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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 20 — Oct. 2, 2006
  • pp: 9269–9276
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Room-temperature InAs/InP Quantum Dots laser operation based on heterogeneous “2.5 D” Photonic Crystal

B. Ben Bakir, Ch. Seassal, X. Letartre, Ph. Regreny, M. Gendry, P. Viktorovitch, M. Zussy, L. Di Cioccio, and J. M. Fedeli  »View Author Affiliations


Optics Express, Vol. 14, Issue 20, pp. 9269-9276 (2006)
http://dx.doi.org/10.1364/OE.14.009269


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Abstract

The authors report on the design, fabrication and operation of heterogeneous and compact “2.5 D” Photonic Crystal microlaser with a single plane of InAs quantum dots as gain medium. The high quality factor photonic structures are tailored for vertical emission. The devices consist of a top two-dimensional InP Photonic Crystal Slab, a SiO2 bonding layer, and a bottom high index contrast Si/SiO2 Bragg mirror deposited on a Si wafer. Despite the fact that no more than about 5% of the quantum dots distribution effectively contribute to the modal gain, room-temperature lasing operation, around 1.5µm, was achieved by photopumping. A low effective threshold, on the order of 350µW, and a spontaneous emission factor, over 0.13, could be deduced from experiments.

© 2006 Optical Society of America

1. Introduction

Additionally, Photonic Crystals (PCs) appear to be the most promising candidates for the design and production of small volume and high quality factor (Q-factor) optical micro-resonators, with a well controlled radiation emission pattern.

Recently, J. Hendrickson et al. have demonstrated low-temperature lasing operation around 1.2µm using a single InAs/GaAs QDs plane and a high Q-factor PC-micro-cavity [4

4. J. Hendrickson, B. C. Richards, J. Sweet, S. Mosor, C. Christenson, D. Lam, G. Khitrova, H. M. Gibbs, T. Yoshie, A. Scherer, O. B. Shchekin, and D. G. Deppe, “Quantum dot photonic-crystal-slab nanocavities: Quality factors and lasing,” Phys. Rev. B. 72, 193303 (2005). [CrossRef]

]. Based on the high Q-factor planar microcavity design developed by Y. Akahane et al. [5

5. Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003). [CrossRef] [PubMed]

], they could achieve a threshold power on the order of 200µW. Using a stacked InAs/GaAs quantum dot layers, room temperature (RT) lasing in photonic crystal microcavities was demonstrated around 1.3µm [6

6. M. Nomura, S. Iwamoto, K. Watanabe, N. Kumagai, Y. Nakata, S. Ishida, and Y. Arakawa, “Room temperature continuous-wave lasing in photonic crystal nanocavity,” Opt. Express 14, 6308–6315 (2006). [CrossRef] [PubMed]

7

7. T. Yoshie, O.B. Shchekin, H. Chen, D.G. Deppe, and A. Scherer, “Quantum dot photonic crystal laser,” Electron. Lett. 38, 967–968 (2002). [CrossRef]

].

We recently introduced the concept of “2.5D” PC lasers combining 2D PC-Slab and Bragg reflectors, for the control of both optical losses and emission pattern [8

8. B. Ben Bakir, Ch. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. Di Cioccio, and J. M. Fedeli, “Surface-emitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror,” Appl. Phys. Lett. 88, 081113 (2006). [CrossRef]

]. On the other hand, InAs/InP QD nanostructures have proven to be quite well suited to efficient light emission in the 1.3–1.55µm wavelength range [9

9. M. Gendry, C. Monat, J. Brault, P. Regreny, G. Hollinger, B. Salem, G. Guillot, T. Benyattou, C. Bruchevallier, G. Bremond, and O. Marty, “From large to low height dispersion for self-organized InAs quantum sticks emitting at 1.55mm on InP (001),” J. Appl. Phys. 95, 4761–4766 (2004). [CrossRef]

]. In this article, we propose to combine such a gain material with a high Q-factor “2.5D” PC resonator, and we investigate the possibility to reach RT laser operation of a single plane of InAs/InP QDs.

