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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 20 — Sep. 24, 2012
  • pp: 22743–22752
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Ultrahigh-Q photonic crystal nanocavities in wide optical telecommunication bands

Ryo Terawaki, Yasushi Takahashi, Masahiro Chihara, Yoshitaka Inui, and Susumu Noda  »View Author Affiliations


Optics Express, Vol. 20, Issue 20, pp. 22743-22752 (2012)
http://dx.doi.org/10.1364/OE.20.022743


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Abstract

We have studied the feasibility of extending the operating wavelength range of high-Q silicon nanocavities above and below the 1.55 μm wavelength band, while maintaining Q factors of more than one million. We have succeeded in developing such nanocavities in the optical telecommunication bands from 1.27 μm to 1.50 μm. Very high Q values of more than two million were obtained even for the 1.30 μm band. The Q values increase proportionally to the resonant wavelength because the scattering loss decreases. We have also analyzed the influence of absorption due to surface water. We conclude that high-Q nanocavities are feasible for an even wider wavelength region including parts of the mid-infrared.

© 2012 OSA

1. Introduction

In 2005, it was discovered how to design photonic heterostructure nanocavities with theoretical Q factors (Qideal) much higher than one million, while an experimental Q factor (Qexp) of 6.0 × 105 was realized in a silicon (Si) slab [2

2. B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-High-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005). [CrossRef]

]. Because 2D-PCs operate on the basis of a periodic refractive index variation arising from nanometer-size air holes, as shown in Fig. 1(a)
Fig. 1 (a) SEM top view of a heterostructure nanocavity where the indicated differences in lattice constants are too small to be distinguished visually (a2 = a1 + 8 nm, a2' = a1 + 4 nm). We fabricated seven nanocavities with different values of a1 ranging from 330 nm to 390 nm. The cavity is excited through evanescent mode coupling via a waveguide with 10% extended width, and dropped light from the cavity is measured. (b) Cross-sectional image of the edge of a Si slab with an air-suspended structure. A tunable laser is incident on one edge of the excitation waveguide.
, improvements in nanofabrication have raised Qexp to values of more than one million. This has enabled us to achieve the highest Qexp so far of ~4.0 million with a resonant wavelength of 1.57 μm [28

28. Y. Taguchi, Y. Takahashi, Y. Sato, T. Asano, and S. Noda, “Statistical studies of photonic heterostructure nanocavities with an average Q factor of three million,” Opt. Express 19(12), 11916–11921 (2011). [CrossRef] [PubMed]

]. A variety of alternative nanocavity designs similar to heterostructures and based on Si slabs have been proposed [29

29. E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006). [CrossRef]

34

34. B. S. Song, S. W. Jeon, and S. Noda, “Symmetrically glass-clad photonic crystal nanocavities with ultrahigh quality factors,” Opt. Lett. 36(1), 91–93 (2011). [CrossRef] [PubMed]

], some of which also exhibit Qexp > 106. A Qexp value of one million roughly corresponds to a spectral linewidth of one picometer and to a photon lifetime of one nanosecond at near-infrared (IR) wavelengths. This photon lifetime is several orders of magnitude longer than the operation speed of cutting-edge optoelectronics. Accordingly, it is becoming possible to dynamically control light-matter interactions in the nanocavities, which will lead to a new field of research in solid-state optics. Taking into account the recent expansion of Si photonics and the fact that these high-Q nanocavities are constructed from commercial crystalline silicon-on-insulator (SOI) wafers using well-developed Si nanofabrication technologies, the potential of high-Q nanocavities is enormous.

One limitation is that the operating wavelengths (λ) of high-Q nanocavities have thus far been restricted to the range between 1.55 μm and 1.60 μm. For wavelengths below 1.50 μm, even nanocavities with Q factors of 105 have not yet been demonstrated. The wavelengths that are used for optical telecommunication are now being extended above and below the 1.55 μm band due to the rapid rise of internet traffic, and for ordinary optical fibers the zero-dispersion wavelength is ~1.30 μm. Furthermore, much of the emission from Si caused by phonon-assisted interband transitions or doped impurities occurs below 1.50 μm [35

35. G. Davies, “The optical properties of luminescence centers in silicon,” Phys. Rep. 176(3-4), 83–188 (1989). [CrossRef]

]. In contrast, the molecular fingerprint region for sensing applications lies at wavelengths above the 1.55 μm band, a region in which cascaded Si Raman lasers have recently been demonstrated [36

36. H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, “A cascaded silicon Raman laser,” Nat. Photonics 2(3), 170–174 (2008). [CrossRef]

]. Therefore, it is important to extend the wavelength range of Si high-Q nanocavities as far as possible while maintaining Qexp values of more than one million.

Because the energy bandgap of Si at room temperature is ~1.12 eV [37

37. V. Alex, S. Finkbeiner, and J. Weber, “Temperature dependence of the indirect energy gap in crystalline silicon,” J. Appl. Phys. 79(9), 6943–6946 (1996). [CrossRef]

], which corresponds to λ ~1.11 μm, it is possible to achieve Qexp values of greater than one million even when λ < 1.50 μm. In order to shorten λ, the photonic structural parameters that characterize 2D PCs (slab thickness, lattice constant, radius of air holes) should be reduced according to a simple scaling law. However, commercial SOI wafers with sufficiently thin top Si layers are not readily available, particularly when the desired thickness is less than 200 nm. In general, it is also technically more difficult to precisely fabricate 2D PCs with smaller structural features. We have previously demonstrated that if the Qideal of a heterostructure nanocavity is more than 10 million, its value is reduced to approximately one million when random variations in the radii and positions of the air holes are on the one-nanometer scale [38

38. H. Hagino, Y. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Effects of fluctuation in air hole radii and positions on optical characteristics in photonic crystal heterostructure nanocavities,” Phys. Rev. B 79(8), 085112 (2009). [CrossRef]

]. These fabrication problems probably represent the main reason why there have been no reports so far of high-Q nanocavities with λ < 1.50 μm. In contrast, we do not expect serious fabrication problems for nanocavities with λ > 1.60 μm. However, absorption due to water that adheres to the Si slab surface might be a challenge to overcome at higher wavelengths because the absorption coefficient of water in the mid-IR region is much larger than in the near-IR region.

