we have chosen micro-ring resonators, which, unlike microdisks [5

5. P. Michler, A. Kiraz, L. Zhang, C. Becher, E. Hu, and A. Imamoğlu, “Laser emission from quantum dots in microdisk structures,” Appl. Phys. Lett. 77(2), 184–186 ( 2000). [CrossRef]

7

7. K. Srinivasan and O. Painter, “Linear and nonlinear optical spectroscopy of a strongly coupled microdisk-quantum dot system,” Nature 450(7171), 862–865 ( 2007). [CrossRef] [PubMed]

], cannot be fabricated on top of GaAs by partial underetching. Compared to microdisks, microrings are advantageous for optical investigations of exciton-mode coupling by means of photoluminescence (PL) spectroscopy, as QDs located in the middle of a microdisk and hence away from the WGMs only produce an undesired background in PL or photon correlation measurements [5

5. P. Michler, A. Kiraz, L. Zhang, C. Becher, E. Hu, and A. Imamoğlu, “Laser emission from quantum dots in microdisk structures,” Appl. Phys. Lett. 77(2), 184–186 ( 2000). [CrossRef]

,8

8. J. Renner, L. Worschech, A. Forchel, S. Mahapatra, and K. Brunner, “Glass supported ZnSe microring strongly coupled to a single CdSe quantum dot,” Appl. Phys. Lett. 93(15), 151109 ( 2008). [CrossRef]

].

Optical modes with quality factors Q exceeding 1.2 × 104 are observed. The application of an external stress produces roughly linear shifts of EX and EM as a function of V, with EM shifting less than EX with applied strain. Unlike other tuning methods, we can achieve both red- and blue-shifts by simply changing the sign of V while keeping the samples at low temperature. Furthermore, no significant quenching of the QD luminescence is observed upon wide-range energy tuning. An intriguing aspect of strain tuning is that different excitonic emission lines attributed to different dots are observed to shift at remarkably different rates. This behavior, which we ascribe to inhomogeneous strain distribution across the microring, may allow spatially separated excitons to be coupled through a cavity mode.

2. Sample preparation and experimental setup

Microcavities were obtained from two samples #1 (#2) grown on semi-insulating GaAs(001) substrates by solid-source molecular beam epitaxy (MBE). After standard deoxidation and buffer growth, a 1 (0.8) μm thick sacrificial Al0.7Ga0.3As layer was deposited followed by the active structure. The latter consists of a layer of self-assembled InGaAs QDs located at the center of a 248 (206) nm thick GaAs layer. Sample #1 is characterized by QDs with low surface density (<108 cm−2) and was treated by rapid thermal annealing for 30 s at 955°C to blue shift the emission of the QDs from ~1.0 eV to ~1.3 eV. Sample #2 contains QDs with high density (>109 cm−2) and emission energies centered around 1.17 eV.

Standard electron beam lithography is used to define circular microrings in a double-layer of polymethylmethacrylate (PMMA: 200 K, 7% and 950 K, 2.5% from Allresist) resist. After thermal evaporation of 80 nm thick Ti and subsequent lift-off, the samples are etched using a 2:1:1 solution of HBr (48 vol% in H2O):K2Cr2O7 (0.5 mol/l in H2O):CH3COOH (pure) [5

5. P. Michler, A. Kiraz, L. Zhang, C. Becher, E. Hu, and A. Imamoğlu, “Laser emission from quantum dots in microdisk structures,” Appl. Phys. Lett. 77(2), 184–186 ( 2000). [CrossRef]

,6

6. E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett. 95, 067401- ( 2005). [CrossRef] [PubMed]

,24

24. A. Rastelli, A. Ulhaq, Ch. Deneke, L. Wang, M. Benyoucef, E. Coric, W. Winter, W. Mendach, F. Horton, F. Cavallo, T. Merdzhanova, S. Kiravittaya, and O. G. Schmidt, “Fabrication and characterization of microdisk resonators with In(Ga)As-GaAs quantum dots,” Phys. Status Solidi 3(11c), 3641–3645 ( 2006). [CrossRef]

]. A scanning electron microscopy (SEM) image of one of the GaAs/AlGaAs structures after Ti removal is shown in Fig. 1(b), where the material contrast between the upper GaAs-ring and the thick AlGaAs pedestal is clearly visible. The AlGaAs layer is then completely removed in HF (10% vol.), so that the microrings lie unbound on the GaAs substrate (see Fig. 1(c)) and can be transferred onto the piezoelectric actuators. The latter are pseudocubic [Pb(Mg1/3Nb2/3)O3]0.72-[PbTiO3]0.28 (lattice constant 4.022 Å, thickness: 300 μm) substrates overgrown with a thin (~20 nm) epitaxial layer of La0.7Sr0.3MnO3 (LSMO) acting as top contact [25

25. C. Thiele, K. Dörr, O. Bilani, J. Rödel, and L. Schultz, “Influence of strain on the magnetization and magnetoelectric effect in La0.7A0.3MnO3-PMN-PT(001) (A=Sr,Ca),” Phys. Rev. B 75(5), 054408 ( 2007). [CrossRef]

