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 V eff 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 V eff ~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

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    [CrossRef]

Appl. Phys. Lett.

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]

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]

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]

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]

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]

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]

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]

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]

Conf. on Lasers and Electro-Optics 2005

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).

IEE Elec. Lett.

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).

IEEE J. Quantum Electron.

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]

IEEE Lasers and Electro-Optics Society, 2005

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).

IEEE Photonics Technol. Lett.

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]

J. Opt. Soc. Am. B

Nature

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]

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]

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

Nature Materials

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

Opt. Express

Opt. Express

Opt. Express

Opt. Express

Opt. Lett.

Phys. Rev. A

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]

Phys. Rev. A

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]

Phys. Rev. B

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]

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]

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).

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]

Phys. Rev. Lett.

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]

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]

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]

Physica Scripta

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

Science

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]

Other

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

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

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

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].

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.

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.

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

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Figures (6)

Fig. 1.
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 TE p=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.

Fig. 2.
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 TE p=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 τ sp = 1 ns is assumed in the calculation of g.

Fig. 3.
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.

Fig. 4.
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 TE p,=1 m=10 WGM.

Fig. 5.
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.

Fig. 6.
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.

Tables (1)

Tables Icon

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

Equations (2)

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V eff = V ε ( r ) | E ( r ) | 2 d 3 r max [ ε ( r ) | E ( r ) | 2 ]
g / 2 π = 1 2 τ s p 3 c λ 0 2 τ s p 2 π n 3 V eff ,

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