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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 3 — Feb. 6, 2006
  • pp: 1094–1105
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Cavity Q, mode volume, and lasing threshold in small diameter AlGaAs microdisks with embedded quantum dots

Kartik Srinivasan, Matthew Borselli, Oskar Painter, Andreas Stintz, and Sanjay Krishna  »View Author Affiliations


Optics Express, Vol. 14, Issue 3, pp. 1094-1105 (2006)
http://dx.doi.org/10.1364/OE.14.001094


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Abstract

The quality factor (Q), mode volume (V eff ), and room-temperature lasing threshold of microdisk cavities with embedded quantum dots (QDs) are investigated. Finite element method simulations of standing wave modes within the microdisk reveal that Veff can be as small as 2(λ/n)3 while maintaining radiation-limited Qs in excess of 105. Microdisks with a 2 μm diameter are fabricated in an AlGaAs material containing a single layer of InAs QDs with peak emission at λ = 1317 nm. For devices with Veff ~2 (λ/n)3, Qs as high as 1.2× 105 are measured passively in the 1.4 μm band, using an optical fiber taper waveguide. Optical pumping yields laser emission in the 1.3 μm band, with room temperature, continuous-wave thresholds as low as 1 μW of absorbed pump power. Out-coupling of the laser emission is also shown to be significantly enhanced through the use of optical fiber tapers, with a laser differential efficiency as high as ξ ~ 16% and out-coupling efficiency in excess of 28% measured after accounting for losses in the optical fiber system.

© 2006 Optical Society of America

1. Introduction

Optical microcavities with embedded quantum dots (QDs) have become a very active area of research, with applications to triggered single photon sources[1

01. P. Michler, A. Kiraz, C. Becher, W. Schoenfeld, P. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A Quantum Dot Single-Photon Turnstile Device,” Science 290, 2282–2285 (2000). [CrossRef] [PubMed]

, 2

02. C. Santori, M. Pelton, G. Solomon, Y. Dale, and Y. Yamamoto, “Triggered Single Photons from a Quantum Dot,” Phys. Rev. Lett. 86, 1502–1505 (2001). [CrossRef] [PubMed]

, 3

03. E. Moreau, I. Robert, J. Gérard, I. Abram, L. Manin, and V. Thierry-Mieg, “Single-mode solid-state photon source based on isolated quantum dots in pillar microcavities,” Appl. Phys. Lett. 79, 2865–2867 (2001). [CrossRef]

], strongly coupled light-matter systems for quantum networking[4

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

, 5

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

, 6

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

], and low threshold microcavity lasers[7

07. H. Cao, J. Xu, W. Xiang, Y. Ma, S.-H. Chang, S. Ho, and G. Solomon, “Optically pumped InAs quantum dot microdisk lasers,” Appl. Phys. Lett. 76, 3519–3521 (2000). [CrossRef]

, 8

08. T. Ide, T. Baba, J. Tatebayashi, S. Iwamoto, T. Nakaoka, and Y. Arakawa, “Room temperature continuous wave lasing InAs quantum-dot microdisks with air cladding,” Opt. Express 13, 1615–1620 (2005). [CrossRef] [PubMed]

, 9

09. T. Yang, O. Schekin, J. O’Brien, and D. Deppe, “Room temperature, continuous-wave lasing near 1300 nm in microdisks with quantum dot active regions,” IEE Elec. Lett. 39 (2003).

]. For these applications some of the most important microcavity parameters are the quality factor (Q), mode volume (V eff), and the efficiency of light collection from the microcavity (ηo). Q and V eff describe the decay rate (κ) and peak electric field strength within the cavity, respectively, which along with the oscillator strength and dephasing rate of the QD exciton determine if the coupled QD-photon system is in the regime of reversible energy exchange (strong coupling) or in a perturbative regime (weak coupling) characterized by a modification of the QD exciton radiative lifetime (the Purcell effect)[10

10. H. J. Kimble, “Strong Interactions of Single Atoms and Photons in Cavity QED,” Physica Scripta T76, 127–137 (1998). [CrossRef]

]. The collection efficiency η0 is of great importance for quantum networking[11

11. J. Cirac, P. Zoller, H. Kimble, and H. Mabuchi, “Quantum state transfer and entanglement distribution among distant nodes in a quantum network,” Phys. Rev. Lett. 78, 3221–3224 (1997). [CrossRef]

] and linear optics quantum computing applications[12

12. E. Knill, R. Laflamme, and G. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001). [CrossRef] [PubMed]

, 13

13. A. Kiraz, M. Atature, and A. Imamoglu, “Quantum-dot single-photon sources: Prospects for applications in linear optics quantum-information processing,” Phys. Rev. A 69 (2004). [CrossRef]

], where near-unity photon pulse collection values are required.

In this article, we continue our study of taper-coupled microdisk-QD structures by considering device performance as the disks are scaled down in size. In Section 2, we use finite element simulations to examine the behavior of Q and V eff as a function of disk diameter. We relate these parameters to those used in cQED, and from this, determine that disks of 1.5 – 2 μm in diameter are optimal for use in future experiments with InAs QDs. Section 3 briefly outlines the methods used to fabricate and test devices consisting of a 2 μm diameter disk created in an Al-GaAs heterostructure with a single layer of self-assembled InAs QDs. In Section 4, we present experimental measurements of the fabricated devices. Through passive characterization, cavity Qs as high as 1.2× 105 are demonstrated for devices with a predicted V eff ~ 2.2(λ/n)3. In addition, photoluminescence measurements show that the devices operate as lasers with RT, continuous-wave thresholds of ~1 μW of absorbed pump power. Finally, the optical fiber taper is used to increase the efficiency of out-coupling by nearly two orders of magnitude, so that an overall fiber-coupled laser differential efficiency of ξ, ~ 16% is achieved. We conclude by presenting some estimates of the number of QDs contributing to lasing and the spontaneous emission coupling factor (β) of the devices.

2. Simulations

To study Q and V eff of the microdisk cavities, finite-element eigenfrequency simulations[18

18. S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005). [CrossRef]

, 19

19. M. Borselli, T. Johnson, and O. Painter, “Measuring the role of surface chemistry in silicon microphotonics,” submitted for publication (2005)

] are performed using the Comsol FEMLAB commercial software. By assuming azimuthal symmetry of the disk structures, only a two-dimensional cross-section of the disk is simulated, albeit using a full-vectorial model. The cavity mode effective volume is calculated according to the formula[20

20. L. Andreani, G. Panzarini, and J.-M. Gerard, “Strong-coupling regime for quantum boxes in pillar microcavi-ties:Theory,” Phys. Rev. B 60, 13276–13279 (1999). [CrossRef]

]:

Veff=Vε(r)|E(r)|2d3rmax[ε(r)|E(r)|2]
(1)

where ε(r) is the dielectric constant, |E(r)| is the electric field strength, and V is a quantization volume encompassing the resonator and with a boundary in the radiation zone of the cavity mode under study. The resonance wavelength λ0 and radiation limited quality factor Q rad are determined from the complex eigenvalue (wavenumber) of the resonant cavity mode, k, obtained by the finite-element solver, with λ0 = 2π/ℜℯ(k) and Q rad = ℜℯ(k)/(2ℑm(k)).

