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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 12 — Jun. 11, 2007
  • pp: 7506–7514
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Room temperature continuous wave operation and controlled spontaneous emission in ultrasmall photonic crystal nanolaser

Kengo Nozaki, Shota Kita, and Toshihiko Baba  »View Author Affiliations


Optics Express, Vol. 15, Issue 12, pp. 7506-7514 (2007)
http://dx.doi.org/10.1364/OE.15.007506


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Abstract

Photonic crystal slab enables us to form an ultrasmall laser cavity with a modal volume close to the diffraction limit of light. However, the thermal resistance of such nanolasers, as high as 106 K/W, has prevented continuous-wave operation at room temperature. The present paper reports on the first successful continuous-wave operation at room temperature for the smallest nanolaser reported to date, achieved through fabrication of a laser with a low threshold of 1.2 μW. Near-thresholdless lasing and spontaneous emission enhancement due to the Purcell effect are also demonstrated in a moderately low Q nanolaser, both of which are well explained by a detailed rate equation analysis.

© 2007 Optical Society of America

1. Introduction

2. Evaluation of room temperature CW lasing characteristics

2.1. Device fabrication

Fig. 1. Scanning electron micrograph of fabricated device. (a) Whole device. (b) Magnified view of the H0 nanolaser. Center two airholes are laterally shifted.
Fig. 2. CW lasing characteristic of H0 nanolaser with lattice constant a = 560 nm, normalized hole diameter 2r/a = 0.57, and normalized hole shift s/a = 0.28. (a) Scanning electron micrograph of fabricated device (top view). (b) Calculated modal distribution (Hz). (c) Mode intensity characteristic and lasing spectrum above the lasing threshold. (d) Logarithmic plots of modal intensity versus normalized pump power characteristic.
Fig. 3. CW lasing characteristic of H1 nanolaser with a = 480 nm, 2r/a = 0.62, and normalized innermost hole diameter 2r′/a = 0.52. (a) Scanning electron micrograph of fabricated device (top view). (b) Calculated modal distribution (Hz). (c) Mode intensity characteristics and lasing spectrum above the lasing threshold. (d) Logarithmic plots of modal intensity versus normalized pump power characteristic.

2.1. Measurement of lasing characteristics

3. Time-resolved measurement of emission decay

From the above equation, the Purcell factors (F) are calculated to be 25 and 13 for the H0 and H1 nanolasers, respectively, assuming typical parameters for the GaInAsP QW wafers at RT (a p = 0.4, n = 3.4, and Δλ= 8.8 nm for a homogeneous broadening of 4.3 meV) [17

17. 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]

]. To evaluate the factor experimentally, the time-resolved measurement of the SpE intensity and decay at RT were carried out under pulsed photopumping at a wavelength of 0.975 μm using a pulse width of 90 ps and spot diameter of 3 μm. The SpE from the device was photon-counted using a photomultiplier tube (R3809-69, Hamamatsu), and the decay lifetime (τ) was determined by taking the deconvolution with respect to the pump pulse. The temporal resolution of the measurement was 100 ps, and the shortest limit of τ thus determined was of 10 ps order. Figure 4 shows the on-resonant emission decay for the H0 nanolaser below the lasing threshold in comparison to an unpatterned wafer and uniform PC area without a nanocavity. The typical value of τ for the wafer is 2–3 ns, shortening to <1 ns in the uniform PC area due to surface recombination at the etched sidewall of airholes. The decay lifetime of the H0 nanolaser is even shorter, <0.4 ns, influenced not only by the Purcell effect, but also by various carrier losses, as discussed below. Figure 5 summarizes the typical characteristics of the mode intensity and lifetime with respect to normalized pump power. The H0 nanolaser exhibits a rapid increase in mode intensity near the threshold and lower SpE intensity below the threshold, whereas the H1 nanolaser displays a gradual increase in mode intensity and higher SpE intensity below the threshold. Both nanolasers exhibit much shorter decay lifetimes than either the unpatterned wafer or the PC area at any pump level. In correspondence to the intensity characteristics, the lifetime of the H0 nanolaser decreases rapidly near the threshold, while the lifetime of the H1 laser decreases gradually. The dissimilarity of these characteristics was observed in all samples of these nanolasers. Notably, SpE enhancement and near-thresholdless operation are more observable for the H1 nanolaser than the H0 device, suggesting that high Q is not necessarily important for achieving thresholdless operation.