Here we demonstrate that the operating wavelength range of Si heterostructure nanocavities can be extended both above and below the 1.55 μm band while maintaining Qexp > 106. We have succeeded in fabricating such nanocavities over a wide range of telecommunication wavelengths from 1.27 μm to 1.50 μm by utilizing our established nanofabrication process and adopting a chemical process to thin the Si layer of the SOI wafers. We have obtained Qexp > 2 × 106 even for the 1.30 μm band, a value that increases almost proportionally to the resonant wavelength; a slight reduction of Qexp was observed at the absorption peak of surface water at ~1.40 μm. By analyzing the influence of water absorption by the Si surface, we conclude that nanocavities with Qexp > 106 can be obtained across the even wider wavelength ranges from 1.20 μm to 2.70 μm and 3.40 μm to 5.00 μm.

2. Sample information

Figure 1 shows scanning electron microscope (SEM) images of a nanocavity investigated in this work. We used 2D PCs with the well-known triangular lattice structure comprised of circular air holes in a Si membrane. The heterostructure nanocavity consisted of a line defect of 17 missing air holes, where the lattice constant in the x-direction increased every two periods as the center of the defect was approached; the lattice constants of the central (a2) and intermediate (a2') sections of the cavity were a2 = a1 + 8 nm and a2' = a1 + 4 nm, respectively. The transmission band-edge frequency decreases with increasing lattice constant, so that the resonant mode in the ground state is confined to the heterostructure and acts as the high-Q nanocavity mode [2

2. B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-High-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005). [CrossRef]

].

3. Fabrication method

We used the well-known chemical solution of ammonia and hydrogen peroxide mixture (APM) to thin the top Si layer of <100> oriented SOI wafers (d = 220 nm, BOX thickness = 3000 nm) [39

39. W. Kern and D. A. Puotinen, “Cleaning solutions based on hydrogen peroxide for use in silicon semiconductor technology,” RCA Rev. 31, 187–206 (1970).

]. Using a mixing ratio with a low density of H2O2, we were able to etch the Si surface at a speed of 1 nm per minute [40

40. K. Yamamoto, A. Nakamura, and Y. Hase, “Control of cleaning performance of an ammonia and hydrogen peroxide mixture (APM) on the basis of a kinetic reaction model,” IEEE Trans. Semicond. Manuf. 12(3), 288–294 (1999). [CrossRef]

]. Figure 2
Fig. 2 AFM images of the SOI wafer surface (a) before and (b) after APM treatment. The average roughness (Ra) of the surface hardly changes.
shows atomic force microscope (AFM) images of a surface (a) before APM treatment and (b) after thinning the top Si layer to 180 nm. This process etches the Si while keeping the surface almost atomically flat and has the additional benefits of low cost, minimal surface damage and efficient surface cleaning.

The samples were fabricated using the following steps. The thin oxidized layer on the prepared SOI wafer was removed with dilute hydrofluoric acid (DHF) and a thin film of electron beam (EB) resist was deposited by spin coating. The PC patterns were drawn on the resist by EB lithography using a probe current of 30 pA. Next, the samples were immersed in the developer at room temperature and the developed mask patterns were transferred to the top Si slab using sulfur hexafluoride-based dry etching. We used high-voltage (100 kV) EB lithography system with small beam size and high density inductively coupled plasma etching at low pressure (0.1 Pa) to reduce random variations of the air holes. These improvements enabled us to precisely fabricate the nanocavities with smaller structural features presented in Table 1. Chips of dimensions 1 mm × 300 μm were formed by polishing and scribing processes and were bonded to small cubic blocks for the optical measurements. Finally, the silicon dioxide (SiO2) layer underneath the patterned region was selectively removed using HF to form an air-bridge structure. Special care was taken to keep the surface clean during all the above steps. The fabricated samples were kept in air at atmospheric pressure.

4. Results

We investigated the basic optical properties of the nanocavities using conventional spectral measurements [41

41. Y. Takahashi, H. Hagino, Y. Tanaka, B. S. Song, T. Asano, and S. Noda, “High-Q nanocavity with a 2-ns photon lifetime,” Opt. Express 15(25), 17206–17213 (2007). [CrossRef] [PubMed]

,42

42. Y. Takahashi, Y. Tanaka, H. Hagino, T. Asano, and S. Noda, “Higher-order resonant modes in a photonic heterostructure nanocavity,” Appl. Phys. Lett. 92(24), 241910 (2008). [CrossRef]

]. The nanocavity was excited through an excitation waveguide using a wavelength-tunable laser with a narrow linewidth and dropped light from the nanocavity in the direction vertical to the slab was measured as illustrated in Fig. 1(a). The distance between the nanocavity and the waveguide was set to 5 rows of air holes for all samples. Six nanocavities with the same structure were fabricated parallel to an excitation waveguide as shown in Fig. 3(a)
Fig. 3 (a) Confocal laser scanning microscope image of a measured sample which has six nanocavities with the same structure. (b) Dropped light spectra for six nanocavities with a1 = 340 nm. The linewidths are smaller than 1.0 pm for all cavities. (c) Magnified view of a single spectrum. The solid line is a Lorentzian fit to the peak.
, thus we measured the spectra of six cavities for each lattice constant.