]. In order to prevent light absorption losses, the LSMO layer is coated with a dielectric layer consisting of 1 μm thermally evaporated SiOx followed by a 300-400 nm thick layer of PMMA (AR.P 671.04 from Allresist, spun for 1 min at 4500 rpm, and baked-out for 1 min at 120°C on a hotplate). Finally the GaAs substrate is gently pressed, face down, onto the actuator. The PMMA acts as “glue”, so that arrays of microrings can be efficiently transferred on the PMN-PT substrates, as shown in the optical microscopy image in Fig. 1(d). (We note that after the HF underetching step, which is performed manually, some rings are occasionally found displaced by a few hundred nm from the original position, so that other methods need to be used if accurate positioning is required.) By measuring the surface topography with atomic force microscopy (not shown), we have verified that rings lie on top of the PMMA layer and are not pressed into the PMMA layer. For optical characterization at low temperature (<10 K), the device is placed on top of a sapphire plate (see Fig. 1(a)) which provides both electric insulation and good thermal contact with the cryostat cold finger. A stripe of silver-paint on the sapphire is used to access the bottom contact of the PMN-PT while leaving the substrate free to deform.

We have chosen PMN-PT because it possesses one of the largest currently available piezoelectric responses, with an in-plane strain at room temperature (RT) of ~0.11% for an out-of-plane electric field F of 10 kV/cm (see Fig. 1(e)) [25

25. C. Thiele, K. Dörr, O. Bilani, J. Rödel, and L. Schultz, “Influence of strain on the magnetization and magnetoelectric effect in La0.7A0.3MnO3-PMN-PT(001) (A=Sr,Ca),” Phys. Rev. B 75(5), 054408 ( 2007). [CrossRef]

]. Upon reversal of the electric field direction, the ferroelectric crystal switches the orientation of its polarization P at the coercitive field |F| = Fc. The surface plane of the crystal is biaxially compressed when P and F are parallel, whereas antiparallel orientation of P and F results in biaxial expansion. In our experiments we have positively poled the crystals at RT so that positive bias corresponds to a compressive in-plane strain, see red curve in Fig. 1(e). While no low-temperature strain data is available thus far, we find here that in-plane compressive and tensile strains of at least 0.1% can be obtained for T<10 K. The sample was cooled while keeping F~10 kV/cm in order to maintain the poled state.

The optical characterization was performed in a standard micro-photoluminescence (PL) setup using a laser with wavelength of 532 nm as excitation source and a 500 or 750 mm focal length spectrometer equipped with a charge coupled device for detection. The laser is focused to a spot with diameter of about 1.5 µm (full width at half maximum) by means of a microscope objective, which is used also for PL collection. The devices are mounted in the vacuum compartment of a He-flow cryostat. PL measurements were performed as a function of laser power, applied voltage V and sample temperature T. The latter are used to discriminate excitonic emission lines and optical modes, since the former shift faster than the latter when T is increased (see, e.g. Fig. 3(a)
Fig. 3 (a) PL map from a microring (with similar parameters as in Fig. 2(a)) showing emission lines associated with cavity modes and excitons vs. temperature T. (b) PL map of the same ring vs. applied voltage at T = 4 K. One excitonic line (X1) and two modes (M1 and M2) are marked. (c) Emission energy EX1 of X1 vs. energy EM1 of M1 for temperature tuning (extracted from (a)) and for strain tuning (extracted from (b)). (d) Energy difference between M2 and M1 as a function of the EM1 for strain- and T-tuning.
).

3. Results and discussion

Figure 2
Fig. 2 (a) Color-coded PL intensity as a function of applied voltage V and emission energy E (PL map) for a ring obtained from sample #1 with Do/Di of ~4.3/2.1 µm and sitting on PMMA (see inset). The voltage is swept between 0 to 1 kV. (b) Plot of the energy shift vs. V for the excitonic emission line shifting in the range indicated by horizontal dashed lines in (a). (c) PL map of the same ring measured in (a) after deposition of a second layer of PMMA (see inset). (d) PL map for a ring obtained from sample #2 with Do/Di of~3.3/1.7 µm. Different lines shift at different rates and cross each other at specific values of the applied bias.
illustrates the behavior of excitonic emission lines in different rings as a function of voltage V applied to the PMN-PT substrates. The color plots (simply referred to as PL maps) represent the color-coded PL intensity (logarithmic scale) as a function of emission energy E and V. Figure 2(a) shows a PL map from a ring obtained from sample #1 and with outer/inner diameters Do/Di of ~4.3/2.1 µm excited with a laser power of 600 nW. Because of the low QD density in this sample, we focus on the sharp emission lines originating from excitons confined at alloy fluctuations in the InGaAs wetting layer. The voltage is swept several times between 0 and 1 kV with steps of 5 V/s and acquisition time 1 s, to demonstrate the reversibility of the tuning. A positive voltage results in an out-of-plane expansion of the PMN-PT crystal and consequent in-plane contraction (see Fig. 1(e)). The resulting biaxial compressive stress, which is transferred to the GaAs microrings through the PMMA/SiOx layers, leads to an increase of the energy bandgap of GaAs and InGaAs and thus a blue-shift of the emission lines. The emission energies of different lines show roughly linear shifts with the applied voltage at similar “rates” of ~1.3 μeV/V. (Lines shifting at lower rate originate from optical modes, which will be discussed later). A closer look at the emission peak between the dashed lines in Fig. 2(a) shows, however, slight deviations from a linear shift, with opposite curvature during voltage increase and decrease, and a slight hysteretic behavior (see Fig. 2(b)). With each additional cycle the emission energy at 0 bias slightly blue-shifts, so that the emission energy at V = 0 and V = 1 kV are respectively offset by ~130 and ~70 µeV after 2.5 cycles. (Only 2 cycles are shown in Fig. 2(a)).