Fig. 1. (a) Scanning electron microscope (SEM) image of a fabricated microdisk device. The disk thickness t=255 nm and sidewall angle θ = 26° from vertical are taken as fixed in the finite-element simulations presented in the work. The measured average diameter for this device (i.e., the diameter at the center of the slab) is ~ 2.12 μm. (b) Finite-element-calculated |E|2 distribution for the TEp=1 m=11 WGM of a microdisk with a diameter of ~ 2.12 μm at the center of the slab. For this mode, λ ~ 1265.41 nm, Q rad ~ 107, and V eff~ 2.8(λ=n)3.

In addition, the modes that we study are standing wave modes that are superpositions of the standard clockwise (CW) and counterclockwise (CCW) traveling wave modes typically studied in microdisks. These standing wave modes form when surface scattering couples and splits the initially degenerate CW and CCW traveling wave modes[21

21. D. S. Weiss, V. Sandoghdar, J. Hare, V. Lefevre-Seguin, J.-M. Raimond, and S. Haroche, “Splitting of high-Q Mie modes induced by light backscattering in silica microspheres,” Opt. Lett. 20, 1835–1837 (1995). [CrossRef] [PubMed]

, 22

22. T. Kippenberg, S. Spillane, and K. Vahala, “Modal coupling in traveling-wave resonators,” Opt. Lett. 27, 1669–1671 (2002). [CrossRef]

, 23

23. M. Borselli, T. Johnson, and O. Painter, “Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment,” Opt. Express 13, 1515–1530 (2005). [CrossRef] [PubMed]

]; this process is contingent upon the loss rates within the disk being small enough for coherent coupling between the traveling wave modes to occur. For the AlGaAs microdisk devices we have studied thus far[16

16. K. Srinivasan, M. Borselli, T. Johnson, P. Barclay, O. Painter, A. Stintz, and S. Krishna, “Optical loss and lasing characteristics of high-quality-factor AlGaAs microdisk resonators with embedded quantum dots,” Appl. Phys. Lett. 86, 151106 (2005). [CrossRef]

, 17

17. K. Srinivasan, A. Stintz, S. Krishna, and O. Painter, “Photoluminescence measurements of quantum-dot-containing semiconductor microdisk resonators using optical fiber taper waveguides,” Phys. Rev. B 72, 205318 (2005). [CrossRef]

], this has indeed been the case. The effective mode volume for a standing wave mode, as defined in Eq. 1, is roughly half that of a traveling wave mode[23

23. M. Borselli, T. Johnson, and O. Painter, “Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment,” Opt. Express 13, 1515–1530 (2005). [CrossRef] [PubMed]

]. This is of particular relevance to cQED experiments involving such microdisks as the coherent coupling rate of light and matter scales as g ~ 1√V eff. A QD positioned at an anti-node of the standing wave will have an exciton-photon coupling rate which is √2 times larger than for the traveling wave mode.

Figures 1(b) and 2(a) show the results of the finite element simulations. We see that V eff for these standing wave modes can be as small as 2(λ/n)3 while maintaining Q rad > 105. Indeed, for microdisk average diameters D > 2 μm[24

24. The average diameter is taken at the center of the slab, or equivalently, is the average of the top and bottom diameters.

], radiation losses are not expected to be the dominant loss mechanism as Q rad quickly exceeds 107, and other sources of field decay such as material absorption or surface scattering are likely to dominate . To translate these results into the standard parameters studied in cQED, we calculate the cavity decay rate κ/2π = ω/(4πQ) (assuming Q = Q rad) and the coherent coupling rate g between the cavity mode and a single QD exciton. In this calculation, a spontaneous emission lifetime τsp = 1 ns is assumed for the QD exciton, and g = dE/h̄ is the vacuum coherent coupling rate between cavity mode and QD exciton, given by[10

10. H. J. Kimble, “Strong Interactions of Single Atoms and Photons in Cavity QED,” Physica Scripta T76, 127–137 (1998). [CrossRef]

, 20

20. L. Andreani, G. Panzarini, and J.-M. Gerard, “Strong-coupling regime for quantum boxes in pillar microcavi-ties:Theory,” Phys. Rev. B 60, 13276–13279 (1999). [CrossRef]

]:

g/2π=12τsp3cλ02τsp2πn3Veff,
(2)

where c is the speed of light and n is the refractive index at the location of the QD. This formula assumes that the QD is optimally positioned within the cavity field, so that the calculated g is the maximum possible coupling rate. The resulting values for g and κ are displayed in Fig. 2(b), and show that g/2π can exceed κ/2π by over an order of magnitude for a range of disk diameters. In addition, for all but the smallest-sized microdisks, κ/2π < 1 GHz. A decay rate of 1 GHz is chosen as a benchmark value as it corresponds to a linewidth of a few μeV at these wavelengths, on par with the narrowest self-assembled InAs QD exciton linewidths that have been measured at cryogenic temperatures[25

25. M. Bayer and A. Forchel, “Temperature dependence of the exciton homogeneous linewidth in In0.60Ga0.40As/GaAs self-assembled quantum dots,” Phys. Rev. B 65, 041308(R) (2002).

]. Indeed, because dissipation in a strongly-coupled QD-photon system can either be due to cavity decay or quantum dot dephasing, in Fig. 3 we examine the ratio of g to the maximum decay rate in the system assuming a fixed QD dephasing rate γ/2π=1 GHz[26

26. Note that γ = γ is in general greater than half the total excitonic decay rate (γ/2) or radiative decay rate (1/2πsp) for QD excitons, due to near-elastic scattering or dephasing events with, for example, acoustic phonons of the lattice.

]. This ratio is roughly representative of the number of coherent exchanges of energy (Rabi oscillations) that can take place between QD and photon. We see that it peaks at a value of about 18 for a disk diameter D ~ 1.5 μm. For diameters smaller than this, loss is dominated by cavity decay due to radiation (so that g/max(γ,κ) = g/κ), while for larger diameters, the dominant loss mechanism is due to dephasing of the QD (g/max(γκ) = g/γ).

Fig. 2. Finite-element method simulation results: (a) Modal volume V eff (left) and radiation-limited cavity quality factor Q rad (right) as a function of microdisk diameter (taken at the center of the slab), calculated for standing wave modes of disks of the shape shown in Fig. 1. The modes studied are TEp=1,m WGMs with resonance wavelength within the 1200 nm band. (b) Coherent coupling rate g/2π (left) and cavity decay rate κ/2π (right) as a function of microdisk diameter. A QD spontaneous emission lifetime τsp = 1 ns is assumed in the calculation of g.