Figure 3(b) presents the spectra of dropped light from the six cavities with a1 = 340 nm. Resonant wavelengths of close to 1.30 μm were obtained, as expected from the calculations. The fluctuation in λ resulting from random variations of the air holes was less than 0.5 nm, which indicates that the fabrication procedure was highly accurate despite the small structural parameters. Although not presented here, we confirmed that the emission patterns and polarization properties of the dropped light were the same as previously reported [42

42. Y. Takahashi, Y. Tanaka, H. Hagino, T. Asano, and S. Noda, “Higher-order resonant modes in a photonic heterostructure nanocavity,” Appl. Phys. Lett. 92(24), 241910 (2008). [CrossRef]

]. Figure 3(c) shows a magnified view of the spectrum for one nanocavity, wherein the linewidth obtained by fitting a Lorentzian function to the peak was 0.66 pm. This value is too small to accurately evaluate the Q factor owing to the resolution limit of our measurement system and to temperature fluctuations of the sample. Therefore, we also performed time-domain measurements in order to obtain the photon lifetime (τ) of the nanocavities, allowing Qexp to be evaluated using the relationship Qexp = ωτ [3

3. Y. Takahashi, Y. Tanaka, H. Hagino, T. Sugiya, Y. Sato, T. Asano, and S. Noda, “Design and demonstration of high-Q photonic heterostructure nanocavities suitable for integration,” Opt. Express 17(20), 18093–18102 (2009). [CrossRef] [PubMed]

].

Figure 4
Fig. 4 Experimentally obtained Q and λ for nanocavities with a1 = 330 nm - 390 nm. The symbols × , □, △, and ○ represent the Qexp of each cavity, the average Qexp for six cavities with the same a1, the additional loss factor, and previously reported Qexp values, respectively. The upper labels show five bands used for optical telecommunications. The dashed line indicates the absorption spectrum of bulk water, taken from Ref [59].
summarizes the experimentally obtained values of Q and λ for nanocavities with seven different values of a1. Wavelengths of ~1.27 μm and ~1.50 μm were obtained for the cavities with a1 = 330 nm and a1 = 390 nm, respectively. All of the measured wavelengths are in good agreement with the calculated values shown in Table 1. We also fabricated nanocavities with a1 = 320 nm, which were expected to have λ ≈1230 nm. However, we were unable to measure their optical properties because there is no high performance tunable laser available for the 1.10 − 1.25 μm range.

The Qexp values of cavities with the same lattice constant fluctuate due to random variations in the air holes. However, only one cavity in all our samples had a Qexp of less than one million. The average values of Qexp for sets of six nanocavities with the same a1 (Qave) all exceeded one million across the three telecommunication bands (O, E, and S-bands). These values are more than one order of magnitude higher than previously reported at these wavelengths. We emphasize that Qexp > 2.0 × 106 was obtained even for the 1.30 μm band, a value that has not previously been achieved even for the 1.55 μm band, excluding our earlier study. When the previously reported Qexp values for nanocavities in the C,L-bands are added to Fig. 4 [43

43. Z. Han, X. Checoury, D. Neel, S. David, M. E. Kurdi, and P. Boucaud, “Optimized design for 2×106 ultra-high Q silicon photonic crystal cavities,” Opt. Commun. 283(21), 4387–4391 (2010). [CrossRef]

,44

44. M. Notomi, “Strong light confinement with periodicity,” Proc. IEEE 99(10), 1768–1779 (2011). [CrossRef]

], it becomes clear that ultrahigh-Q nanocavities are feasible for most currently used optical communication bands.

Recently, PC high-Q nanocavities or microcavities have been realized in many materials and we briefly refer to them for the comparison. The InP-based cavities, which are used for low-threshold laser embedded with InGaAsP quantum wells [15

15. S. Kita, S. Otsuka, S. Hachuda, T. Endo, Y. Imai, Y. Nishijima, H. Misawa, and T. Baba, “Photonic crystal nanolaser biosensors,” IEICE Trans. Electron. E 95C, 188–198 (2012).

,16

16. K. Nozaki, S. Kita, and T. Baba, “Room temperature continuous wave operation and controlled spontaneous emission in ultrasmall photonic crystal nanolaser,” Opt. Express 15(12), 7506–7514 (2007). [CrossRef] [PubMed]

,19

19. S. Matsuo, K. Takeda, T. Sato, M. Notomi, A. Shinya, K. Nozaki, H. Taniyama, K. Hasebe, and T. Kakitsuka, “Room-temperature continuous-wave operation of lateral current injection wavelength-scale embedded active-region photonic-crystal laser,” Opt. Express 20(4), 3773–3780 (2012). [CrossRef] [PubMed]

], the chalcogenide glass cavities, and GaAs cavities have achieved Qexp more than 1.0 × 105 in the C,L-bands [45

45. A. Shinya, S. Matsuo, T. Yosia, T. Tanabe, E. Kuramochi, T. Sato, T. Kakitsuka, and M. Notomi, “All-optical on-chip bit memory based on ultra high Q InGaAsP photonic crystal,” Opt. Express 16(23), 19382–19387 (2008). [CrossRef] [PubMed]

48

48. R. Herrmann, T. Sünner, T. Hein, A. Löffler, M. Kamp, and A. Forchel, “Ultrahigh-quality photonic crystal cavity in GaAs,” Opt. Lett. 31(9), 1229–1231 (2006). [CrossRef] [PubMed]