For small strains we would expect a linear shift of the energy bandgap with applied strain. Deviations from linearity of the shifts with applied electric field can be primarily ascribed to a non-linear irreversible strain contribution from the PMN-PT substrate. While the RT strain vs. F characteristic shows no hysteresis and only a small deviation from linear behaviour if P is not switched (red curve in Fig. 1 (e)), increased non-linearity and hysteresis could occur at low temperatures. Additionally, a time-dependent creep results from slow changes of domain configuration after a change of the electrical field. Poled PMN-PT(001) has the advantage of a stable domain configuration (no wall displacements) under a changing field along the [001] direction [26

26. S. E. Park and T. R. Shrout, “Ultrahigh strain and piezoelectric behavior in relaxor based ferroelectric single crystals,” J. Appl. Phys. 82(4), 1804–1811 ( 1997). [CrossRef]

], but the poling cannot be done at the low working temperature since Fc is too large (F c > 37 kV/cm). Instead, RT poling and cooling at a field of 10 kV/cm have been applied, which may lead to an imperfectly poled state at low temperature. We note that whereas poled PMN-PT of the applied composition is considered as a normal ferroelectric, the unpoled state shows the slow relaxation phenomena of a relaxor ferroelectric [27

27. J. P. Han and W. W. Cao, “Electric field effects on the phase transitions in [001]-oriented (1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 single crystals with compositions near the morphotropic phase boundary,” Phys. Rev. B 68(13), 134102 ( 2003). [CrossRef]

]. By keeping V constant, we find that the creep tends to saturate within 5-7 min (not shown).

Remarkably, the maximum energy shift of excitonic lines ΔEX ~1.4 meV (see Fig. 2(b)) is already the highest reported so far for in situ tuning of the QD emission using stress applied from a piezoelectric substrate [28

28. S. Seidl, M. Kroner, A. Högele, K. Karrai, R. J. Warburton, A. Badolato, and P. M. Petroff, “Effect of uniaxial stress on exitons in a self-assembled quantum dot,” Appl. Phys. Lett. 88(20), 203113 ( 2006). [CrossRef]

]. The absolute shift can be doubled by inverting the polarity of V (see Fig. 3) and may be possibly extended by further increasing the electric field. (In this case thinner PMN-PT substrates would be required to keep voltages reasonably low). An alternative approach to further extend the tunability range of EX consists in coating the sample with a second layer of PMMA with a thickness similar to the first (see insets of Fig. 2(a) and (c)). A PL map of the same ring considered in Fig. 2(a) is shown in Fig. 2 (c). It is evident that the energy shifts for the same voltage range increase after PMMA coating. While prior to coating, lines shift at an average rate of (1.29 ± 0.22) µeV/V, the rate increases to (2.19 ± 0.13) µeV/V and the scatter in the energy shifts of different lines is reduced after complete encapsulation of the microcavities in PMMA. In the latter case, the sidewalls and top surface of the microcavity are not free to relax, so that the average strain in the structure increases, and the strain distribution becomes more uniform as confirmed by our finite-element method (FEM) calculations (see below).

Figure 2(d) shows a PL map for a ring obtained from sample #2 with Do/Di of ~3.3/1.7 µm. Different from the rings discussed above, excitonic lines in this ring are observed to shift at markedly different rates (with a maximum rate of ~2.7 µeV/V), so that two excitonic lines labeled as X1 and X2 merge at a voltage of ~890 V, whereas X2 and another line labeled as X3 cross at ~270 V. Similar behavior is observed also for rings with Do/Di of ~4.3/2.1 µm processed from sample #2. We qualitatively ascribe this to inhomogeneous distribution of strain in the rings, produced by the biaxial strain together with the strain relaxation at the ring sidewalls, and possibly an inhomogeneous adhesion of the rings to the PMMA layer.

We now turn our attention to the behavior of optical modes upon application of biaxial stress. Figure 3(a) shows a PL map for a ring similar to that considered in Fig. 2(a) when the temperature T is increased continuously (but not linearly) from 0 to 40 K at zero voltage. We observe both excitonic emission lines, such as that labeled as X1, and sharp optical modes, such as those labeled as M1 and M2, which we discriminate by their different dependence on T. Figure 3(b) shows a PL map of the same ring acquired at T = 4 K in a wide voltage range from −1.1 to 1.1 kV, with the sweep starting at 0 V. The width of the optical modes is close to the resolution limit of our PL setup, so that quality factors exceed 1.2 × 104. Both excitonic and mode lines shift in the same direction, and their energy shows a slightly non-linear dependence on V, as discussed previously. The excitonic emission energies EX shift at a rate of ~1.6 µeV/V, resulting in a full-range shift of ~3.81 meV. The mode energies EM shift at a lower rate of ~0.9 µeV/V, demonstrating that biaxial strain tuning can be used to scan EX through EM. X1 and M1 are in fact superimposed at 0 V, they become spectrally separated by 0.78 meV at 1.1 kV, and cross again with decreasing electric field. The second crossing occurs at a slightly negative voltage of about −100 V, which is ascribed to strain-creep and hysteresis. The fact that we can apply both large compressive and tensile strains is a consequence of the high coercitive fields of the PMN-PT substrate at low temperatures (∣Fc∣>37 kV/cm from the present experiment). This allows us to achieve EX = EM regardless of whether EX >EM or EX <EM at 0 bias, which is a noteworthy advantage over other tuning techniques.