For other types of atomic-like media besides the self-assembled InAs QDs considered here one need not assume a limit of γ/2π = 1 GHz, and we note that due to the exponential dependence of Q rad and approximately linear dependence of V eff on microdisk diameter, Q rad/V eff rapidly rises above 107 for microdisks of diameter only D = 2.5 μm. These values of Q rad and V eff are comparable to those found in recent high-Q photonic crystal microcavity designs[27

27. K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express 10, 670–684 (2002). [PubMed]

, 28

28. H.-Y Ryu, M. Notomi, and Y.-H. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett. 83, 4294–4296 (2003). [CrossRef]

, 29

29. B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nature Materials 4, 207–210 (2005). [CrossRef]

, 30

30. E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Photonic crystal nanocavity formed by local width modulation of line-defect with Q of one million,” In LEOS 2005, Post-Deadline Session PD 1.1, (IEEE Lasers and Electro-Optics Society, 2005).

, 31

31. Z. Zhang and M. Qiu, “Small-volume waveguide-section high Q microcavities in 2D photonic crystal slabs,” Opt. Express 12, 3988–3995 (2004). [CrossRef] [PubMed]

]. In fact a similar scaling for high-Q planar photonic crystal micro-cavities, in which one may trade-off a linear increase in V eff for an exponential increase in Q, has recently been described by Englund, et al., in Ref. [32

32. D. Englund, I. Fushman, and J. Vučković, “General recipe for designing photonic crystal cavities,” Opt. Express 13, 5961–5975 (2005). [CrossRef] [PubMed]

]. For now, however, we take the ratio g/max(γ,κ) with γ/2π = 1 GHz as our metric, and as such focus on 1.5-2 μm diameter microdisks.

Fig. 3. Ratio of the calculated coupling rate g to the maximum decay rate in the system, max(γ,κ), as a function of the microdisk diameter at the center of the slab. A fixed QD decay rate γ/2π=1 GHz is assumed, and the cavity decay rate κ is taken to be solely due to radiation loss.

3. Growth, fabrication, and test set-up

The samples used were grown by molecular beam epitaxy, and consist of a single layer of InAs QDs embedded in an In0.15Ga0.85As quantum well, which is in turn sandwiched between layers of Al0.30Ga0.70As and GaAs to form a 255 nm thick waveguide layer. This dot-in-a-well (DWELL) structure is grown on top of a 1.5 μm thick Al0.70Ga0.30As buffer layer that is later undercut to form the disk pedestal. Growth parameters were adjusted[33

33. A. Stintz, G. Liu, H. Li, L. Lester, and K. Malloy, “Low-Threshold Current Density 1.3-μm InAs Quantum-Dot Lasers with the Dots-in-a-Well (DWELL) structure,” IEEE Photonics Technol. Lett. 12, 591–593 (2000). [CrossRef]

] to put the material’s RT ground state emission peak at λ = 1317 nm. Fabrication of the microdisk cavities begins with the deposition of a 180 nm thick SiNx etch mask layer through plasma-enhanced chemical vapor deposition. This is followed by electron-beam lithography to define a linear array of disks, a post-development reflow of the resist, and a SF6/C4F8 inductively coupled plasma reaction ion etch (ICP-RIE) of the nitride mask. The DWELL material is then etched using Ar/Cl2 ICP-RIE, and the array of disks is isolated onto a mesa stripe through standard photolithography and an ICP-RIE etch. Finally, the disks are undercut using a dilute solution of hydrofluoric acid (20:1 H2O:HF); an image of a fabricated device is shown in Fig. 1. During the fabrication, two goals were given special consideration. As discussed within the context of silicon microdisks in Ref. [23

23. M. Borselli, T. Johnson, and O. Painter, “Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment,” Opt. Express 13, 1515–1530 (2005). [CrossRef] [PubMed]

], elimination of radial variations in the disk geometry is important for reducing scattering loss; this is accomplished through optimization of the electron-beam lithography, and in particular, use of the post-development resist reflow technique of Ref. [23

23. M. Borselli, T. Johnson, and O. Painter, “Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment,” Opt. Express 13, 1515–1530 (2005). [CrossRef] [PubMed]

]. In addition, a premium was placed on sidewall smoothness, even at the expense of sidewall verticality. This required an optimization of the ICP-RIE processes used to etch both the SiNx mask and GaAs/AlGaAs waveguide layer. In particular, a low bias voltage, C4F8-rich plasma is used to etch the SiNx, and a low Cl2 percentage is used in the Ar/Cl2 etch of the waveguide to eliminate any sidewall pitting due to excessive chemical etching.

The microdisks are studied in a photoluminescence (PL) measurement setup that provides normal incidence pumping and free-space collection from the samples. The pump laser is an 830 nm laser diode that is operated continuous-wave, and the pump beam is shaped into a Gaussian-like profile by sending it through a section of single mode optical fiber, after which it is then focused onto the sample with an ultra-long working distance objective lens (NA = 0.4). The free-space photoluminescence is first collected at normal incidence from the sample surface using the same objective lens for pump focusing, and is then coupled into a multi-mode fiber (MMF) using an objective lens with NA = 0.14. The luminescence collected by this MMF is wavelength resolved by a Hewlett Packard 70452B optical spectrum analyzer (OSA).

The PL setup has been modified[17

17. K. Srinivasan, A. Stintz, S. Krishna, and O. Painter, “Photoluminescence measurements of quantum-dot-containing semiconductor microdisk resonators using optical fiber taper waveguides,” Phys. Rev. B 72, 205318 (2005). [CrossRef]

] to allow for devices to be probed by optical fiber tapers. The fiber taper is formed by heating (with a hydrogen torch) and adiabatically stretching a single mode fiber until its minimum diameter is approximately 1 μm. It is mounted onto an acrylic mount that is attached to a motorized Z-axis stage (50 nm encoded resolution), so that the fiber taper can be precisely aligned to the microdisk, which is in turn mounted on a motorized XY stage. When doing passive measurements of cavity Q, the taper input is connected to a scanning tunable laser (5 MHz linewidth) with a tuning range between 1420–1480 nm, and the taper output is connected to a photodetector to monitor the transmitted power. Alternately, when collecting emission from the microdisk through the fiber taper, the taper input is left unconnected and the output is sent into the OSA.

4. Experimental results

We begin our measurements by using the fiber taper to passively probe the Q of the microdisks. Based on the simulations presented in Section 2, we have focused on 2 μm diameter microdisks. Due to the small diameter of these microdisks, the finite-element-calculated free-spectral range of resonant modes is relatively large, with resonances occurring at 1265, 1346, and 1438 nm for the TEp=1 WGMs with azimuthal mode numbers m = 11,10, and 9, respectively. The simulations presented in Section 2 were done for the TE1,11 mode in the λ = 1200 nm band due to the applicability of that wavelength region for future low temperature cQED experiments. However, for the current room-temperature measurements, the absorption due to the QD layer at those wavelengths is significant, so we probe the devices within the λ = 1400 nm band (~100 nm red-detuned from the peak ground-state manifold QD emission). At these longer wavelengths the radiation-limited Q rad for a given disk diameter will be smaller than its value in the shorter λ = 1200 nm band. Table 1 summarizes the properties of the TEp=1 WGMs within the 1200–1400 wavelength band for a D = 2 μm microdisk with shape as shown in Fig. 1.