2. Design

As depicted in Fig. 1(a), we designed a high index contrast “2.5 D” PC constituted of a top 2D PC patterned in a 250nm-thick InP membrane, a SiO2 bonding layer, a Bragg mirror formed by three pairs of Si/SiO2 quarter-wavelength layers on a Si substrate. The principle of operation of the device is fully discussed in reference [8

8. B. Ben Bakir, Ch. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. Di Cioccio, and J. M. Fedeli, “Surface-emitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror,” Appl. Phys. Lett. 88, 081113 (2006). [CrossRef]

]. Basically, the 2D PC-Slab, which is a graphite lattice of air holes, is targeted for vertical operation, i.e., we exploit a resonant band-edge mode located in the center of the first Brillouin zone. Near this point, where the group velocity is very low, the electromagnetic field is laterally confined and is weakly coupled to the radiated continuum. In order to achieve further control over the photon lifetime in such a resonator, we add a reflective vertical structure (Bragg mirror) below the 2D PCSlab. This perturbative approach can lead to a strong modification of the dynamic behaviour of the resonant mode. Using this concept, the Q-factor can be maximized with an optimum bonding layer optical thickness of 3λ/4.

Fig. 1. (a) Generic configuration of the simulated devices. (b) In-plane and (c) cross-sectional view of the electromagnetic energy density pattern calculated using 3D plane wave expansion method. The lattice-constant, the radius and the thickness of the PC membrane are: a=775nm, r=130nm, h=250nm. The thickness of the Si and SiO2 λ/4 layers are 110nm and 255nm, respectively.

Additionally, as depicted in Fig. 1(b) and Fig. 1(c), the electromagnetic energy density of the photonic mode is strongly localized in the semiconductor region of the 2D PC-Slab, ensuring a very efficient light-matter interaction.

3. Device fabrication and optical characterization

On the one hand, the III–V heterostructure used for the devices is grown by solid source molecular beam epitaxy. A 300nm-thick sacrificial/etch-stop layer of In0.53Ga0.47As is grown on a 2-inch InP(001) wafer. Then, a 250nm InP layer is grown, including at mid-height a single plane of InAs QDs. The QDs are elongated in the [1

1. Ch. Seassal, C. Monat, J. Mouette, E. Touraille, B. Ben Bakir, H.T. Hattori, J.L. Leclercq, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “InP Bonded Membrane Photonics Components and Circuits: Toward 2.5 Dimensional Micro-Nano-Photonics,” IEEE J. Sel. Top. Quantum Electron. 11, 395–407 (2005). [CrossRef]

10

10. G. Björk, A. Karlsson, and Y. Yamamoto, “Definition of a laser threshold,” Phys. Rev. A 50, 1675–1680 (1994). [CrossRef] [PubMed]

] direction so that they present a dash-like shape [9

9. M. Gendry, C. Monat, J. Brault, P. Regreny, G. Hollinger, B. Salem, G. Guillot, T. Benyattou, C. Bruchevallier, G. Bremond, and O. Marty, “From large to low height dispersion for self-organized InAs quantum sticks emitting at 1.55mm on InP (001),” J. Appl. Phys. 95, 4761–4766 (2004). [CrossRef]

]. On the other hand, the Si/SiO2 Bragg mirror is deposited on a Si wafer by low pressure chemical vapor deposition. Then, the III–V heterostructure is transferred on top of the Bragg reflector, using SiO2-SiO2 wafer bonding [1

1. Ch. Seassal, C. Monat, J. Mouette, E. Touraille, B. Ben Bakir, H.T. Hattori, J.L. Leclercq, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “InP Bonded Membrane Photonics Components and Circuits: Toward 2.5 Dimensional Micro-Nano-Photonics,” IEEE J. Sel. Top. Quantum Electron. 11, 395–407 (2005). [CrossRef]

]. The InP substrate and etch-stop layer are eliminated by selective wet chemical etching, leading to the final vertical structure presented in Fig. 2(a) and Fig. 2(b). A 90nm-thick SiO2 layer is then deposited on top of the structure using plasma-assisted sputtering. Finally, PCs are patterned in a 150nm-thick PMMA mask using electron beam lithography and transferred into silica and InP layers by means of reactive ion etching (Fig. 2(c)). The final devices have a lateral extension of 30µm×30µm.