Fig. 4. SpE decay for H0 nanolaser under on-resonant condition observed at pump power of 0.45–0.85P th. Results for a uniform PC area without nanocavity and an unpatterned wafer at 0.85P th are also shown.

4. Theoretical fitting of Purcell factor

The theoretical characteristics are estimated through a rate equation analysis of the carrier density N(x,y,z;t) and photon density of the laser mode S(t) with respect to positions x, y, z and time t, as given by [30

30. K. Nozaki and T. Baba, “Carrier and photon analyses of photonic microlasers by two-dimensional rate equations,” IEEE J. Sel. Area. Commun. 23, 1411–1417 (2005). [CrossRef]

]

dNdt=PpumpħωpumpGSn2E2Vm[FCn2E2Vm+(1C)]BN2+CAN3+D2N
(1)
dSdt=QWGSn2E2dxdydz+QWFCBN2n2E2dxdydzSτph
(2)
eNνs=eDN(atsemiconductor/airboundaries)
(3)

5. Discussion

Fig. 5. Logarithmic plots of experimental and theoretical results for modal intensity (upper) and decay lifetime (lower) characteristics for pulsed measurements. (a) H0 nanolaser with Q = 20,000. Results for unpatterned wafer and PC area without cavity are also shown. (b) H1 nanolaser with Q = 1,500.

5.1. Origin of the carrier losses

In this section, carrier losses in the nanolaser and their dependence on the cavity Q are explained by the rate equation analysis. Figure 6(a) shows the laser characteristics calculated for the H0 nanolaser under CW condition. Parameters used for (A) – (D) are summarized in Table I. (A) shows the result for typical parameters of υ s = 2 × 104 cm/s, D = 2 cm2/s, and FC = 10 (F = 25, C = 0.4). The SpE intensity is attenuated two orders lower than the thresholdless level by surface recombination, carrier diffusion, and nonlaser mode emission. When the surface recombination and carrier diffusion are neglected by assuming υ s = 0 cm/s and D = 0 cm2/s, the SpE intensity becomes 30 times higher, as shown in (B) and (C). The remaining carrier loss is the nonlaser modes, which originates from the assumption C = 0.4. (When the surface recombination and carrier diffusion are neglected, (1-C) term in Eq. (1) cannot be ignored.) Actually, (D) calculated for C = 1 well traces the ideal thresholdless line. But particularly large attenuation of the SpE in (C) is caused by a photon recycling process. Figure 6(b) shows the schematic showing the carrier and photon behaviors in the cavity. In a high-Q nanocavity, emitted photons coupled to the laser mode are strongly reabsorbed below the transparent condition due to the long photon lifetime. (It is different from the so-called strong coupling regime of electron and photon, because the electronic coherent state is hardly maintained within the photon lifetime in the QW active region at RT.) The recycled carriers are partly redistributed to nonlaser mode emission, which quickly escapes from the cavity, or wasted by nonradiative recombinations. This recycling process severely accelerates carrier losses and reduces the SpE intensity.

Fig. 6. SpE intensity dependence on carrier losses. (a) Calculated modal intensity characteristics for different loss parameters whose details are shown in Table I. (b) Simplified schematic of carrier and photon behaviors in the cavity.