Table 1. Finite-element calculated TEp,=1 m modes of a D = 2μm microdisk.

table-icon
View This Table
Fig. 4. (a) Normalized transmission spectrum when a fiber taper is positioned a few hundred nm away from the microdisk edge. (b) Light-in-light-out (L-L) curve for a device operated with free-space collection. The laser threshold absorbed pump power Pth is ~1.0 μW, and its differential efficiency ξ ~ 0.02%. (inset) Spectrum from the device above threshold, showing emission at λ ~ 1345 nm corresponding to the TEp,=1 m=10 WGM.

Figure 4(a) shows a wavelength scan of the transmitted signal when a fiber taper is positioned a few hundred nanometer away from the disk edge. The doublet resonance appearing at λ ~1440 nm in the spectrum is the signature of the standing wave modes described earlier[21

21. D. S. Weiss, V. Sandoghdar, J. Hare, V. Lefevre-Seguin, J.-M. Raimond, and S. Haroche, “Splitting of high-Q Mie modes induced by light backscattering in silica microspheres,” Opt. Lett. 20, 1835–1837 (1995). [CrossRef] [PubMed]

]. The measured linewidths correspond to Q factors of 1.2 × 105, and in general Qs of 0.9–1.3 × 105 have been measured for these 2 μm diameter microdisks. The Qs of these modes are approaching the radiation-limited value of 3.7× 105, and are some of the highest measured values for near-IR wavelength-scale microcavities in AlGaAs[5

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

, 15

15. B. Gayral, J. M. Gerard, A. Lemaître, C. Dupuis, L. Manin, and J. L. Pelouard, “High-Q wet-etched GaAs microdisks containing InAs quantum boxes,” Appl. Phys. Lett. 75, 1908–1910 (1999). [CrossRef]

, 16

16. K. Srinivasan, M. Borselli, T. Johnson, P. Barclay, O. Painter, A. Stintz, and S. Krishna, “Optical loss and lasing characteristics of high-quality-factor AlGaAs microdisk resonators with embedded quantum dots,” Appl. Phys. Lett. 86, 151106 (2005). [CrossRef]

, 34

34. A. Loffler, J. Reithmaier, G. Sek, C. Hofmann, S. Reitzenstein, M. Kamp, and A. Forchel, “Semiconductor quantum dot microcavity pillars with high-quality factors and enlarged dot dimensions,” Appl. Phys. Lett. 86, 111105 (2005). [CrossRef]

]. The corresponding cavity decay rates are κ/2π ~ 0.8 – 1.3 GHz, over an order of magnitude smaller than the predicted coupling rate g for an optimally placed QD. In addition, these Qs, if replicated within the QD emission band at λ = 1300 nm, are high enough to ensure that room-temperature lasing should be achievable from the single layer of QDs in these devices[33

33. A. Stintz, G. Liu, H. Li, L. Lester, and K. Malloy, “Low-Threshold Current Density 1.3-μm InAs Quantum-Dot Lasers with the Dots-in-a-Well (DWELL) structure,” IEEE Photonics Technol. Lett. 12, 591–593 (2000). [CrossRef]

]. From calculations of the intrinsic radiation loss, the shorter 1300 nm wavelength modes should in fact have a significantly increased Q rad of 1.9 ×106, although surface scattering may also slightly increase due to its approximate cubic dependence on frequency[23

23. M. Borselli, T. Johnson, and O. Painter, “Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment,” Opt. Express 13, 1515–1530 (2005). [CrossRef] [PubMed]

].

The emission properties of the QD-containing microdisks are tested at room temperature by continuous-wave optical pumping through a high-NA objective lens at normal incidence on to the sample and, initially, collecting the vertically emitted light through the same lens. The pump spot size, ~ 18 μm2, is sufficiently large to pump the entirety of the disk area. A light-in versus light-out (L-L) curve for one of the D ~ 2 μm microdisks with a resonant emission peak at λ ~ 1345 nm is shown in Fig. 4(b), and displays a lasing threshold kink at approximately 1.0 μW of absorbed pump power. The laser mode wavelength corresponds well with the TEp=1 m=10 mode from finite-element simulations (see Table 1). The absorbed pump power is estimated to be 11% of the incident pump power on the microdisk, and was determined by first taking the fraction of the pump spot that actually impinges on the disk, and then assuming an absorption coefficient of 104 cm-1 for the GaAs layers and quantum well layer and accounting for reflections at the GaAs/air interfaces[17

17. K. Srinivasan, A. Stintz, S. Krishna, and O. Painter, “Photoluminescence measurements of quantum-dot-containing semiconductor microdisk resonators using optical fiber taper waveguides,” Phys. Rev. B 72, 205318 (2005). [CrossRef]

]. This threshold level is approximately two orders of magnitude smaller than those in recent demonstrations of RT, continuous-wave microdisk QD lasers[8

08. T. Ide, T. Baba, J. Tatebayashi, S. Iwamoto, T. Nakaoka, and Y. Arakawa, “Room temperature continuous wave lasing InAs quantum-dot microdisks with air cladding,” Opt. Express 13, 1615–1620 (2005). [CrossRef] [PubMed]

, 9

09. T. Yang, O. Schekin, J. O’Brien, and D. Deppe, “Room temperature, continuous-wave lasing near 1300 nm in microdisks with quantum dot active regions,” IEE Elec. Lett. 39 (2003).

], although the active regions in those devices contain five stacked layers of QDs while the devices presented here contain only a single layer of QDs.

Fig. 5. (a) (left) L-L curve for another microdisk device operated with free-space collection, with Pth ~ 1.1 μW and ξ ~ 0.1%. (right) Spectrum from the device near laser threshold, showing emission at λ ~ 1330 nm. (b) (left) L-L curve for the same device using an optical fiber taper to collect the emission. Pth has increased to 1.6 μW while ξ, increased to 4% for collection in the forward fiber taper channel. (inset) Optical microscope image of the taper output coupler aligned to the microdisk. (right) Spectrum of the fiber taper collected light below threshold.