Figure 3(d) shows the energy separation between the modes M2 and M1 ΔE = EM2- EM1 as a function of EM1 for strain and T tuning. For both data sets, ΔE increases slightly with compatible slopes of ~0.4, as determined from linear fits. The increase of ΔE with increasing EM1 is a direct consequence of the increased confinement, and no appreciable difference between T and strain tuning can be detected within the uncertainties of our measurement.

Since no data is at present available on the in-plane strain vs. electric field for PMN-PT at T<70 K, and no attempt was made to directly measure the strain on top of the PMMA layer, we have performed a calculation of strain-induced bandgap shift using FEM to estimate the magnitude of the biaxial strains in our microrings. The simulation also allows us to estimate the contributions of refractive index change and physical deformation to the mode energy shift. The studied system is modeled as a ring with the same nominal geometry of the ring discussed in Fig. 2(a,c). This ring is either placed on top of a PMMA and SiOx layer or completely embedded in PMMA to interpret the results shown in Fig. 2(a,c). Only a quarter of the ring (with symmetric boundary conditions) is considered in order to lower the required computational resources. The ring is placed on top of a 400 nm thick PMMA layer and 1 µm SiOx. The whole ring is assumed to be isotropic GaAs with Young’s modulus of 87 GPa and Poisson’s ratio of 0.31 while we consider PMMA (SiOx) to have a Young modulus of 7.5 (70) GPa and Poisson ratio of 0.35 (0.17) [30

30. M. Fukuhara and A. Sampei, “Low-temperature elastic moduli and internal dilational and shear friction of polymethyl methacrylate,” J. Polym. Sci. B 33(12), 1847–1850 ( 1995). [CrossRef]

,31

31. H. J. McSkimin, “Measurement of elastic constants at low temperatures by means of ultrasonic waves–data for silicon and germanium single crystals, and for fused silica,” J. Appl. Phys. 24(8), 988–997 ( 1953). [CrossRef]

]. The strain is applied by defining the displacement of the bottom surface of the SiOx layer. After strain relaxation, the bandgap energy shift ΔEg is calculated as:
ΔEg=a(εxx+εyy+εzz)b22((εxxεyy)2+(εyyεzz)2+(εzzεxx)2)+d2(εxy2+εyz2+εxz2),
(1)
where a = −8.33 eV, b = −1.7 eV, and d = −4.55 eV are the deformation potentials for GaAs. Because of the experimental uncertainties, we avoid the explicit calculation of the QD energy shift.

Figure 4(a)
Fig. 4 (a) Result from FEM calculation of the deformation of a ring on PMMA due to an applied 0.1% compressive strain on the PMN-PT substrate. The dashed curve represents the ring perimeter before application of strain and the displacement undergone by the ring is enlarged by a factor of 100. The calculated energy bandgap shift ΔEg in the QD plane due to strain is color coded. (b) ΔEg along one of the two strained axes and 45°-to-strained axis (dotted lines in (a)). Rings are assumed to be located on top of a PMMA layer (blue lines) or to be completely embedded in PMMA (red lines).
shows the deformation and the energy bandgap shift ΔEg due to an applied 0.1% compressive strain. Across most of the ring area (excluding the edges), blueshifts of 0.9-1.2 meV are observed (slightly lower than the maximum shifts observed in the experiment). Since we assume an isotropic material in the model, we attribute this spread of blueshifts to the directional dependence of the applied strain by the PMT-PT substrate. Including anisotropic properties of GaAs with random alignment of the crystallographic axes with respect to the substrate will further reduce the inhomogeneity of the observed profile. The FEM modeling of an embedded ring in PMMA is also shown in Fig. 4(b). We found that the shift is ~2.2 times larger than for the freestanding ring case. For numerical comparison, the ΔEg at the QD plane along a strained axis and 45° to a strained axis (dotted lines in Fig. 4(a)) are plotted in Fig. 4(b). From our simulation we also find that the strain at the bottom surface of the GaAs ring is reduced to about 25% of the value at the bottom surface of the SiOx layer, which is mainly due to the low stiffness value of PMMA even at low temperatures [30

30. M. Fukuhara and A. Sampei, “Low-temperature elastic moduli and internal dilational and shear friction of polymethyl methacrylate,” J. Polym. Sci. B 33(12), 1847–1850 ( 1995). [CrossRef]

]. This finding indicates that the large strains produced by PMN-PT could be more effectively transferred to the microring by either reducing the thickness of the PMMA layer or by replacing the PMMA with a stiffer material, resulting in a further increase in the energy tuning range.

Concerning the shift of optical modes due to the biaxial stress, it has been shown that this shift can be well described by first-order perturbation theory [32

32. C. W. Wong, P. T. Rakich, S. G. Johnson, M. Qi, H. I. Smith, E. P. Ippen, L. C. Kimerling, Y. Jeon, G. Barbastathis, and S.-G. Kim, “Strain-tunable silicon photonic band gap microcavities in optical waveguides,” Appl. Phys. Lett. 84(8), 1242–1244 ( 2004). [CrossRef]

,33

33. S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 ( 2002). [CrossRef] [PubMed]

]. However, we have performed here an analytic calculation of the WGMs. For the vertical confinement, the effective refractive index theory is applied. The effective refractive index is calculated using the transfer matrix method with a realistic layer structures as input. Conventional dispersion of the refractive index is assumed for GaAs [29