Tabel I. Calculation parameters.

table-icon
View This Table

5.2. Discussion for effective spontaneous emission enhancement

The SpE intensity can be improved in several ways. The first one is the suppression of the surface recombination at sidewall of airholes. The surface passivation technique gives some degree of improvement [34

34. H. Ichikawa, K. Inoshita, and T. Baba, “Reduction in surface recombination of GaInAsP/InP micro-columns by CH4 plasma irradiation,” Appl. Phys. Lett., 78, 2119–2121 (2001). [CrossRef]

]. The second one is the enhancement of the Purcell factor F. For a large F, the SpE rate for the laser mode becomes higher than the nonradiative recombination rate, and the spatial hole burning of carriers formed by the intensified mode suppresses the carrier diffusion to outside of the cavity. In addition, the coupling of SpE to nonlaser modes is relatively suppressed. As a result, the SpE intensity is enhanced almost in proportional to F, as shown in Fig. 7(a). However, F in this experiment cannot be enhanced by the cavity Q but constrained by the homogeneous broadening. Therefore, a significant enhancement is not expected without employing another material with a narrower homogeneous broadening. The third one is the optimization of the cavity Q. Figure 7(b) shows the intensity characteristics calculated against different Qs. As mentioned above, a high Q accelerates carrier losses through the photon recycling process. The SpE intensity is clearly enhanced for lower Q, even though the threshold also increases.

Fig. 7. Calculated modal intensity characteristics, where F and cavity Q are taken as a parameter for (a) and (b), respectively. Other parameters are the same as for (A) in Fig. 5.

6. Conclusion

Acknowledgment

This work was supported by the Core Research for Evolutional Science and Technology (CREST) Project of the Japan Science and Technology (JST) Agency, by a Grant-in-Aid, the Focused Research and Development Project for the Realization of the World’s Most Advanced IT Nation, and the 21st Century Center of Excellence (COE) Program of the Ministry of Education, Culture, Sports, Science and Technology of Japan, and by a Grant-In-Aid and a Research Fellowship from the Japan Society for the Promotion of Science (JSPS).

References and links

1.

T. H. Maiman, “Stimulated optical radiation in ruby,” Nature 187, 493–494 (1960). [CrossRef]

2.

I. Hayashi, M. B. Panish, P. W. Foy, and S. Sumski, “Junction lasers which operate continuously at room temperature,” Appl. Phys. Lett. 17, 109–111 (1970). [CrossRef]

3.

K. Iga, F. Koyama, and S. Kinoshita, “Surface emitting semiconductor lasers,” IEEE J. Quantum Electron, 24, 1845–1855 (1988). [CrossRef]

4.

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, and L. T. Florez, “Vertical-cavity surface emitting lasers: design, growth, fabrication, characterization,” IEEE J. Quantum Electron. 27, 1332–1347 (1991). [CrossRef]

5.

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

6.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, D. D. Dapkus, and I. Kim, “Two dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999). [CrossRef] [PubMed]

7.

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

8.

T. Kobayashi, Y. Morimoto, and T. Sueta, “Closed microcavity laser,” Nat. Top. Meet. Rad. Sci. RS85-06 (1985).

9.

E. Yablonovitch and T. J. Gmitter, “Inhibited spontaneous emission in solid state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987). [CrossRef] [PubMed]

10.

Y. Yamamoto, ed., “Coherence, Amplification, and Quantum effects in Semiconductor Lasers,” (John Wiley & Sons, New York, 1991).

11.

H. Yokoyama and K. Ujihara, eds., “Spontaneous Emission and Laser Oscillation in Microcavities,” (CRC Press, New York, 1995).

12.

T. Baba, “Photonic crystals and microdisk cavities based on GaInAsP-InP system,” IEEE J. Sel. Top. Quantum Electron. 3, 808–830 (1997). [CrossRef]

13.

J. M. Gérard and B. Gayral, “Strong purcell effect for InAs quantum boxes in three-dimensional solid-state microcavities,” J. Lightwave Technol. 17, 2089–2095 (1999). [CrossRef]

14.

M. Loncâr, T. Yoshie, A. Scherer, P. Gogna, and Y. Qiu, “Low-threshold photonic crystal laser,” Appl. Phys. Lett. 81, 2680–2682 (2002). [CrossRef]

15.