The low lasing threshold of the device presented in Fig. 4(b) was consistently measured for the set of devices on this sample (approximately 20 devices). In Fig. 5(a) we show another L-L curve, this time for a device that has a TEp=1 ,m=10 WGM emission peak at λ = 1330 nm and has a threshold absorbed pump power of 1.1 μW. As demonstrated in Ref. [17

17. K. Srinivasan, A. Stintz, S. Krishna, and O. Painter, “Photoluminescence measurements of quantum-dot-containing semiconductor microdisk resonators using optical fiber taper waveguides,” Phys. Rev. B 72, 205318 (2005). [CrossRef]

], the same fiber taper used to measure the cavity Q can efficiently out-couple light from the lasing mode. We do this by maintaining the free-space pumping used above while contacting a fiber taper to the side of the microdisk as shown in the inset of Fig. 5(b). From the corresponding L-L curve (Fig. 5(b)) we see that the laser threshold under fiber taper loading has increased from 1.1 μW to 1.6 μW, but in addition the differential laser efficiency ξ, is now 4% compared to 0.1% when employing free-space collection (Fig. 5(a)–(b)). Furthermore, because the microdisk modes are standing waves they radiate into both the forwards and backwards channels of the fiber. With collection from both the forward and backward channels the differential efficiency was measured to be twice that of the single forward channel. Collecting from both channels and adjusting for all fiber losses in the system (roughly 50% due to fiber splices and taper loss in this case; tapers with losses < 10% are routinely fabricated in our lab), the total differential laser efficiency with fiber taper collection is 16%. Due to the difference in photon energy of the pump laser and microdisk emission, this laser differential efficiency corresponds to a conversion efficiency of 28% from pump photons to fiber-collected microdisk laser photons. 28% is thus a lower bound on the fiber-taper collection efficiency and/or quantum efficiency of the QD active region.

Fig. 6. L-L curve experimental data (red circles) and rate-equation model fit (blue line) to data for the fiber taper coupled laser of Fig. 5(b) : (a) log-log plot and (b) linear plot (inset shows deep sub-threshold data and fit). β′ ~ 3% is the spontaneous emission factor estimated directly from the slope change in the data, and thus includes a large non-radiative component, while β ~ 15.5% is the value used in the rate-equation model fit.

In addition to the improved laser differential efficiency of the TEp=1 m=10 laser mode when using the fiber taper to out-couple the laser light, we also see in the below-threshold spectrum of Fig. 5(b) that two additional resonances appear at λ = 1310 nm and λ = 1306 nm. The long wavelength mode is identified as TMp=1,m=8 and the short wavelength mode as TEp=2,m=7 from finite-element simulations. These modes are not discernible in the free-space collected spectrum due to their low radiation-limited Q factors (800 and 5000 for the TE2,7 and TM1,8, respectively), but show up in the taper coupled spectrum due to their alignment with the QD ground-state exciton emission peak and the heightened sensitivity of the taper coupling method. The single-mode lasing and limited number of WGM resonances (6 when including the degeneracy of the WGMs) in the emission spectrum in these D = 2 μm microdisks is a result of the large 80–100 nm free-spectral-range of modes in the 1300–1500 wavelength band. As a result, one would expect the spontaneous emission factor (β) of these microdisk lasers to be relatively high.

A log-log plot of the fiber taper coupled laser emission of Fig. 5(b) is shown in Fig. 6(a) along with a rate-equation model fit to the data. Of particular note is the well defined subthreshold linear slope of the log-log plot. In this case the sensitivity of the fiber taper collection allows for the sub-threshold slope to be accurately estimated at m=1.67, corresponding to a near quadratic dependence of spontaneous emission intensity on pump power (Fig. 6(b), inset) and indicating that there is likely significant non-radiative recombination. Assuming that radiative recombination occurs as a bi-particle process[35

35. As has been discussed recently in Ref [36] this may not be an accurate model for QD state-filling, but for our simple analysis here it will suffice.

], the larger than unity power law dependence of sub-threshold emission on pump power is indicative of single-particle non-radiative recombination processes such as surface recombination[37

37. G. P. Agrawal and N. K. Dutta, Semiconductor Lasers (Van Nostrand Reinhold, New York, NY, 1993).

]. Given the close proximity of the WGM laser mode to the periphery of the microdisk and the above-band pumping, the presence of significant surface recombination is not surprising. Unfortunately, due to this large non-radiative component one can only provide a weak lower bound β′ for the (β-factor directly from the L-L curve. From Fig. 6 we estimate β ≥ β′ ~ 3%.

A rate-equation model incorporating bi-particle spontaneous emission proportional to N 2 and surface recombination with a N 1.22 carrier dependence (the ratio of the power law dependences is set equal to the measured sub-threshold slope of m=1.67) is fit to the data and shown as a solid curve in Fig. 6. In this model the measured fiber taper collection efficiency was used, along with the previously measured and estimated QD density, maximum gain, and quantum efficiency from stripe lasers[33

33. A. Stintz, G. Liu, H. Li, L. Lester, and K. Malloy, “Low-Threshold Current Density 1.3-μm InAs Quantum-Dot Lasers with the Dots-in-a-Well (DWELL) structure,” IEEE Photonics Technol. Lett. 12, 591–593 (2000). [CrossRef]

]. An estimate for the actual radiative β-factor of 15.5% was used, corresponding closely with the partitioning of spontaneous emission amongst the 6 localized and high-Q WGM resonances within the QD ground-state manifold emission band[38

38. This estimate was based upon considering Purcell enhancement at RT for QDs spatially and spectrally aligned with the WGMs (FP ~ 6), and suppression of spontaneous emission for QDs spatially and spectrally misaligned from the WGMs (FP ~ 0.4). This simple estimate is consistent with accurate finite-difference time-domain calculations of similar sized microdisks[39].

]. The reference spontaneous emission lifetime of the ground-state QD exciton in bulk was taken as τsp = 1 ns. The data was fit by varying only the effective surface recombination velocity. As seen in Fig. 6, the fit is quite good over the entire sub-threshold and threshold regions of the laser data. The inferred surface recombination velocity from the fit is vs ~ 75 cm/s, extremely slow for the AlGaAs material system[40

40. L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (John Wiley & Sons, Inc., New York, NY, 1995).

] but perhaps indicative of the fast capture rate of carriers, and consequent localization, into QDs[41

41. T. Sosnowski, T. Norris, H. Jiang, J. Singh, K. Kamath, and P. Bhattacharya, “Rapid carrier relaxation in In0.4Ga0.60As/GaAs quantum dots characterized by differential transmission spectroscopy,” Phys. Rev. B 57, R9423–R9426 (1998). [CrossRef]

, 42

42. D. Yarotski, R. Averitt, N. Negre, S. Crooker, A. Taylor, G. Donati, A. Stintz, L. Lester, and K. Malloy, “Ultrafast carrier-relaxation dynamics in self-assembled InAs/GaAs quantum dots,” J. Opt. Soc. Am. B 19, 1480–1484 (2002). [CrossRef]

]. Due to the large perimeter-to-area ratio in these small D = 2 μm microdisks, even with this low velocity the model predicts that laser threshold pump power is dominated by surface recombination with an effective lifetime τs ~ 300 ps. Such a surface recombination lifetime has also been estimated by Baba, et al., in their recent work on QD-microdisk lasers[43

43. T. Ide, T. Baba, J. Tatebayashi, S. Iwamoto, T. Nakaoka, and Y. Arakawa, “Lasing characteristics of InAs quantum-dot microdisk from 3K to room temperature,” Appl. Phys. Lett. 85, 1326–1328 (2004). [CrossRef]

].