The devices are photopumped using a pulsed laser diode emitting at 780nm. The pulse width is 6ns, with a 1.2% duty cycle. The pump beam is focussed under normal incidence with a ×20 achromatic objective lens (0.4 numerical aperture), onto an area of about 4µm in diameter. Emission spectra are measured using a high resolution spectrometer and an InGaAs photodetector array.

Figure 3 presents the measured Bragg mirror reflectivity (Fig. 3(a)) which is higher than 98% in a broad spectral range (1400–1650nm), and the unpatterned heterostructure emission spectrum (Fig. 3(b)), compared to the typical emission spectrum corresponding to the laser peak of the resonant mode (Fig. 3(c)).

Fig. 2. Scanning electron micrograph: (a) cross-sectional view of the unpatterned heterostructure and (c) top view of the graphite lattice PC membrane. Transmission electron micrograph: (b) cross-sectional view of the InAs quantum dots.
Fig. 3. (a) Reflectivity of the Bragg mirror, and (b) unpatterned heterostructure emission spectrum compared to (c) the typical emission spectrum corresponding to the laser peak of the resonant mode.

4. Results and discussion

Figure 4(a) shows the output emission intensity of the main resonant mode against the incident peak power, Pi (L-L curve) for a first structure. On this figure, we also display the ratio λ/δλ as a function of Pi, where δλ is the spectral linewidth (Q-L curve). This ratio will be further referred to as the “experimental Q-factor”. Output emission spectra are also shown in the insets. These spectra show multimode emission for various pumping rate. The main mode, located at 1495nm, is more intense than the others, and exhibits a low linewidth, but the corresponding peak does not dominate the emission spectrum. This resonant mode lies in the region of the QDs distribution where the gain is reasonably high. The L-L curve exhibits a sub-linear increase of the output intensity. The Q-L curve shows a strong increase of λ/δλ, and then a saturation, for a pumping power over 6mW. For this structure, there is no evidence of laser emission, and the linewidth clamping can be attributed to the saturation of the absorption in the gain medium. The obtained λ/δλ value can then give an estimate of the optical Q-factor of the resonator, which should be around 4200.

Finally, we obtained a laser power threshold of about 1mW, but if we take into account that, according to our simulations, only 35% of the optical pump power is absorbed by the InP barriers, this leads to an effective threshold of Peff≈350µW. Moreover, because of the size dispersion in the self-organized QDs distribution, the gain spectrum of a large collection of QDs is inhomogeneously broadened. Consequently, not all the QDs contribute to the lasing action, resulting in a relatively high threshold. In our devices, we estimate that only 5% of the QDs are spectrally coupled to the resonant mode. By improving the epitaxial growth processes, in order to reduce size dispersion, we expect, with such devices, a strongly reduced effective laser threshold.

βΓrλl44π2nInP3VmodeΔλQD
(1)
Fig. 4. (a) Emission characteristics obtained on structure 1 and (b) structure 2. Output emission power intensity, spontaneous emission (SE) background and measured Q-factors against the incident pump power. The bold dashed-line indicates the maximum resolution of the spectrometer. The dashed circles emphasize the change of behavior around the threshold. Output emission spectra obtained for various pumping powers are displayed in the insets.

where Γr is the relative confinement factor, nInP is the refractive index of the patterned InP layer, V mode is the volume of the resonant mode, λl the resonant wavelength of the lasing mode and ΔλQD is the spectral homogeneous broadening at room temperature of the QDs participating to the lasing action. It is always difficult to evaluate experimentally the mode volume of a band-edge microlaser. Indeed, the technological imperfections tend to reduce drastically the lateral extension of the resonant mode compared to the patterned membrane area. We estimated, by infrared near field imaging, the mode volume, V mode=1.2 10-11 cm-3. Assuming an averaged relative confinement factor, Γ¯ r=2, and an homogeneous broadening of individual QD, ΔλQD=5 nm, we found β>0.13. In equation (1), the enhancement of spontaneous emission in the lasing mode is taken into account but it is assumed that the total spontaneous emission rate (in all optical modes) remains equal to the value of a QD in a bulk semiconductor. However, as described in [15