]. The GaAs-based nanocavities embedded with InAs quantum dots have achieved Qexp of several tens of thousand in the wavelength range from 900 and 1200 nm [17

17. M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot–nanocavity system,” Nat. Phys. 6(4), 279–283 (2010). [CrossRef]

, 25

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

27

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

], which are widely used for nano-lasers [17

17. M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot–nanocavity system,” Nat. Phys. 6(4), 279–283 (2010). [CrossRef]

,18

18. B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, and J. Vuckovic, “Ultralow-threshold electrically pumped quantumdot photonic-crystal nanocavity laser,” Nat. Photonics 5(5), 297–300 (2011). [CrossRef]

], single photon emitters [20

20. D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vucković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95(1), 013904 (2005). [CrossRef] [PubMed]

22

22. S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1(8), 449–458 (2007). [CrossRef]

], and cavity quantum electrodynamics [25

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

27

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

]. In the visible wavelength range, nanocavities with Qexp of thousands have been reported using diamond [49

49. A. Faraon, C. Santori, Z. Huang, V. M. Acosta, and R. G. Beausoleil, “Coupling of nitrogen-vacancy centers to photonic crystal cavities in monocrystalline diamond,” Phys. Rev. Lett. 109(3), 033604 (2012). [CrossRef] [PubMed]

], SiC [50

50. S. Yamada, B. S. Song, T. Asano, and S. Noda, “Silicon carbide-based photonic crystal nanocavities for ultra-broadband operation from infrared to visible wavelengths,” Appl. Phys. Lett. 99(20), 201102 (2011). [CrossRef]

], GaN [51

51. N. V. Trivino, G. Rossbach, U. Dharanipathy, J. Levrat, A. Castiglia, J. F. Carlin, K. A. Atlasov, R. Butte, R. Houdre, and N. Grandjean, “High quality factor two dimensional GaN photonic crystal cavity membranes grown on silicon substrate,” Appl. Phys. Lett. 100(7), 071103 (2012). [CrossRef]

], and GaP [52

52. D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vučković, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett. 10(10), 3922–3926 (2010). [CrossRef] [PubMed]

] while SiN cavities have achieved Qexp of 55,000 [53

53. M. Khan, T. Babinec, M. W. McCutcheon, P. Deotare, and M. Lončar, “Fabrication and characterization of high-quality-factor silicon nitride nanobeam cavities,” Opt. Lett. 36(3), 421–423 (2011). [CrossRef] [PubMed]

]. In the UV region, AlN nanocavities have reported Qexp about 5,000 [54

54. D. Sam-Giao, D. Neel, S. Sergent, B. Gayral, M. J. Rashid, F. Semond, J. Y. Duboz, M. Mexis, T. Guillet, C. Brimont, S. David, X. Checoury, and P. Boucaud, “High quality factor AlN nanocavities embedded in a photonic crystal waveguide,” Appl. Phys. Lett. 100(19), 191104 (2012). [CrossRef]

,55

55. S. Sergent, M. Arita, S. Kako, S. Iwamoto, and Y. Arakawa, “High-Q (>5000) AlN nanobeam photonic crystal cavity embedding GaN quantum dots,” Appl. Phys. Lett. 100(12), 121103 (2012). [CrossRef]

]. Both improving the quality of the substrates and developing the nanofabrication process are important for increasing Qexp factors of these cavities.

5. Discussion

The high Qave of 3.1 million at λ = 1.50 μm decreased gradually to 1.7 million at λ = 1.39 μm. It increased once more to 2.1 million at λ = 1.34 μm and then steadily decreased to 1.5 million at λ = 1.27 μm. The Qloss factors plotted in Fig. 4 are due to imperfections in the fabricated samples; these values were derived using the relationship 1/Qloss = 1/Qave − 1/Qideal. Because Qloss follows the same trend as Qave, the reduction in Qave with decreasing wavelength is mainly caused by the decrease in Qloss rather than that of Qideal. It is known that there are contributions to Qloss both from the scattering loss due to air hole variations and from the absorption loss [56

56. T. Asano, B. S. Song, and S. Noda, “Analysis of the experimental Q factors (~ 1 million) of photonic crystal nanocavities,” Opt. Express 14(5), 1996–2002 (2006). [CrossRef] [PubMed]

]. We consider that an increase in the scattering loss is the most likely cause of the decrease in Qloss with decreasing λ because the fabrication accuracy should deteriorate for 2D PCs that have a relatively thick slab compared to a1. A large discontinuity is apparent between the cavities with a1 = 350 nm and 360 nm. Furthermore, the contribution of the scattering loss to Qloss should be proportional to λ3 in these samples according to the Rayleigh scattering law, even when the magnitude of the air hole variations is constant. We are sure that the absorption coefficient (α) of crystalline Si is negligibly small at these wavelengths [57

57. D. F. Edwards, “Silicon (Si),” in Handbook of Optical Constants of Solids vol. 1 E. D. Palik, ed. (Academic Press, 1985).

].

From these results, we can assume that a Qexp of one million can be obtained down to λ = 1.20 μm. These values will be difficult to achieve below 1.20 μm because the interband absorption of Si rapidly increases with the aid of phonons [57

57. D. F. Edwards, “Silicon (Si),” in Handbook of Optical Constants of Solids vol. 1 E. D. Palik, ed. (Academic Press, 1985).