The number of QDs contributing to lasing in these small microdisks can also be estimated. From the finite-element simulations the area of the standing wave WGM lasing mode in the plane of the QD layer is approximately 1 μm2, and the predicted QD density for this sample is 300 μm-2, so that ~ 300 QDs are spatially aligned with the cavity mode. Assuming a RT homogeneous linewidth on the order of a few meV[25

25. M. Bayer and A. Forchel, “Temperature dependence of the exciton homogeneous linewidth in In0.60Ga0.40As/GaAs self-assembled quantum dots,” Phys. Rev. B 65, 041308(R) (2002).

], compared to a measured inhomogeneous Gaussian broadening of 35 meV, and considering the location of the lasing mode in the tail of the Gaussian distribution, we estimate < 10% of these dots are spectrally aligned with the cavity mode. By this estimate, on the order of 25 QDs contribute to lasing.

5. Conclusions

We have demonstrated fiber-coupled 2 μm diameter quantum-dot-containing microdisks that have a quality factor Q in excess of 105 for a predicted mode volume V eff as small as ~ 2.2(λ/n)3. Such devices are predicted to be suitable for future experiments in single quantum dot, single photon experiments in cavity QED, where these Q and V eff values can enable strong coupling at GHz-scale speeds. An initial application of this work is in continuous wave, optically pumped microcavity lasers. Here, the high Q ensures that lasing can be achieved with the modest gain provided by a single layer of quantum dots, and combined with the ultra-small V eff, results in thresholds as low as 1.0 μW of absorbed power. In addition, the fiber taper coupling is shown to be an efficient method to collect the laser emission with a measured 28% lower bound on out-coupling efficiency.

This work was partly supported by the Charles Lee Powell Foundation. The authors thank Christopher P. Michael, Paul E. Barclay, and Thomas J. Johnson for helpful discussions. KS thanks the Hertz Foundation and MB thanks the Moore Foundation, NPSC, and HRL Laboratories for their graduate fellowship support.

References and links

01.

P. Michler, A. Kiraz, C. Becher, W. Schoenfeld, P. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A Quantum Dot Single-Photon Turnstile Device,” Science 290, 2282–2285 (2000). [CrossRef] [PubMed]

02.

C. Santori, M. Pelton, G. Solomon, Y. Dale, and Y. Yamamoto, “Triggered Single Photons from a Quantum Dot,” Phys. Rev. Lett. 86, 1502–1505 (2001). [CrossRef] [PubMed]

03.

E. Moreau, I. Robert, J. Gérard, I. Abram, L. Manin, and V. Thierry-Mieg, “Single-mode solid-state photon source based on isolated quantum dots in pillar microcavities,” Appl. Phys. Lett. 79, 2865–2867 (2001). [CrossRef]

04.

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

05.

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

06.

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

07.

H. Cao, J. Xu, W. Xiang, Y. Ma, S.-H. Chang, S. Ho, and G. Solomon, “Optically pumped InAs quantum dot microdisk lasers,” Appl. Phys. Lett. 76, 3519–3521 (2000). [CrossRef]

08.

T. Ide, T. Baba, J. Tatebayashi, S. Iwamoto, T. Nakaoka, and Y. Arakawa, “Room temperature continuous wave lasing InAs quantum-dot microdisks with air cladding,” Opt. Express 13, 1615–1620 (2005). [CrossRef] [PubMed]

09.

T. Yang, O. Schekin, J. O’Brien, and D. Deppe, “Room temperature, continuous-wave lasing near 1300 nm in microdisks with quantum dot active regions,” IEE Elec. Lett. 39 (2003).

10.

H. J. Kimble, “Strong Interactions of Single Atoms and Photons in Cavity QED,” Physica Scripta T76, 127–137 (1998). [CrossRef]

11.

J. Cirac, P. Zoller, H. Kimble, and H. Mabuchi, “Quantum state transfer and entanglement distribution among distant nodes in a quantum network,” Phys. Rev. Lett. 78, 3221–3224 (1997). [CrossRef]

12.

E. Knill, R. Laflamme, and G. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001). [CrossRef] [PubMed]

13.

A. Kiraz, M. Atature, and A. Imamoglu, “Quantum-dot single-photon sources: Prospects for applications in linear optics quantum-information processing,” Phys. Rev. A 69 (2004). [CrossRef]

14.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode lasers,” Appl. Phys. Lett. 60, 289–291 (1992). [CrossRef]

15.

B. Gayral, J. M. Gerard, A. Lemaître, C. Dupuis, L. Manin, and J. L. Pelouard, “High-Q wet-etched GaAs microdisks containing InAs quantum boxes,” Appl. Phys. Lett. 75, 1908–1910 (1999). [CrossRef]

16.

K. Srinivasan, M. Borselli, T. Johnson, P. Barclay, O. Painter, A. Stintz, and S. Krishna, “Optical loss and lasing characteristics of high-quality-factor AlGaAs microdisk resonators with embedded quantum dots,” Appl. Phys. Lett. 86, 151106 (2005). [CrossRef]

17.

K. Srinivasan, A. Stintz, S. Krishna, and O. Painter, “Photoluminescence measurements of quantum-dot-containing semiconductor microdisk resonators using optical fiber taper waveguides,” Phys. Rev. B 72, 205318 (2005). [CrossRef]

18.

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005). [CrossRef]

19.

M. Borselli, T. Johnson, and O. Painter, “Measuring the role of surface chemistry in silicon microphotonics,” submitted for publication (2005)

20.

L. Andreani, G. Panzarini, and J.-M. Gerard, “Strong-coupling regime for quantum boxes in pillar microcavi-ties:Theory,” Phys. Rev. B 60, 13276–13279 (1999). [CrossRef]

21.

D. S. Weiss, V. Sandoghdar, J. Hare, V. Lefevre-Seguin, J.-M. Raimond, and S. Haroche, “Splitting of high-Q Mie modes induced by light backscattering in silica microspheres,” Opt. Lett. 20, 1835–1837 (1995). [CrossRef] [PubMed]

22.

T. Kippenberg, S. Spillane, and K. Vahala, “Modal coupling in traveling-wave resonators,” Opt. Lett. 27, 1669–1671 (2002). [CrossRef]

23.

M. Borselli, T. Johnson, and O. Painter, “Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment,” Opt. Express 13, 1515–1530 (2005). [CrossRef] [PubMed]

24.

The average diameter is taken at the center of the slab, or equivalently, is the average of the top and bottom diameters.

25.