15. P. Pottier, C. Seassal, X. Letartre, JL Leclercq, P. Viktorovitch, D. Cassagne, and C. Jouanin, “Triangular and hexagonal high Q-factor 2-D photonic bandgap cavities on III–V suspended membranes,” J. Lightwave Technol. 17, 2058–2062 (1999). [CrossRef]

], in our specific vertical configuration, the direct vertical light emission is significantly inhibited. Then, the calculated value of β is certainly underestimated. Finally, even with a mode volume higher than usual PC microcavities, this estimate shows that the β-factor is relatively large. Considering both this factor and the reduced non-radiative recombination, we are typically in the case where the L-L curve presents a smooth evolution around the threshold.

Fig. 5. Blue-shift of the peak wavelength of the laser mode as a function of the incident pump power

5. Conclusion

We also discussed the influence of the high spontaneous emission factor on the L-L curve characteristics and on the blue-shift of the lasing wavelength above the threshold. We estimated this factor to be higher than 0.13.

Combining our original approach for the design of the micro-resonator with improved QDs growth conditions should result in the production of ultra-low threshold micro-lasers.

Acknowledgments

This work was supported by the French National Nanoscience “NALIM” Project and by the ePIX-net European Network of Excellence. We would like to thank Michel Garrigues for fruitful discussions and Olivier Marty for TEM characterization of the QDs.

References and Links

1.

Ch. Seassal, C. Monat, J. Mouette, E. Touraille, B. Ben Bakir, H.T. Hattori, J.L. Leclercq, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “InP Bonded Membrane Photonics Components and Circuits: Toward 2.5 Dimensional Micro-Nano-Photonics,” IEEE J. Sel. Top. Quantum Electron. 11, 395–407 (2005). [CrossRef]

2.

P. Caroff, C. Paranthoen, C. Platz, O. Dehaese, H. Folliot, N. Bertru, C. Labbé, R. Piron, E. Homeyer, A. Le Corre, and S. Loualiche, “High-gain and low-threshold InAs quantum-dot lasers on InP,” Appl. Phys. Lett. 87, 243107 (2005). [CrossRef]

3.

H. Saito, K. Nishi, A. Kamei, and S. Sugou, “Low Chirp Observed in Directly Modulated Quantum Dot Lasers,” IEEE photonic Technol. Lett. 12, 1298–1300 (2000). [CrossRef]

4.

J. Hendrickson, B. C. Richards, J. Sweet, S. Mosor, C. Christenson, D. Lam, G. Khitrova, H. M. Gibbs, T. Yoshie, A. Scherer, O. B. Shchekin, and D. G. Deppe, “Quantum dot photonic-crystal-slab nanocavities: Quality factors and lasing,” Phys. Rev. B. 72, 193303 (2005). [CrossRef]

5.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003). [CrossRef] [PubMed]

6.

M. Nomura, S. Iwamoto, K. Watanabe, N. Kumagai, Y. Nakata, S. Ishida, and Y. Arakawa, “Room temperature continuous-wave lasing in photonic crystal nanocavity,” Opt. Express 14, 6308–6315 (2006). [CrossRef] [PubMed]

7.

T. Yoshie, O.B. Shchekin, H. Chen, D.G. Deppe, and A. Scherer, “Quantum dot photonic crystal laser,” Electron. Lett. 38, 967–968 (2002). [CrossRef]

8.

B. Ben Bakir, Ch. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. Di Cioccio, and J. M. Fedeli, “Surface-emitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror,” Appl. Phys. Lett. 88, 081113 (2006). [CrossRef]

9.