29. M. R. Brozel, and G. E. Stillman, eds., Properties of Gallium Arsenide (INSPEC: London, 1996)

]. The WGMs are calculated by matching the field profiles (magnetic field for TE and electric field for TM) at the inner and outer ring surfaces. When a compressive strain is applied, the mode shifts are calculated by first considering the geometry changes. For 0.1% compressive strain, the ring radius decreases by ~1 nm, while the circular shape is substantially preserved. The calculated mode energy shows a blueshift of 0.5 meV. This value is lower than the one observed in experiment (see Fig. 3(b)). However, by including the photoelastic effect [34

34. R. W. Dixon, “Photoelastic properties of selected materials and their relevance for applications to acoustic light modulators and scanners,” J. Appl. Phys. 38(13), 5149–5153 ( 1967). [CrossRef]

], the blueshift is enhanced by ~0.3 meV. Therefore, we attribute the optical mode shifts to the contribution of both geometric changes (due to strain) and the change in refractive index produced by the photoelastic effect.

4. Conclusion

In conclusion, we have presented a new method for in situ reversible tuning of the emission energy of localized excitons and optical modes in microcavities. The method is based on the use of a piezoelectric actuator (PMN-PT), which allows in-plane biaxial strains of at least 1 × 10−3 to be applied to microcavities at low temperature (<10 K). This is a remarkable result, as the maximum in-plane strains reported up to now for conventional lead-zirconate-titanate (PZT) at comparable temperatures are below 10−4 [35

35. M. Shayegan, K. Karrai, Y. P. Shkolnikov, K. Vakili, E. P. De Poortere, and S. Manus, “Low temperature in-situ tunable, uniaxial stress measurements in semiconductors using a piezoelectric actuator,” Appl. Phys. Lett. 83(25), 5235–5237 ( 2003). [CrossRef]

]. By taking advantage of the high coercive fields of PMN-PT at low temperature (>37 kV/cm), both blue- and red-shifts of the excitonic EX and mode EM emission energy can be achieved. Compared to temperature tuning, the application of strain produces smaller relative shifts |EX - EM |for a given shift in EX, due to the additional effect of strain in modifying the physical size of the resonator. On the other hand, substantially larger total shifts of |EX - EM | are obtained by strain (>1.7 meV), without appreciable deterioration of the excitonic linewidth and intensity. These values are comparable with those obtained by electric fields [17

17. A. Laucht, F. Hofbauer, N. Hauke, J. Angele, S. Stobbe, M. Kaniber, G. Boehm, P. Lodahl, M.-C. Amann, and J. J. Finley, “Electrical control of spontaneous emission and strong coupling for a single quantum dot,” N. J. Phys. 11(2), 023034 ( 2009). [CrossRef]

,23

23. C. Kistner, T. Heindel, C. Schneider, A. Rahimi-Iman, S. Reitzenstein, S. Höfling, and A. Forchel, “Demonstration of strong coupling via electro-optical tuning in high-quality QD-micropillar systems,” Opt. Express 16(19), 15006–15012 ( 2008). [CrossRef] [PubMed]

], where the maximum tunability range is limited by field-induced charge carrier tunneling. An appealing feature of strain tuning is that strain inhomogeneities can produce substantial relative shifts of different excitonic lines confined in different QDs in the same resonator. By combining strain with gas condensation/desorption [19

19. S. Mosor, J. Hendrickson, B. C. Richards, J. Sweet, G. Khitrova, H. M. Gibbs, T. Yoshie, A. Scherer, O. B. Shchekin, and D. G. Deppe, “Scanning a photonic crystal slab nanocavity by condensation of xenon,” Appl. Phys. Lett. 87(14), 141105 ( 2005). [CrossRef]

,20

20. A. Rastelli, A. Ulhaq, S. Kiravittaya, L. Wang, A. Zrenner, and O. G. Schmidt, “In situ laser microprocessing of single self-assembled quantum dots and optical microcavities,” Appl. Phys. Lett. 90(7), 073120 ( 2007). [CrossRef]

] it may be possible to tune simultaneously into resonance different dots with a cavity mode, which may allow for mode-mediated coupling of spatially separated quantum emitters [36

36. A. Imamoğlu, D. D. Awschalom, G. Burkard, D. P. Di Vincenzo, D. Loss, M. Sherwin, and A. Small, “Quantum Information processing using quantum dot spins and cavity QED,” Phys. Rev. Lett. 83(20), 4204–4207 ( 1999). [CrossRef]

].

Acknowledgment

The authors acknowledge H. S. Lee and B. Eichler for experimental assistance and S. Mendach, R. Hafenbrak and P. Michler for fruitful discussions. This work was supported by the DFG (FOR730, FOR520) and the BMBF (03X5518).

References and links

1.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81(5), 1110–1113 ( 1998). [CrossRef]

2.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 ( 2004). [CrossRef] [PubMed]

3.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 ( 2004). [CrossRef] [PubMed]

4.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 ( 2007). [CrossRef] [PubMed]

5.

P. Michler, A. Kiraz, L. Zhang, C. Becher, E. Hu, and A. Imamoğlu, “Laser emission from quantum dots in microdisk structures,” Appl. Phys. Lett. 77(2), 184–186 ( 2000). [CrossRef]

6.

E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett. 95, 067401- ( 2005). [CrossRef] [PubMed]

7.