]. For example, Qloss = 105 at 1.13 μm and Qloss = 104 at 1.05 μm according to the equation Qloss = 2πn/αλ [56

56. T. Asano, B. S. Song, and S. Noda, “Analysis of the experimental Q factors (~ 1 million) of photonic crystal nanocavities,” Opt. Express 14(5), 1996–2002 (2006). [CrossRef] [PubMed]

].

Finally, we consider the influence of water absorption on Qloss and the feasibility of realizing high-Q nanocavities in the mid-IR range. As discussed above, Qexp is one order of magnitude smaller than the designed Qideal due to Qloss. Although we have investigated the scattering loss in detail [28

28. Y. Taguchi, Y. Takahashi, Y. Sato, T. Asano, and S. Noda, “Statistical studies of photonic heterostructure nanocavities with an average Q factor of three million,” Opt. Express 19(12), 11916–11921 (2011). [CrossRef] [PubMed]

,38

38. H. Hagino, Y. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Effects of fluctuation in air hole radii and positions on optical characteristics in photonic crystal heterostructure nanocavities,” Phys. Rev. B 79(8), 085112 (2009). [CrossRef]

], the influence of absorption is still unclear; it has often been suspected that water adhering to the Si surface must be taken into account [56

56. T. Asano, B. S. Song, and S. Noda, “Analysis of the experimental Q factors (~ 1 million) of photonic crystal nanocavities,” Opt. Express 14(5), 1996–2002 (2006). [CrossRef] [PubMed]

]. When the absorption loss is comparable to the scattering loss or larger, Qexp cannot be significantly increased even if the fabrication accuracy is improved. Because the absorption coefficient of water in the mid-IR region is more than one order of magnitude larger than that for the 1.55 μm band [58

58. M. R. Querry, D. M. Wieliczka, and D. J. Segelstein, “Water (H20),” in Handbook of Optical Constants of Solids vol. 2 E. D. Palik, ed. (Academic Press, 1991).

], it is very important to investigate the influence of water absorption.

The dashed line in Fig. 4 represents the absorption spectrum of bulk water at room temperature [59

59. L. Kou, D. Labrie, and P. Chylek, “Refractive indices of water and ice in the 0.65- to 2.5-µm spectral range,” Appl. Opt. 32(19), 3531–3540 (1993). [CrossRef] [PubMed]

], which exhibits a broad peak at ~1.45 μm originating from the first overtone combination involving the symmetric and asymmetric stretching vibration modes of water molecules. There is seemingly no correlation between Qexp and the absorption spectrum because the maximum Qexp of 3.6 million is obtained at λ = 1.46 μm. However, it appears that Qexp at λ = 1.39 μm and 1.43 μm is slightly smaller than expected from the data at λ = 1.46 μm and 1.50 μm. It is known that the broad peak at 1.45 μm becomes sharper and shifts to ~1.40 μm for water that is weakly hydrogen bonded, as is the case for surface water (water vapor has a peak at 1.38 μm) [60

60. L. G. Weyer and S. C. Lo, “Spectra-Structure Correlations in the Near-infrared,” in Handbook of Vibrational Spectroscopy vol. 3 J. M. Chalmers and P. R. Griffiths, ed. (Wiley, 2002).

]. Therefore, we conclude that water adhering to the Si surface probably contributes to the Qloss of these samples in the domain λ > 1.38 μm.

In the wavelength region above 1.60 μm, the contribution to Qloss from the absorption of Si is negligible up to 5.00 μm [57

57. D. F. Edwards, “Silicon (Si),” in Handbook of Optical Constants of Solids vol. 1 E. D. Palik, ed. (Academic Press, 1985).

]. The Qloss due to surface water can be evaluated using the equation Qloss = 2πn/ηαλ, where η is conversion factor based on the volume ratio of surface water to Si. Here we assume from the result in Fig. 4 that the absorption value of α = 50 cm−1 in bulk water roughly corresponds to Qloss = 107. Because the maximum value of α in the near-IR band below 2.50 μm is at most 120 cm−1, Qexp > 106 will easily be possible. In the mid-IR region, α exceeds 500 cm−1 between 2.70 μm and 3.40 μm due to a very strong peak centered at ~3.00 μm (where α > 10,000 cm−1), originating from the fundamental stretching modes. In the range from 3.40 μm and 5.00 μm, α fluctuates between 100 cm−1 and 500 cm−1 [58

58. M. R. Querry, D. M. Wieliczka, and D. J. Segelstein, “Water (H20),” in Handbook of Optical Constants of Solids vol. 2 E. D. Palik, ed. (Academic Press, 1991).

]. Therefore, a Qexp of one million would be possible in some regions of the mid-IR range below 5.00 μm.

6. Summary

We have attempted to extend the operating wavelength range of Si heterostructure nanocavities while maintaining Qexp values of more than one million. We have successfully developed such high-Q nanocavities with resonant wavelengths ranging from 1.27 μm to 1.50 μm. In particular, nanocavities with Qexp exceeding two million at the 1.30 μm band have been fabricated. By estimating the influences of absorption by Si and surface water, we conclude that nanocavities with Qexp > 106 can be obtained over wider wavelength ranges from 1.20 μm to 2.70 μm and 3.40 μm and 5.00 μm. We believe that these findings will stimulate research into novel applications including ultrasmall optics for the 1.30 μm band, highly sensitive sensors in the mid-IR band, Si emitters and lasers, and hybrid nanocavity devices combined with various nanomaterials, all of which will further expand the utilization of Si photonics.

Acknowledgment

The authors thank Prof. M. Takeuchi of Osaka Prefecture University and Prof. T. Asano of Kyoto University for fruitful discussions regarding surface water and scattering loss. This work was partly supported by Funds for the Development of Human Resources in Science and Technology commissioned by MEXT, by JST, PRESTO, by MEXT KAKENHI Grant Number 23104721 and JSPS KAKENHI Grant Number 23686015, 20226002, and by FIRST program.