M. Bayer and A. Forchel, “Temperature dependence of the exciton homogeneous linewidth in In0.60Ga0.40As/GaAs self-assembled quantum dots,” Phys. Rev. B 65, 041308(R) (2002).

26.

Note that γ = γ is in general greater than half the total excitonic decay rate (γ/2) or radiative decay rate (1/2πsp) for QD excitons, due to near-elastic scattering or dephasing events with, for example, acoustic phonons of the lattice.

27.

K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express 10, 670–684 (2002). [PubMed]

28.

H.-Y Ryu, M. Notomi, and Y.-H. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett. 83, 4294–4296 (2003). [CrossRef]

29.

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nature Materials 4, 207–210 (2005). [CrossRef]

30.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Photonic crystal nanocavity formed by local width modulation of line-defect with Q of one million,” In LEOS 2005, Post-Deadline Session PD 1.1, (IEEE Lasers and Electro-Optics Society, 2005).

31.

Z. Zhang and M. Qiu, “Small-volume waveguide-section high Q microcavities in 2D photonic crystal slabs,” Opt. Express 12, 3988–3995 (2004). [CrossRef] [PubMed]

32.

D. Englund, I. Fushman, and J. Vučković, “General recipe for designing photonic crystal cavities,” Opt. Express 13, 5961–5975 (2005). [CrossRef] [PubMed]

33.

A. Stintz, G. Liu, H. Li, L. Lester, and K. Malloy, “Low-Threshold Current Density 1.3-μm InAs Quantum-Dot Lasers with the Dots-in-a-Well (DWELL) structure,” IEEE Photonics Technol. Lett. 12, 591–593 (2000). [CrossRef]

34.

A. Loffler, J. Reithmaier, G. Sek, C. Hofmann, S. Reitzenstein, M. Kamp, and A. Forchel, “Semiconductor quantum dot microcavity pillars with high-quality factors and enlarged dot dimensions,” Appl. Phys. Lett. 86, 111105 (2005). [CrossRef]

35.

As has been discussed recently in Ref [36] this may not be an accurate model for QD state-filling, but for our simple analysis here it will suffice.

36.

H. Pask, H. Summer, and P. Blood, “Localized Recombination and Gain in Quantum Dots,” In Tech. Dig. Conf. on Lasers and Electro-Optics, CThH3, (Optical Society of America, Baltimore, MD, 2005).

37.

G. P. Agrawal and N. K. Dutta, Semiconductor Lasers (Van Nostrand Reinhold, New York, NY, 1993).

38.

This estimate was based upon considering Purcell enhancement at RT for QDs spatially and spectrally aligned with the WGMs (FP ~ 6), and suppression of spontaneous emission for QDs spatially and spectrally misaligned from the WGMs (FP ~ 0.4). This simple estimate is consistent with accurate finite-difference time-domain calculations of similar sized microdisks[39].

39.

J. Vučković, O. Painter, Y. Xu, A. Yariv, and A. Scherer, “FDTD Calculation of the Spontaneous Emission Coupling Factor in Optical Microcavities,” IEEE J. Quantum Electron. 35, 1168–1175 (1999). [CrossRef]

40.

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (John Wiley & Sons, Inc., New York, NY, 1995).

41.

T. Sosnowski, T. Norris, H. Jiang, J. Singh, K. Kamath, and P. Bhattacharya, “Rapid carrier relaxation in In0.4Ga0.60As/GaAs quantum dots characterized by differential transmission spectroscopy,” Phys. Rev. B 57, R9423–R9426 (1998). [CrossRef]

42.

D. Yarotski, R. Averitt, N. Negre, S. Crooker, A. Taylor, G. Donati, A. Stintz, L. Lester, and K. Malloy, “Ultrafast carrier-relaxation dynamics in self-assembled InAs/GaAs quantum dots,” J. Opt. Soc. Am. B 19, 1480–1484 (2002). [CrossRef]

43.

T. Ide, T. Baba, J. Tatebayashi, S. Iwamoto, T. Nakaoka, and Y. Arakawa, “Lasing characteristics of InAs quantum-dot microdisk from 3K to room temperature,” Appl. Phys. Lett. 85, 1326–1328 (2004). [CrossRef]

OCIS Codes
(140.5960) Lasers and laser optics : Semiconductor lasers
(230.5750) Optical devices : Resonators
(270.0270) Quantum optics : Quantum optics

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: November 17, 2005
Revised Manuscript: January 13, 2006
Manuscript Accepted: January 24, 2006
Published: February 6, 2006

Citation
Kartik Srinivasan, Matthew Borselli, Oskar Painter, Andreas Stintz, and Sanjay Krishna, "Cavity Q, mode volume, and lasing threshold in small diameter AlGaAs microdisks with embedded quantum dots," Opt. Express 14, 1094-1105 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-3-1094