K. Srinivasan and O. Painter, “Linear and nonlinear optical spectroscopy of a strongly coupled microdisk-quantum dot system,” Nature 450(7171), 862–865 ( 2007). [CrossRef] [PubMed]

8.

J. Renner, L. Worschech, A. Forchel, S. Mahapatra, and K. Brunner, “Glass supported ZnSe microring strongly coupled to a single CdSe quantum dot,” Appl. Phys. Lett. 93(15), 151109 ( 2008). [CrossRef]

9.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoğlu, “A quantum dot single-photon turnstile device,” Science 290(5500), 2282–2285 ( 2000). [CrossRef] [PubMed]

10.

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vučković, “Controlled phase shifts with a single quantum dot,” Science 320(5877), 769–772 ( 2008). [CrossRef] [PubMed]

11.

A. Dousse, L. Lanco, J. Suffczyński, E. Semenova, A. Miard, A. Lemaître, I. Sagnes, C. Roblin, J. Bloch, and P. Senellart, “Controlled light-matter coupling for a single quantum dot embedded in a pillar microcavity using far-field optical lithography,” Phys. Rev. Lett. 101(26), 267404 ( 2008). [CrossRef] [PubMed]

12.

A. Badolato, K. Hennessy, M. Atatüre, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoglu, “Deterministic coupling of single quantum dots to single nanocavity modes,” Science 308(5725), 1158–1161 ( 2005). [CrossRef] [PubMed]

13.

K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atatüre, J. Dreiser, and A. Imamoğlu, “Tuning photonic crystal nanocavity modes by wet chemical digital etching,” Appl. Phys. Lett. 87(2), 021108 ( 2005). [CrossRef]

14.

X. D. Yang, C. J. Chen, C. A. Husko, and C. W. Wong, “Digital resonance tuning of high-Q/Vm silicon photonic crystal nanocavities by atomic layer deposition,” Appl. Phys. Lett. 91, 161114–1-3 ( 2007). [CrossRef]

15.

A. Faraon, D. Englund, D. Bulla, B. Luther-Davies, B. J. Eggleton, N. Stoltz, P. Petroff, and J. Vučković, “Local tuning of photonic crystal cavities using chalcogenide glasses,” Appl. Phys. Lett. 92(4), 043123 ( 2008). [CrossRef]

16.

K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoğlu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett. 89(4), 041118 ( 2006). [CrossRef]

17.

A. Laucht, F. Hofbauer, N. Hauke, J. Angele, S. Stobbe, M. Kaniber, G. Boehm, P. Lodahl, M.-C. Amann, and J. J. Finley, “Electrical control of spontaneous emission and strong coupling for a single quantum dot,” N. J. Phys. 11(2), 023034 ( 2009). [CrossRef]

18.

A. Faraon, D. Englund, I. Fushman, J. Vučković, N. Stoltz, and P. M. Petroff, “Local quantum dot tuning on photonic crystal chips,” Appl. Phys. Lett. 90(21), 213110 ( 2007). [CrossRef]

19.

S. Mosor, J. Hendrickson, B. C. Richards, J. Sweet, G. Khitrova, H. M. Gibbs, T. Yoshie, A. Scherer, O. B. Shchekin, and D. G. Deppe, “Scanning a photonic crystal slab nanocavity by condensation of xenon,” Appl. Phys. Lett. 87(14), 141105 ( 2005). [CrossRef]

20.

A. Rastelli, A. Ulhaq, S. Kiravittaya, L. Wang, A. Zrenner, and O. G. Schmidt, “In situ laser microprocessing of single self-assembled quantum dots and optical microcavities,” Appl. Phys. Lett. 90(7), 073120 ( 2007). [CrossRef]

21.

F. Intonti, S. Vignolini, F. Riboli, A. Vinattieri, D. S. Wiersma, M. Colocci, L. Balet, C. Monat, C. Zinoni, L. H. Li, R. Houdre, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Spectral tuning and near-field imaging of photonic crystal microcavities,” Phys. Rev. B78,041401(R) ( 2008). [CrossRef]

22.

S. Mendach, S. Kiravittaya, A. Rastelli, M. Benyoucef, R. Songmuang, and O. G. Schmidt, “Bidirectional wavelength tuning of individual semiconductor quantum dots in a flexible rolled-up microtube,” Phys. Rev. B 78(3), 035317 ( 2008). [CrossRef]

23.

C. Kistner, T. Heindel, C. Schneider, A. Rahimi-Iman, S. Reitzenstein, S. Höfling, and A. Forchel, “Demonstration of strong coupling via electro-optical tuning in high-quality QD-micropillar systems,” Opt. Express 16(19), 15006–15012 ( 2008). [CrossRef] [PubMed]

24.

A. Rastelli, A. Ulhaq, Ch. Deneke, L. Wang, M. Benyoucef, E. Coric, W. Winter, W. Mendach, F. Horton, F. Cavallo, T. Merdzhanova, S. Kiravittaya, and O. G. Schmidt, “Fabrication and characterization of microdisk resonators with In(Ga)As-GaAs quantum dots,” Phys. Status Solidi 3(11c), 3641–3645 ( 2006). [CrossRef]

25.

C. Thiele, K. Dörr, O. Bilani, J. Rödel, and L. Schultz, “Influence of strain on the magnetization and magnetoelectric effect in La0.7A0.3MnO3-PMN-PT(001) (A=Sr,Ca),” Phys. Rev. B 75(5), 054408 ( 2007). [CrossRef]

26.