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

16.

T. Baba, D. Sano, K. Nozaki, K. Inoshita, Y. Kuroki, and F. Koyama, “Observation of fast spontaneous emission decay in GaInAsP photonic crystal point defect nanocavity at room temperature,” Appl. Phys. Lett. 85, 3989–3991 (2004). [CrossRef]

17.

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]

18.

R. Coccioli, M. Boroditsky, K.W. Kim, Y. Rahmat-Samii, and E. Yablonovitch, “Smallest possible electromagnetic mode volume in a dielectric cavity,” IEE Proc.-Optoelectron. 145, 391–397 (1998). [CrossRef]

19.

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

20.

K. Nozaki, T. Ide, J. Hashimoto, W. H. Zheng, and T. Baba, “Photonic crystal point shift nanolaser with ultimate small modal volume,” Electron. Lett. 41, 843–845 (2005). [CrossRef]

21.

K. Nozaki and T. Baba, “Laser characteristics with ultimate-small modal volume in photonic crystal slab point-shift nanolasers,” Appl. Phys. Lett. 88, 211101 (2006). [CrossRef]

22.

K. Inoshita and T. Baba, “Fabrication of GaInAsP/InP photonic crystal lasers by ICP etching and control of resonant mode in point and line composite defects,” IEEE J. Sel. Top. Quantum Electron. 9, 1347–1354 (2003). [CrossRef]

23.

J. K. Hwang, H. Y. Ryu, D. S. Song, I. Y. Han, H. K. Park, D. H. Jang, and Y. H. Lee, “Continuous room-temperature operation of optically pumped two-dimensional photonic crystal lasers at 1.6 μm,” Photon. Tech. Lett. 12, 1295–1297 (2000). [CrossRef]

24.

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. Exp. 14, 6308–6315 (2006). [CrossRef]

25.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005). [CrossRef] [PubMed]

26.

W. H. Chang, W. Y. Chen, H. S. Chang, T. P. Hsieh, J. I. Chyi, and T. M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. 96, 117401 (2006). [CrossRef] [PubMed]

27.

M. Fujita, A. Sugitatsu, T. Uesugi, and S. Noda, “Fabrication of indium phosphide compound photonic crystal by iodine/xenon inductively coupled plasma etching,” Jpn. J. Appl. Phys. 43, L1400–1402 (2004). [CrossRef]

28.

T. Ide, J. Hashimoto, K. Nozaki, E. Mizuta, and T. Baba, “InP etching by HI/Xe inductively coupled plasma for photonic-crystal device fabrication,” Jpn. J. Appl. Phys. 45, L102–L104 (2006). [CrossRef]

29.

K. Nozaki, A. Nakagawa, D. Sano, and T. Baba, “Ultralow threshold and singlemode lasing in microgear lasers and its fusion with quasiperiodic photonic crystals,” IEEE J. Sel. Top. Quantum Electron. 9, 1355–1360 (2003). [CrossRef]

30.

K. Nozaki and T. Baba, “Carrier and photon analyses of photonic microlasers by two-dimensional rate equations,” IEEE J. Sel. Area. Commun. 23, 1411–1417 (2005). [CrossRef]

31.

M. Fujita, A. Sakai, and T. Baba, “Ultra-small and ultra-low threshold microdisk injection laser - design, fabrication, lasing characteristics and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron. 5, 673–681 (1999). [CrossRef]

32.

J. Vučkovič, O. Painter, Y. Xu, A. Yariv, and A. Scherer, “Finite-difference time-domain calculation of the spontaneous emission coupling factor in optical microcavities,” IEEE J. Quantum Electron. 35, 1168–1175 (1999). [CrossRef]

33.

Y. Suematsu and S. Akiba, “High-speed pulse modulation of injection lasers at non-bias condition,” Trans. IECE of Japan 59, 1–8 (1976).

34.