References and links

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Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003). [CrossRef] [PubMed]

2.

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-High-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005). [CrossRef]

3.

Y. Takahashi, Y. Tanaka, H. Hagino, T. Sugiya, Y. Sato, T. Asano, and S. Noda, “Design and demonstration of high-Q photonic heterostructure nanocavities suitable for integration,” Opt. Express 17(20), 18093–18102 (2009). [CrossRef] [PubMed]

4.

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407(6804), 608–610 (2000). [CrossRef] [PubMed]

5.

H. Takano, B. S. Song, T. Asano, and S. Noda, “Highly efficient multi-channel drop filter in a two-dimensional hetero photonic crystal,” Opt. Express 14(8), 3491–3496 (2006). [CrossRef] [PubMed]

6.

B. S. Song, T. Nagashima, T. Asano, and S. Noda, “Resonant-wavelength control of nanocavities by nanometer-scaled adjustment of two-dimensional photonic crystal slab structures,” IEEE Photon. Technol. Lett. 20(7), 532–534 (2008). [CrossRef]

7.

Y. Tanaka, J. Upham, T. Nagashima, T. Sugiya, T. Asano, and S. Noda, “Dynamic control of the Q factors in a photonic crystal nanocavity,” Nat. Mater. 6(11), 862–865 (2007). [CrossRef] [PubMed]

8.

M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics 2(12), 741–747 (2008). [CrossRef]

9.

J. Upham, Y. Tanaka, Y. Kawamoto, Y. Sato, T. Nakamura, B. S. Song, T. Asano, and S. Noda, “Time-resolved catch and release of an optical pulse from a dynamic photonic crystal nanocavity,” Opt. Express 19(23), 23377–23385 (2011). [CrossRef] [PubMed]

10.

Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, and S. Noda, “Strong coupling between distant photonic nanocavities and its dynamic control,” Nat. Photonics 6(1), 56–61 (2011). [CrossRef]

11.

T. Tanabe, H. Sumikura, H. Taniyama, A. Shinya, and M. Notomi, “All-silicon sub-Gb/s telecom detector with low dark current and high quantum efficiency on chip,” Appl. Phys. Lett. 96(10), 101103 (2010). [CrossRef]

12.

L. D. Haret, X. Checoury, Z. Han, P. Boucaud, S. Combrié, and A. De Rossi, “All-silicon photonic crystal photoconductor on silicon-on-insulator at telecom wavelength,” Opt. Express 18(23), 23965–23972 (2010). [CrossRef] [PubMed]

13.

A. Falco, L. O’Faolain, and T. F. Krauss, “Chemical sensing in slotted photonic crystal heterostructure cavities,” Appl. Phys. Lett. 94(6), 063503 (2009). [CrossRef]

14.

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15.

S. Kita, S. Otsuka, S. Hachuda, T. Endo, Y. Imai, Y. Nishijima, H. Misawa, and T. Baba, “Photonic crystal nanolaser biosensors,” IEICE Trans. Electron. E 95C, 188–198 (2012).

16.

K. Nozaki, S. Kita, and T. Baba, “Room temperature continuous wave operation and controlled spontaneous emission in ultrasmall photonic crystal nanolaser,” Opt. Express 15(12), 7506–7514 (2007). [CrossRef] [PubMed]

17.

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot–nanocavity system,” Nat. Phys. 6(4), 279–283 (2010). [CrossRef]

18.

B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, and J. Vuckovic, “Ultralow-threshold electrically pumped quantumdot photonic-crystal nanocavity laser,” Nat. Photonics 5(5), 297–300 (2011). [CrossRef]

19.

S. Matsuo, K. Takeda, T. Sato, M. Notomi, A. Shinya, K. Nozaki, H. Taniyama, K. Hasebe, and T. Kakitsuka, “Room-temperature continuous-wave operation of lateral current injection wavelength-scale embedded active-region photonic-crystal laser,” Opt. Express 20(4), 3773–3780 (2012). [CrossRef] [PubMed]

20.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vucković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95(1), 013904 (2005). [CrossRef] [PubMed]

21.

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S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1(8), 449–458 (2007). [CrossRef]

23.

S. Iwamoto, Y. Arakawa, and A. Gomyo, “Observation of enhanced photoluminescence from silicon photonic crystal nanocavity at room temperature,” Appl. Phys. Lett. 91(21), 211104 (2007). [CrossRef]

24.

X. Yang and C. W. Wong, “Coupled-mode theory for stimulated Raman scattering in high-Q/Vm silicon photonic band gap defect cavity lasers,” Opt. Express 15(8), 4763–4780 (2007). [CrossRef] [PubMed]

25.

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

26.

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

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

28.

Y. Taguchi, Y. Takahashi, Y. Sato, T. Asano, and S. Noda, “Statistical studies of photonic heterostructure nanocavities with an average Q factor of three million,” Opt. Express 19(12), 11916–11921 (2011). [CrossRef] [PubMed]

29.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006). [CrossRef]

30.

S. Tomljenovic-Hanic, C. M. de Sterke, M. J. Steel, B. J. Eggleton, Y. Tanaka, and S. Noda, “High-Q cavities in multilayer photonic crystal slabs,” Opt. Express 15(25), 17248–17253 (2007). [CrossRef] [PubMed]

31.

S. H. Kwon, T. Sünner, M. Kamp, and A. Forchel, “Ultrahigh-Q photonic crystal cavity created by modulating air hole radius of a waveguide,” Opt. Express 16(7), 4605–4614 (2008). [CrossRef] [PubMed]

32.