M. Gendry, C. Monat, J. Brault, P. Regreny, G. Hollinger, B. Salem, G. Guillot, T. Benyattou, C. Bruchevallier, G. Bremond, and O. Marty, “From large to low height dispersion for self-organized InAs quantum sticks emitting at 1.55mm on InP (001),” J. Appl. Phys. 95, 4761–4766 (2004). [CrossRef]

10.

G. Björk, A. Karlsson, and Y. Yamamoto, “Definition of a laser threshold,” Phys. Rev. A 50, 1675–1680 (1994). [CrossRef] [PubMed]

11.

T. Baba, “Photonic Crystals and Microdisk Cavities Based on GaInAsP-InP System,” IEEE J. Sel. Top. Quantum Electron. 3, 808–830 (1997). [CrossRef]

12.

Y. Yamamoto, S. Machida, and G. Björk, “A Microcavity laser with enhanced spontaneous emission,” Phys. Rev. A 44, 657–668 (1991). [CrossRef] [PubMed]

13.

T. Baba and D. Sano, “Low-Threshold Lasing and Purcell Effect in Microdisk Lasers at Room Temperature,” IEEE J. Sel. Top. Quantum Electron. 9, 1340–1346 (2003). [CrossRef]

14.

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits, New York: Wiley (1995)

15.

P. Pottier, C. Seassal, X. Letartre, JL Leclercq, P. Viktorovitch, D. Cassagne, and C. Jouanin, “Triangular and hexagonal high Q-factor 2-D photonic bandgap cavities on III–V suspended membranes,” J. Lightwave Technol. 17, 2058–2062 (1999). [CrossRef]

16.

F. Raineri, C. Cojocaru, R. Raj, P. Monnier, A. Levenson, C. Seassal, X. Letartre, and P. Viktorovitch, “Tuning of a two-dimensional photonic crystal resonance via optical carrier injection,” Opt. Lett. 30, 64–66 (2005). [CrossRef] [PubMed]

17.

M. Fujuta, R. Ushigome, and T. Baba, “Large Spontaneous Emission Factor of 0.1 in Microdisk Injection Laser,” IEEE photonic Technol. Lett. 13, 403–405 (2001). [CrossRef]

18.

H. Y. Ryu, N. Notomi, E. Kuramoti, and T. Segawa, “Large spontaneous emission factor (>0.1) in the photonic crystal monopole laser,” Appl. Phys. Lett. 84, 1067–1069 (2004). [CrossRef]

OCIS Codes
(000.0000) General : General
(140.5960) Lasers and laser optics : Semiconductor lasers
(230.3990) Optical devices : Micro-optical devices
(230.4170) Optical devices : Multilayers
(230.5750) Optical devices : Resonators
(250.5230) Optoelectronics : Photoluminescence

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: July 3, 2006
Revised Manuscript: September 20, 2006
Manuscript Accepted: September 22, 2006
Published: October 2, 2006

Citation
Badhise Ben Bakir, Christian Seassal, Xavier Letartre, Philippe Regreny, Michel Gendry, Pierre Viktorovitch, Marc Zussy, Léa Di Cioccio, and Jean-Marc Fedeli, "Room-temperature InAs/InP Quantum Dots laser operation based on heterogeneous “2.5 D” Photonic Crystal," Opt. Express 14, 9269-9276 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-20-9269