H. Ichikawa, K. Inoshita, and T. Baba, “Reduction in surface recombination of GaInAsP/InP micro-columns by CH4 plasma irradiation,” Appl. Phys. Lett., 78, 2119–2121 (2001). [CrossRef]

OCIS Codes
(140.5960) Lasers and laser optics : Semiconductor lasers
(230.3990) Optical devices : Micro-optical devices

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: April 19, 2007
Revised Manuscript: May 28, 2007
Manuscript Accepted: May 28, 2007
Published: June 4, 2007

Citation
Kengo Nozaki, Shota Kita, and Toshihiko Baba, "Room temperature continuous wave operation and controlled spontaneous emission in ultrasmall photonic crystal nanolaser," Opt. Express 15, 7506-7514 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-12-7506


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References

  1. T. H. Maiman, "Stimulated optical radiation in ruby," Nature 187, 493−494 (1960). [CrossRef]
  2. I. Hayashi, M. B. Panish, P. W. Foy and S. Sumski, "Junction lasers which operate continuously at room temperature," Appl. Phys. Lett. 17, 109−111 (1970). [CrossRef]
  3. K. Iga, F. Koyama and S. Kinoshita, "Surface emitting semiconductor lasers," IEEE J. Quantum Electron.,  24, 1845−1855 (1988). [CrossRef]
  4. J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee and L. T. Florez, "Vertical-cavity surface emitting lasers: design, growth, fabrication, characterization," IEEE J. Quantum Electron. 27, 1332-1347 (1991). [CrossRef]
  5. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton and R. A. Logan, "Whispering gallery mode microdisk lasers," Appl. Phys. Lett. 60, 289−291 (1992). [CrossRef]
  6. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, D. D. Dapkus, and I. Kim, "Two dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999). [CrossRef] [PubMed]
  7. E. M. Purcell, "Spontaneous emission probabilities at radio frequencies," Phys. Rev. 69, 681 (1946).
  8. T. Kobayashi, Y. Morimoto and T. Sueta, "Closed microcavity laser," Nat. Top. Meet. Rad. Sci. RS85-06 (1985).
  9. E. Yablonovitch and T. J. Gmitter, "Inhibited spontaneous emission in solid state physics and electronics," Phys. Rev. Lett. 58, 2059−2062 (1987). [CrossRef] [PubMed]
  10. Y. Yamamoto, ed., "Coherence, Amplification, and Quantum effects in Semiconductor Lasers," (John Wiley & Sons, New York, 1991).
  11. H. Yokoyama and K. Ujihara, eds., "Spontaneous Emission and Laser Oscillation in Microcavities," (CRC Press, New York, 1995).
  12. T. Baba, "Photonic crystals and microdisk cavities based on GaInAsP-InP system," IEEE J. Sel. Top. Quantum Electron. 3, 808-830 (1997). [CrossRef]
  13. J. M. Gérard and B. Gayral, "Strong purcell effect for InAs quantum boxes in three-dimensional solid-state microcavities," J. Lightwave Technol. 17, 2089-2095 (1999). [CrossRef]
  14. M. Loncâr, T. Yoshie, A. Scherer, P. Gogna and Y. Qiu, "Low-threshold photonic crystal laser," Appl. Phys. Lett. 81, 2680-2682 (2002). [CrossRef]
  15. H. Y. Ryu, M. Notomi, E. Kuramochi, and T. Segawa, "Large spontaneous emission factor (>0.1) in the photonic crystal monopole-mode laser," Appl. Phys. Lett. 84, 1067-1069 (2004). [CrossRef]
  16. T. Baba, D. Sano, K. Nozaki, K. Inoshita, Y. Kuroki and F. Koyama, "Observation of fast spontaneous emission decay in GaInAsP photonic crystal point defect nanocavity at room temperature," Appl. Phys. Lett. 85, 3989−3991 (2004). [CrossRef]
  17. 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]