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94(12), 121106 (2009). [CrossRef]

33.

A. Yokoo, T. Tanabe, E. Kuramochi, and M. Notomi, “Ultrahigh-Q nanocavities written with a nanoprobe,” Nano Lett. 11(9), 3634–3642 (2011). [CrossRef] [PubMed]

34.

B. S. Song, S. W. Jeon, and S. Noda, “Symmetrically glass-clad photonic crystal nanocavities with ultrahigh quality factors,” Opt. Lett. 36(1), 91–93 (2011). [CrossRef] [PubMed]

35.

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V. Alex, S. Finkbeiner, and J. Weber, “Temperature dependence of the indirect energy gap in crystalline silicon,” J. Appl. Phys. 79(9), 6943–6946 (1996). [CrossRef]

38.

H. Hagino, Y. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Effects of fluctuation in air hole radii and positions on optical characteristics in photonic crystal heterostructure nanocavities,” Phys. Rev. B 79(8), 085112 (2009). [CrossRef]

39.

W. Kern and D. A. Puotinen, “Cleaning solutions based on hydrogen peroxide for use in silicon semiconductor technology,” RCA Rev. 31, 187–206 (1970).

40.

K. Yamamoto, A. Nakamura, and Y. Hase, “Control of cleaning performance of an ammonia and hydrogen peroxide mixture (APM) on the basis of a kinetic reaction model,” IEEE Trans. Semicond. Manuf. 12(3), 288–294 (1999). [CrossRef]

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Y. Takahashi, H. Hagino, Y. Tanaka, B. S. Song, T. Asano, and S. Noda, “High-Q nanocavity with a 2-ns photon lifetime,” Opt. Express 15(25), 17206–17213 (2007). [CrossRef] [PubMed]

42.

Y. Takahashi, Y. Tanaka, H. Hagino, T. Asano, and S. Noda, “Higher-order resonant modes in a photonic heterostructure nanocavity,” Appl. Phys. Lett. 92(24), 241910 (2008). [CrossRef]

43.

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44.

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45.

A. Shinya, S. Matsuo, T. Yosia, T. Tanabe, E. Kuramochi, T. Sato, T. Kakitsuka, and M. Notomi, “All-optical on-chip bit memory based on ultra high Q InGaAsP photonic crystal,” Opt. Express 16(23), 19382–19387 (2008). [CrossRef] [PubMed]

46.

M. W. Lee, C. Grillet, S. Tomljenovic-Hanic, E. C. Mägi, D. J. Moss, B. J. Eggleton, X. Gai, S. Madden, D. Y. Choi, D. A. P. Bulla, and B. Luther-Davies, “Photowritten high-Q cavities in two-dimensional chalcogenide glass photonic crystals,” Opt. Lett. 34(23), 3671–3673 (2009). [CrossRef] [PubMed]

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OCIS Codes
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(230.5298) Optical devices : Photonic crystals

ToC Category:
Photonic Crystals

History
Original Manuscript: July 23, 2012
Revised Manuscript: September 4, 2012
Manuscript Accepted: September 16, 2012
Published: September 19, 2012

Citation
Ryo Terawaki, Yasushi Takahashi, Masahiro Chihara, Yoshitaka Inui, and Susumu Noda, "Ultrahigh-Q photonic crystal nanocavities in wide optical telecommunication bands," Opt. Express 20, 22743-22752 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-20-22743