S. E. Park and T. R. Shrout, “Ultrahigh strain and piezoelectric behavior in relaxor based ferroelectric single crystals,” J. Appl. Phys. 82(4), 1804–1811 ( 1997). [CrossRef]

27.

J. P. Han and W. W. Cao, “Electric field effects on the phase transitions in [001]-oriented (1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 single crystals with compositions near the morphotropic phase boundary,” Phys. Rev. B 68(13), 134102 ( 2003). [CrossRef]

28.

S. Seidl, M. Kroner, A. Högele, K. Karrai, R. J. Warburton, A. Badolato, and P. M. Petroff, “Effect of uniaxial stress on exitons in a self-assembled quantum dot,” Appl. Phys. Lett. 88(20), 203113 ( 2006). [CrossRef]

29.

M. R. Brozel, and G. E. Stillman, eds., Properties of Gallium Arsenide (INSPEC: London, 1996)

30.

M. Fukuhara and A. Sampei, “Low-temperature elastic moduli and internal dilational and shear friction of polymethyl methacrylate,” J. Polym. Sci. B 33(12), 1847–1850 ( 1995). [CrossRef]

31.

H. J. McSkimin, “Measurement of elastic constants at low temperatures by means of ultrasonic waves–data for silicon and germanium single crystals, and for fused silica,” J. Appl. Phys. 24(8), 988–997 ( 1953). [CrossRef]

32.

C. W. Wong, P. T. Rakich, S. G. Johnson, M. Qi, H. I. Smith, E. P. Ippen, L. C. Kimerling, Y. Jeon, G. Barbastathis, and S.-G. Kim, “Strain-tunable silicon photonic band gap microcavities in optical waveguides,” Appl. Phys. Lett. 84(8), 1242–1244 ( 2004). [CrossRef]

33.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 ( 2002). [CrossRef] [PubMed]

34.

R. W. Dixon, “Photoelastic properties of selected materials and their relevance for applications to acoustic light modulators and scanners,” J. Appl. Phys. 38(13), 5149–5153 ( 1967). [CrossRef]

35.

M. Shayegan, K. Karrai, Y. P. Shkolnikov, K. Vakili, E. P. De Poortere, and S. Manus, “Low temperature in-situ tunable, uniaxial stress measurements in semiconductors using a piezoelectric actuator,” Appl. Phys. Lett. 83(25), 5235–5237 ( 2003). [CrossRef]

36.

A. Imamoğlu, D. D. Awschalom, G. Burkard, D. P. Di Vincenzo, D. Loss, M. Sherwin, and A. Small, “Quantum Information processing using quantum dot spins and cavity QED,” Phys. Rev. Lett. 83(20), 4204–4207 ( 1999). [CrossRef]

OCIS Codes
(160.2260) Materials : Ferroelectrics
(270.5580) Quantum optics : Quantum electrodynamics
(140.3945) Lasers and laser optics : Microcavities
(140.3948) Lasers and laser optics : Microcavity devices
(250.5590) Optoelectronics : Quantum-well, -wire and -dot devices

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: July 30, 2009
Revised Manuscript: October 30, 2009
Manuscript Accepted: October 30, 2009
Published: November 23, 2009

Citation
Tim Zander, Andreas Herklotz, Suwit Kiravittaya, Mohamed Benyoucef, Fei Ding, Paola Atkinson, Santosh Kumar, Johannes D. Plumhof, Kathrin Dörr, Armando Rastelli, and Oliver G. Schmidt, "Epitaxial quantum dots in stretchable optical microcavities," Opt. Express 17, 22452-22461 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-25-22452