  18. R. Coccioli, M. Boroditsky, K.W. Kim, Y. Rahmat-Samii and E. Yablonovitch, "Smallest possible electromagnetic mode volume in a dielectric cavity," IEE Proc.-Optoelectron. 145, 391−397 (1998). [CrossRef]
  19. Z. Zhang and M. Qiu, "Small-volume waveguide-section high Q microcavities in 2D photonic crystal slabs," Opt. Exp. 12, 3988−3995 (2004). [CrossRef]
  20. K. Nozaki, T. Ide, J. Hashimoto, W. H. Zheng and T. Baba, "Photonic crystal point shift nanolaser with ultimate small modal volume," Electron. Lett. 41, 843−845 (2005). [CrossRef]
  21. K. Nozaki and T. Baba, "Laser characteristics with ultimate-small modal volume in photonic crystal slab point-shift nanolasers," Appl. Phys. Lett. 88, 211101 (2006). [CrossRef]
  22. K. Inoshita and T. Baba, "Fabrication of GaInAsP/InP photonic crystal lasers by ICP etching and control of resonant mode in point and line composite defects," IEEE J. Sel. Top. Quantum Electron. 9, 1347−1354 (2003). [CrossRef]
  23. J. K. Hwang, H. Y. Ryu, D. S. Song, I. Y. Han, H. K. Park, D. H. Jang and Y. H. Lee, "Continuous room-temperature operation of optically pumped two-dimensional photonic crystal lasers at 1.6 μm," Photon. Tech. Lett. 12, 1295−1297 (2000). [CrossRef]
  24. 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]
  25. D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto and J. Vuèkoviæ, "Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal," Phys. Rev. Lett. 95, 013904 (2005). [CrossRef] [PubMed]
  26. W. H. Chang, W. Y. Chen, H. S. Chang, T. P. Hsieh, J. I. Chyi and T. M. Hsu, "Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities," Phys. Rev. Lett. 96, 117401 (2006). [CrossRef] [PubMed]
  27. M. Fujita, A. Sugitatsu, T. Uesugi and S. Noda, "Fabrication of indium phosphide compound photonic crystal by iodine/xenon inductively coupled plasma etching," Jpn. J. Appl. Phys. 43, L1400−1402 (2004). [CrossRef]
  28. T. Ide, J. Hashimoto, K. Nozaki, E. Mizuta and T. Baba, "InP etching by HI/Xe inductively coupled plasma for photonic-crystal device fabrication," Jpn. J. Appl. Phys. 45, L102−L104 (2006). [CrossRef]
  29. K. Nozaki, A. Nakagawa, D. Sano and T. Baba, "Ultralow threshold and singlemode lasing in microgear lasers and its fusion with quasiperiodic photonic crystals," IEEE J. Sel. Top. Quantum Electron. 9, 1355−1360 (2003). [CrossRef]
  30. K. Nozaki and T. Baba, "Carrier and photon analyses of photonic microlasers by two-dimensional rate equations," IEEE J. Sel. Area. Commun. 23, 1411−1417 (2005). [CrossRef]
  31. M. Fujita, A. Sakai and T. Baba, "Ultra-small and ultra-low threshold microdisk injection laser - design, fabrication, lasing characteristics and spontaneous emission factor," IEEE J. Sel. Top. Quantum Electron. 5, 673−681 (1999). [CrossRef]
  32. J. Vuèkoviè, O. Painter, Y. Xu, A. Yariv and A. Scherer, "Finite-difference time-domain calculation of the spontaneous emission coupling factor in optical microcavities," IEEE J. Quantum Electron. 35, 1168−1175 (1999). [CrossRef]
  33. Y. Suematsu and S. Akiba, "High-speed pulse modulation of injection lasers at non-bias condition," Trans. IECE of Japan 59, 1−8 (1976).
  34. H. Ichikawa, K. Inoshita and T. Baba, "Reduction in surface recombination of GaInAsP/InP micro-columns by CH4 plasma irradiation," Appl. Phys. Lett.,  78, 2119−2121 (2001). [CrossRef]

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