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References

  1. P. Michler, A. Kiraz, C. Becher, W. Schoenfeld, P. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A Quantum Dot Single-Photon Turnstile Device,” Science 290, 2282–2285 (2000). [CrossRef] [PubMed]
  2. C. Santori, M. Pelton, G. Solomon, Y. Dale, and Y. Yamamoto, “Triggered Single Photons from a Quantum Dot,” Phys. Rev. Lett. 86, 1502–1505 (2001). [CrossRef] [PubMed]
  3. E. Moreau, I. Robert, J. Gérard, I. Abram, L. Manin, and V. Thierry-Mieg, “Single-mode solid-state photon source based on isolated quantum dots in pillar microcavities,” Appl. Phys. Lett. 79, 2865–2867 (2001). [CrossRef]
  4. J. Reithmaier, G. Sek, A. Loffer, C. Hoffman, S. Kuhn, S. Reitzenstein, L. Keldysh, V. Kulakovskii, T. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197–200 (2004). [CrossRef] [PubMed]
  5. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, Q. Schenkin, and D. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004). [CrossRef] [PubMed]
  6. E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. Gérard, and J. Bloch, “Exciton photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett. 95 (2005). [CrossRef] [PubMed]
  7. H. Cao, J. Xu, W. Xiang, Y. Ma, S.-H. Chang, S. Ho, and G. Solomon, “Optically pumped InAs quantum dot microdisk lasers,” Appl. Phys. Lett. 76, 3519–3521 (2000). [CrossRef]
  8. T. Ide, T. Baba, J. Tatebayashi, S. Iwamoto, T. Nakaoka, and Y. Arakawa, “Room temperature continuous wave lasing InAs quantum-dot microdisks with air cladding,” Opt. Express 13, 1615–1620 (2005). [CrossRef] [PubMed]
  9. T. Yang, O. Schekin, J. O’Brien, and D. Deppe, “Room temperature, continuous-wave lasing near 1300 nm in microdisks with quantum dot active regions,” IEE Elec. Lett. 39 (2003).
  10. H. J. Kimble, “Strong Interactions of Single Atoms and Photons in Cavity QED,” Physica Scripta T76, 127–137 (1998). [CrossRef]
  11. J. Cirac, P. Zoller, H. Kimble, and H. Mabuchi, “Quantum state transfer and entanglement distribution among distant nodes in a quantum network,” Phys. Rev. Lett. 78, 3221–3224 (1997). [CrossRef]
  12. E. Knill, R. Laflamme, and G. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001). [CrossRef] [PubMed]
  13. A. Kiraz, M. Atature, and A. Imamoglu, “Quantum-dot single-photon sources: Prospects for applications in linear optics quantum-information processing,” Phys. Rev. A 69 (2004). [CrossRef]
  14. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode lasers,” Appl. Phys. Lett. 60, 289–291 (1992). [CrossRef]
  15. B. Gayral, J. M. Gérard, A. Lemaître, C. Dupuis, L. Manin, and J. L. Pelouard, “High-Q wet-etched GaAs microdisks containing InAs quantum boxes,” Appl. Phys. Lett. 75, 1908–1910 (1999). [CrossRef]
  16. K. Srinivasan, M. Borselli, T. Johnson, P. Barclay, O. Painter, A. Stintz, and S. Krishna, “Optical loss and lasing characteristics of high-quality-factor AlGaAs microdisk resonators with embedded quantum dots,” Appl. Phys. Lett. 86, 151106 (2005). [CrossRef]
  17. K. Srinivasan, A. Stintz, S. Krishna, and O. Painter, “Photoluminescence measurements of quantum-dot-containing semiconductor microdisk resonators using optical fiber taper waveguides,” Phys. Rev. B 72, 205318 (2005). [CrossRef]
  18. S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005). [CrossRef]
  19. M. Borselli, T. Johnson, and O. Painter, “Measuring the role of surface chemistry in silicon microphotonics,” submitted for publication (2005)
  20. L. Andreani, G. Panzarini, and J.-M. Gérard, “Strong-coupling regime for quantum boxes in pillar microcavities: Theory,” Phys. Rev. B 60, 13276–13279 (1999). [CrossRef]
  21. D. S. Weiss, V. Sandoghdar, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, “Splitting of high-Q Mie modes induced by light backscattering in silica microspheres,” Opt. Lett. 20, 1835–1837 (1995). [CrossRef] [PubMed]
  22. T. Kippenberg, S. Spillane, and K. Vahala, “Modal coupling in traveling-wave resonators,” Opt. Lett. 27, 1669–1671 (2002). [CrossRef]
  23. M. Borselli, T. Johnson, and O. Painter, “Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment,” Opt. Express 13, 1515–1530 (2005). [CrossRef] [PubMed]
  24. The average diameter is taken at the center of the slab, or equivalently, is the average of the top and bottom diameters.
  25. M. Bayer and A. Forchel, “Temperature dependence of the exciton homogeneous linewidth in In0:60Ga0:40As/GaAs self-assembled quantum dots,” Phys. Rev. B 65, 041308(R) (2002).
  26. Note that γ≡γ is in general greater than half the total excitonic decay rate (γ√2) radiative decay rate (1/2τsp) for QD excitons, due to near-elastic scattering or dephasing events with, for example, acoustic phonons of the lattice.
  27. K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express 10, 670–684 (2002). [PubMed]
  28. H.-Y. Ryu, M. Notomi, and Y.-H. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett. 83, 4294–4296 (2003). [CrossRef]
  29. B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nature Materials 4, 207–210 (2005). [CrossRef]
  30. E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Photonic crystal nanocavity formed by local width modulation of line-defect with Q of one million,” In LEOS 2005, Post-Deadline Session PD 1.1, (IEEE Lasers and Electro-Optics Society, 2005).
  31. Z. Zhang and M. Qiu, “Small-volume waveguide-section high Q microcavities in 2D photonic crystal slabs,” Opt. Express 12, 3988–3995 (2004). [CrossRef] [PubMed]
  32. D. Englund, I. Fushman, and J. Vučković, “General recipe for designing photonic crystal cavities,” Opt. Express 13, 5961–5975 (2005). [CrossRef] [PubMed]
  33. A. Stintz, G. Liu, H. Li, L. Lester, and K. Malloy, “Low-Threshold Current Density 1.3-µm InAs Quantum-Dot Lasers with the Dots-in-a-Well (DWELL) structure,” IEEE Photonics Technol. Lett. 12, 591–593 (2000). [CrossRef]
  34. A. Loffler, J. Reithmaier, G. Sek, C. Hofmann, S. Reitzenstein, M. Kamp, and A. Forchel, “Semiconductor quantum dot microcavity pillars with high-quality factors and enlarged dot dimensions,” Appl. Phys. Lett. 86, 111105 (2005). [CrossRef]
  35. As has been discussed recently in Ref. [36] this may not be an accurate model for QD state-filling, but for our simple analysis here it will suffice.
  36. H. Pask, H. Summer, and P. Blood, “Localized Recombination and Gain in Quantum Dots,” In Tech. Dig. Conf. on Lasers and Electro-Optics, CThH3, (Optical Society of America, Baltimore, MD, 2005).
  37. G. P. Agrawal and N. K. Dutta, Semiconductor Lasers (Van Nostrand Reinhold, New York, NY, 1993).
  38. This estimate was based upon considering Purcell enhancement at RT for QDs spatially and spectrally aligned with the WGMs (FP ~ 6), and suppression of spontaneous emission for QDs spatially and spectrally misaligned from the WGMs (FP ~ 0:4). This simple estimate is consistent with accurate finite-difference time-domain calculations of similar sized microdisks[39].
  39. J. Vučković, O. Painter, Y. Xu, A. Yariv, and A. Scherer, “FDTD Calculation of the Spontaneous Emission Coupling Factor in Optical Microcavities,” IEEE J. Quantum Electron. 35, 1168–1175 (1999). [CrossRef]
  40. L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (John Wiley & Sons, Inc., New York, NY, 1995).
  41. T. Sosnowski, T. Norris, H. Jiang, J. Singh, K. Kamath, and P. Bhattacharya, “Rapid carrier relaxation in In0:4Ga0:60As/GaAs quantum dots characterized by differential transmission spectroscopy,” Phys. Rev. B 57, R9423–R9426 (1998). [CrossRef]
  42. D. Yarotski, R. Averitt, N. Negre, S. Crooker, A. Taylor, G. Donati, A. Stintz, L. Lester, and K. Malloy, “Ultrafast carrier-relaxation dynamics in self-assembled InAs/GaAs quantum dots,” J. Opt. Soc. Am. B 19, 1480–1484 (2002). [CrossRef]
  43. T. Ide, T. Baba, J. Tatebayashi, S. Iwamoto, T. Nakaoka, and Y. Arakawa, “Lasing characteristics of InAs quantum-dot microdisk from 3K to room temperature,” Appl. Phys. Lett. 85, 1326–1328 (2004). [CrossRef]

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