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References

  1. Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature425(6961), 944–947 (2003). [CrossRef] [PubMed]
  2. B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-High-Q photonic double-heterostructure nanocavity,” Nat. Mater.4(3), 207–210 (2005). [CrossRef]
  3. Y. Takahashi, Y. Tanaka, H. Hagino, T. Sugiya, Y. Sato, T. Asano, and S. Noda, “Design and demonstration of high-Q photonic heterostructure nanocavities suitable for integration,” Opt. Express17(20), 18093–18102 (2009). [CrossRef] [PubMed]
  4. S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature407(6804), 608–610 (2000). [CrossRef] [PubMed]
  5. H. Takano, B. S. Song, T. Asano, and S. Noda, “Highly efficient multi-channel drop filter in a two-dimensional hetero photonic crystal,” Opt. Express14(8), 3491–3496 (2006). [CrossRef] [PubMed]
  6. B. S. Song, T. Nagashima, T. Asano, and S. Noda, “Resonant-wavelength control of nanocavities by nanometer-scaled adjustment of two-dimensional photonic crystal slab structures,” IEEE Photon. Technol. Lett.20(7), 532–534 (2008). [CrossRef]
  7. Y. Tanaka, J. Upham, T. Nagashima, T. Sugiya, T. Asano, and S. Noda, “Dynamic control of the Q factors in a photonic crystal nanocavity,” Nat. Mater.6(11), 862–865 (2007). [CrossRef] [PubMed]
  8. M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics2(12), 741–747 (2008). [CrossRef]
  9. J. Upham, Y. Tanaka, Y. Kawamoto, Y. Sato, T. Nakamura, B. S. Song, T. Asano, and S. Noda, “Time-resolved catch and release of an optical pulse from a dynamic photonic crystal nanocavity,” Opt. Express19(23), 23377–23385 (2011). [CrossRef] [PubMed]
  10. Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, and S. Noda, “Strong coupling between distant photonic nanocavities and its dynamic control,” Nat. Photonics6(1), 56–61 (2011). [CrossRef]
  11. T. Tanabe, H. Sumikura, H. Taniyama, A. Shinya, and M. Notomi, “All-silicon sub-Gb/s telecom detector with low dark current and high quantum efficiency on chip,” Appl. Phys. Lett.96(10), 101103 (2010). [CrossRef]
  12. L. D. Haret, X. Checoury, Z. Han, P. Boucaud, S. Combrié, and A. De Rossi, “All-silicon photonic crystal photoconductor on silicon-on-insulator at telecom wavelength,” Opt. Express18(23), 23965–23972 (2010). [CrossRef] [PubMed]
  13. A. Falco, L. O’Faolain, and T. F. Krauss, “Chemical sensing in slotted photonic crystal heterostructure cavities,” Appl. Phys. Lett.94(6), 063503 (2009). [CrossRef]
  14. T. W. Lu, P. T. Lin, K. U. Sio, and P. T. Lee, “Optical sensing of square lattice photonic crystal point-shifted nanocavity for protein adsorption detection,” Appl. Phys. Lett.96(21), 213702 (2010). [CrossRef]
  15. S. Kita, S. Otsuka, S. Hachuda, T. Endo, Y. Imai, Y. Nishijima, H. Misawa, and T. Baba, “Photonic crystal nanolaser biosensors,” IEICE Trans. Electron.E 95C, 188–198 (2012).
  16. K. Nozaki, S. Kita, and T. Baba, “Room temperature continuous wave operation and controlled spontaneous emission in ultrasmall photonic crystal nanolaser,” Opt. Express15(12), 7506–7514 (2007). [CrossRef] [PubMed]
  17. M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot–nanocavity system,” Nat. Phys.6(4), 279–283 (2010). [CrossRef]
  18. B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, and J. Vuckovic, “Ultralow-threshold electrically pumped quantumdot photonic-crystal nanocavity laser,” Nat. Photonics5(5), 297–300 (2011). [CrossRef]
  19. S. Matsuo, K. Takeda, T. Sato, M. Notomi, A. Shinya, K. Nozaki, H. Taniyama, K. Hasebe, and T. Kakitsuka, “Room-temperature continuous-wave operation of lateral current injection wavelength-scale embedded active-region photonic-crystal laser,” Opt. Express20(4), 3773–3780 (2012). [CrossRef] [PubMed]
  20. D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vucković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett.95(1), 013904 (2005). [CrossRef] [PubMed]
  21. 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(11), 117401 (2006). [CrossRef] [PubMed]
  22. S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics1(8), 449–458 (2007). [CrossRef]
  23. S. Iwamoto, Y. Arakawa, and A. Gomyo, “Observation of enhanced photoluminescence from silicon photonic crystal nanocavity at room temperature,” Appl. Phys. Lett.91(21), 211104 (2007). [CrossRef]
  24. X. Yang and C. W. Wong, “Coupled-mode theory for stimulated Raman scattering in high-Q/Vm silicon photonic band gap defect cavity lasers,” Opt. Express15(8), 4763–4780 (2007). [CrossRef] [PubMed]
  25. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature432(7014), 200–203 (2004). [CrossRef] [PubMed]
  26. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature445(7130), 896–899 (2007). [CrossRef] [PubMed]
  27. I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlled phase shifts with a single quantum dot,” Science320(5877), 769–772 (2008). [CrossRef] [PubMed]
  28. Y. Taguchi, Y. Takahashi, Y. Sato, T. Asano, and S. Noda, “Statistical studies of photonic heterostructure nanocavities with an average Q factor of three million,” Opt. Express19(12), 11916–11921 (2011). [CrossRef] [PubMed]
  29. E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett.88(4), 041112 (2006). [CrossRef]
  30. S. Tomljenovic-Hanic, C. M. de Sterke, M. J. Steel, B. J. Eggleton, Y. Tanaka, and S. Noda, “High-Q cavities in multilayer photonic crystal slabs,” Opt. Express15(25), 17248–17253 (2007). [CrossRef] [PubMed]
  31. S. H. Kwon, T. Sünner, M. Kamp, and A. Forchel, “Ultrahigh-Q photonic crystal cavity created by modulating air hole radius of a waveguide,” Opt. Express16(7), 4605–4614 (2008). [CrossRef] [PubMed]
  32. P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett.94(12), 121106 (2009). [CrossRef]
  33. A. Yokoo, T. Tanabe, E. Kuramochi, and M. Notomi, “Ultrahigh-Q nanocavities written with a nanoprobe,” Nano Lett.11(9), 3634–3642 (2011). [CrossRef] [PubMed]
  34. B. S. Song, S. W. Jeon, and S. Noda, “Symmetrically glass-clad photonic crystal nanocavities with ultrahigh quality factors,” Opt. Lett.36(1), 91–93 (2011). [CrossRef] [PubMed]
  35. G. Davies, “The optical properties of luminescence centers in silicon,” Phys. Rep.176(3-4), 83–188 (1989). [CrossRef]
  36. H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, “A cascaded silicon Raman laser,” Nat. Photonics2(3), 170–174 (2008). [CrossRef]
  37. V. Alex, S. Finkbeiner, and J. Weber, “Temperature dependence of the indirect energy gap in crystalline silicon,” J. Appl. Phys.79(9), 6943–6946 (1996). [CrossRef]
  38. H. Hagino, Y. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Effects of fluctuation in air hole radii and positions on optical characteristics in photonic crystal heterostructure nanocavities,” Phys. Rev. B79(8), 085112 (2009). [CrossRef]
  39. W. Kern and D. A. Puotinen, “Cleaning solutions based on hydrogen peroxide for use in silicon semiconductor technology,” RCA Rev.31, 187–206 (1970).
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