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References

  1. Ch. Seassal, C. Monat, J. Mouette, E. Touraille, B. Ben Bakir, H.T. Hattori, J.L. Leclercq, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, "InP Bonded Membrane Photonics Components and Circuits: Toward 2.5 Dimensional Micro-Nano-Photonics," IEEE J. Sel. Top. Quantum Electron. 11,395-407 (2005). [CrossRef]
  2. P. Caroff, C. Paranthoen, C. Platz, O. Dehaese, H. Folliot, N. Bertru, C. Labbé, R. Piron, E. Homeyer, A. Le Corre, and S. Loualiche, "High-gain and low-threshold InAs quantum-dot lasers on InP," Appl. Phys. Lett. 87,243107 (2005). [CrossRef]
  3. H. Saito, K. Nishi, A. Kamei, and S. Sugou, "Low Chirp Observed in Directly Modulated Quantum Dot Lasers," IEEE photonic Technol. Lett. 12,1298-1300 (2000). [CrossRef]
  4. J. Hendrickson, B. C. Richards, J. Sweet, S. Mosor, C. Christenson, D. Lam, G. Khitrova, H. M. Gibbs, T. Yoshie, A. Scherer, O. B. Shchekin, and D. G. Deppe, "Quantum dot photonic-crystal-slab nanocavities: Quality factors and lasing," Phys. Rev. B. 72,193303 (2005). [CrossRef]
  5. Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425,944-947 (2003). [CrossRef] [PubMed]
  6. M. Nomura, S. Iwamoto, K. Watanabe, N. Kumagai, Y. Nakata, S. Ishida, and Y. Arakawa, "Room temperature continuous-wave lasing in photonic crystal nanocavity," Opt. Express 14,6308-6315 (2006). [CrossRef] [PubMed]
  7. T. Yoshie, O.B. Shchekin, H. Chen, D.G. Deppe, and A. Scherer, "Quantum dot photonic crystal laser," Electron. Lett. 38,967-968 (2002). [CrossRef]
  8. B. Ben Bakir, Ch. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. Di Cioccio, and J. M. Fedeli, "Surface-emitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror," Appl. Phys. Lett. 88,081113 (2006). [CrossRef]
  9. M. Gendry, C. Monat, J. Brault, P. Regreny, G. Hollinger, B. Salem, G. Guillot, T. Benyattou, C. Bru-chevallier, G. Bremond, and O. Marty, "From large to low height dispersion for self-organized InAs quantum sticks emitting at 1.55mm on InP (001)," J. Appl. Phys. 95,4761-4766 (2004). [CrossRef]
  10. G. Björk, A. Karlsson, and Y. Yamamoto, "Definition of a laser threshold," Phys. Rev. A 50,1675-1680 (1994). [CrossRef] [PubMed]
  11. T. Baba, "Photonic Crystals and Microdisk Cavities Based on GaInAsP-InP System," IEEE J. Sel. Top. Quantum Electron. 3,808-830 (1997). [CrossRef]
  12. Y. Yamamoto, S. Machida, G. Björk, "A Microcavity laser with enhanced spontaneous emission," Phys. Rev. A 44,657-668 (1991). [CrossRef] [PubMed]
  13. T. Baba and D. Sano, "Low-Threshold Lasing and Purcell Effect in Microdisk Lasers at Room Temperature," IEEE J. Sel. Top. Quantum Electron. 9,1340-1346 (2003). [CrossRef]
  14. L. A. Coldren, S. W. Corzine, Diode Lasers and Photonic Integrated Circuits, New York: Wiley (1995)
  15. P. Pottier, C. Seassal, X. Letartre, JL Leclercq, P. Viktorovitch; D. Cassagne, C. Jouanin, "Triangular and hexagonal high Q-factor 2-D photonic bandgap cavities on III-V suspended membranes," J. Lightwave Technol. 17,2058-2062 (1999). [CrossRef]
  16. F. Raineri, C. Cojocaru, R. Raj, P. Monnier, A. Levenson, C. Seassal, X. Letartre, and P. Viktorovitch, "Tuning of a two-dimensional photonic crystal resonance via optical carrier injection," Opt. Lett. 30,64-66 (2005). [CrossRef] [PubMed]
  17. M. Fujuta, R. Ushigome, and T. Baba, "Large Spontaneous Emission Factor of 0.1 in Microdisk Injection Laser," IEEE photonic Technol. Lett. 13,403-405 (2001). [CrossRef]
  18. H. Y. Ryu, N. Notomi, E. Kuramoti, and T. Segawa, "Large spontaneous emission factor (>0.1) in the photonic crystal monopole laser," Appl. Phys. Lett. 84,1067-1069 (2004). [CrossRef]

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