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References

  1. J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81(5), 1110–1113 (1998). [CrossRef]
  2. J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004). [CrossRef] [PubMed]
  3. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004). [CrossRef] [PubMed]
  4. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007). [CrossRef] [PubMed]
  5. P. Michler, A. Kiraz, L. Zhang, C. Becher, E. Hu, and A. Imamoğlu, “Laser emission from quantum dots in microdisk structures,” Appl. Phys. Lett. 77(2), 184–186 (2000). [CrossRef]
  6. E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett . 95, 067401- (2005). [CrossRef] [PubMed]
  7. K. Srinivasan and O. Painter, “Linear and nonlinear optical spectroscopy of a strongly coupled microdisk-quantum dot system,” Nature 450(7171), 862–865 (2007). [CrossRef] [PubMed]
  8. J. Renner, L. Worschech, A. Forchel, S. Mahapatra, and K. Brunner, “Glass supported ZnSe microring strongly coupled to a single CdSe quantum dot,” Appl. Phys. Lett. 93(15), 151109 (2008). [CrossRef]
  9. P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoğlu, “A quantum dot single-photon turnstile device,” Science 290(5500), 2282–2285 (2000). [CrossRef] [PubMed]
  10. I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vučković, “Controlled phase shifts with a single quantum dot,” Science 320(5877), 769–772 (2008). [CrossRef] [PubMed]
  11. A. Dousse, L. Lanco, J. Suffczyński, E. Semenova, A. Miard, A. Lemaître, I. Sagnes, C. Roblin, J. Bloch, and P. Senellart, “Controlled light-matter coupling for a single quantum dot embedded in a pillar microcavity using far-field optical lithography,” Phys. Rev. Lett. 101(26), 267404 (2008). [CrossRef] [PubMed]
  12. A. Badolato, K. Hennessy, M. Atatüre, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoglu, “Deterministic coupling of single quantum dots to single nanocavity modes,” Science 308(5725), 1158–1161 (2005). [CrossRef] [PubMed]
  13. K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atatüre, J. Dreiser, and A. Imamoğlu, “Tuning photonic crystal nanocavity modes by wet chemical digital etching,” Appl. Phys. Lett. 87(2), 021108 (2005). [CrossRef]
  14. X. D. Yang, C. J. Chen, C. A. Husko, and C. W. Wong, “Digital resonance tuning of high-Q/Vm silicon photonic crystal nanocavities by atomic layer deposition,” Appl. Phys. Lett . 91, 161114–1-3 (2007). [CrossRef]
  15. A. Faraon, D. Englund, D. Bulla, B. Luther-Davies, B. J. Eggleton, N. Stoltz, P. Petroff, and J. Vučković, “Local tuning of photonic crystal cavities using chalcogenide glasses,” Appl. Phys. Lett. 92(4), 043123 (2008). [CrossRef]
  16. K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoğlu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett. 89(4), 041118 (2006). [CrossRef]
  17. A. Laucht, F. Hofbauer, N. Hauke, J. Angele, S. Stobbe, M. Kaniber, G. Boehm, P. Lodahl, M.-C. Amann, and J. J. Finley, “Electrical control of spontaneous emission and strong coupling for a single quantum dot,” N. J. Phys. 11(2), 023034 (2009). [CrossRef]
  18. A. Faraon, D. Englund, I. Fushman, J. Vučković, N. Stoltz, and P. M. Petroff, “Local quantum dot tuning on photonic crystal chips,” Appl. Phys. Lett. 90(21), 213110 (2007). [CrossRef]
  19. S. Mosor, J. Hendrickson, B. C. Richards, J. Sweet, G. Khitrova, H. M. Gibbs, T. Yoshie, A. Scherer, O. B. Shchekin, and D. G. Deppe, “Scanning a photonic crystal slab nanocavity by condensation of xenon,” Appl. Phys. Lett. 87(14), 141105 (2005). [CrossRef]
  20. A. Rastelli, A. Ulhaq, S. Kiravittaya, L. Wang, A. Zrenner, and O. G. Schmidt, “In situ laser microprocessing of single self-assembled quantum dots and optical microcavities,” Appl. Phys. Lett. 90(7), 073120 (2007). [CrossRef]
  21. F. Intonti, S. Vignolini, F. Riboli, A. Vinattieri, D. S. Wiersma, M. Colocci, L. Balet, C. Monat, C. Zinoni, L. H. Li, R. Houdre, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Spectral tuning and near-field imaging of photonic crystal microcavities,” Phys. Rev. B 78,041401(R) (2008). [CrossRef]
  22. S. Mendach, S. Kiravittaya, A. Rastelli, M. Benyoucef, R. Songmuang, and O. G. Schmidt, “Bidirectional wavelength tuning of individual semiconductor quantum dots in a flexible rolled-up microtube,” Phys. Rev. B 78(3), 035317 (2008). [CrossRef]
  23. C. Kistner, T. Heindel, C. Schneider, A. Rahimi-Iman, S. Reitzenstein, S. Höfling, and A. Forchel, “Demonstration of strong coupling via electro-optical tuning in high-quality QD-micropillar systems,” Opt. Express 16(19), 15006–15012 (2008). [CrossRef] [PubMed]
  24. A. Rastelli, A. Ulhaq, Ch. Deneke, L. Wang, M. Benyoucef, E. Coric, W. Winter, W. Mendach, F. Horton, F. Cavallo, T. Merdzhanova, S. Kiravittaya, and O. G. Schmidt, “Fabrication and characterization of microdisk resonators with In(Ga)As-GaAs quantum dots,” Phys. Status Solidi 3(11c), 3641–3645 (2006). [CrossRef]
  25. C. Thiele, K. Dörr, O. Bilani, J. Rödel, and L. Schultz, “Influence of strain on the magnetization and magnetoelectric effect in La0.7A0.3MnO3-PMN-PT(001) (A=Sr,Ca),” Phys. Rev. B 75(5), 054408 (2007). [CrossRef]
  26. S. E. Park and T. R. Shrout, “Ultrahigh strain and piezoelectric behavior in relaxor based ferroelectric single crystals,” J. Appl. Phys. 82(4), 1804–1811 (1997). [CrossRef]
  27. J. P. Han and W. W. Cao, “Electric field effects on the phase transitions in [001]-oriented (1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 single crystals with compositions near the morphotropic phase boundary,” Phys. Rev. B 68(13), 134102 (2003). [CrossRef]
  28. S. Seidl, M. Kroner, A. Högele, K. Karrai, R. J. Warburton, A. Badolato, and P. M. Petroff, “Effect of uniaxial stress on exitons in a self-assembled quantum dot,” Appl. Phys. Lett. 88(20), 203113 (2006). [CrossRef]
  29. M. R. Brozel, and G. E. Stillman, eds., Properties of Gallium Arsenide (INSPEC: London, 1996)
  30. M. Fukuhara and A. Sampei, “Low-temperature elastic moduli and internal dilational and shear friction of polymethyl methacrylate,” J. Polym. Sci. B 33(12), 1847–1850 (1995). [CrossRef]
  31. H. J. McSkimin, “Measurement of elastic constants at low temperatures by means of ultrasonic waves–data for silicon and germanium single crystals, and for fused silica,” J. Appl. Phys. 24(8), 988–997 (1953). [CrossRef]
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