Abstract

Raman silicon (Si) lasers based on high-quality-factor photonic crystal nanocavities are very compact and can operate at excitation powers of less than one microwatt. For the best performance, the nanocavity of the Raman Si laser has to be fabricated along the [100] crystal direction of the Si-on-insulator (SOI) wafer to enhance the Raman gain. On the other hand, Si photonic devices are usually fabricated along the [110] direction because crystalline Si can be easily cleaved along [110]. This rotation by 45 degrees of the nanocavity with respect to the cleavable direction can be problematic for various applications. Here we report a Raman Si nanocavity laser fabricated on a modified (100) SOI wafer in which the crystal orientation of the top Si layer is rotated in plane by 45 degrees relative to the crystal direction of the support substrate. We observe room temperature continuous wave laser oscillation with a sub-microwatt threshold and a maximum energy efficiency of 5.6%. It is found that the photonic-slab warpage induced by compressive stress is reduced in this 45°-rotated SOI wafer.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (1)

M. Kuwabara, S. Noda, and Y. Takahashi, “Ultrahigh-Q photonic nanocavity devices on a dual thickness SOI substrate operating at both 1.31- and 1.55-µm telecommunication wavelength bands,” Laser Photonics Rev. 13(2), 1800258 (2019).
[Crossref]

2018 (7)

D. Yamashita, Y. Takahashi, J. Kurihara, T. Asano, and S. Noda, “Lasing dynamics of optically-pumped ultralow-threshold Raman silicon nanocavity lasers,” Phys. Rev. Appl. 10(2), 024039 (2018).
[Crossref]

D. Yamashita, T. Asano, S. Noda, and Y. Takahashi, “Strongly asymmetric wavelength dependence of optical gain in nanocavity-based Raman silicon lasers,” Optica 5(10), 1256–1263 (2018).
[Crossref]

M. R. Billah, M. Blaicher, T. Hoose, P. I. Dietrich, P. M. Palomo, N. Lindenmann, A. Nesic, A. Hofmann, U. Troppenz, M. Moehrle, S. Randel, W. Freude, and C. Koos, “Hybrid integration of silicon photonics circuits and InP lasers by photonic wire bonding,” Optica 5(7), 876–883 (2018).
[Crossref]

R. Katsumi, Y. Ota, M. Kakuda, S. Iwamoto, and Y. Arakawa, “Transfer-printed single-photon sources coupled to wire waveguides,” Optica 5(6), 691–694 (2018).
[Crossref]

G. Takeuchi, Y. Terada, M. Takeuchi, H. Abe, H. Ito, and T. Baba, “Thermally controlled Si photonic crystal slow light waveguide beam steering device,” Opt. Express 26(9), 11529–11537 (2018).
[Crossref]

K. Ashida, M. Okano, M. Ohtsuka, M. Seki, N. Yokoyama, K. Koshino, K. Yamada, and Y. Takahashi, “Photonic Crystal Nanocavities with an Average Q factor of 1.9 million Fabricated on a 300-mm-Wide SOI Wafer Using a CMOS-Compatible Process,” J. Lightwave Technol. 36(20), 4774–4782 (2018).
[Crossref]

T. Asano and S. Noda, “Optimization of photonic crystal nanocavities based on deep learning,” Opt. Express 26(25), 32704–32716 (2018).
[Crossref]

2017 (7)

2015 (4)

K. K. Mehta, J. S. Orcutt, O. Tehar-Zahav, Z. Sternberg, R. Bafrali, R. Meade, and R. J. Ram, “High-Q CMOS-integrated photonic crystal microcavity devices,” Sci. Rep. 4(1), 4077 (2015).
[Crossref]

D. Yamashita, Y. Takahashi, T. Asano, and S. Noda, “Raman shift and strain effect in high-Q photonic crystal silicon nanocavity,” Opt. Express 23(4), 3951–3959 (2015).
[Crossref]

Y.-H. Hsiao, S. Iwamoto, and Y. Arakawa, “Spontaneous and stimulated Raman scattering in silica-cladded silicon photonic crystal waveguides,” Jpn. J. Appl. Phys. 54(4S), 04DG02 (2015).
[Crossref]

W. H. Teh, D. S. Boning, and R. E. Welsch, “Multi-Strata Stealth Dicing Before Grinding for Singulation-Defects Elimination and Die Strength Enhancement: Experiment and Simulation,” IEEE Trans. Semicon. Manufact. 28(3), 408–423 (2015).
[Crossref]

2014 (2)

2013 (3)

H. C. Nguyen, N. Yazawa, S. Hashimoto, S. Otsuka, and T. Baba, “Sub-100 µm Photonic Crystal Si Optical Modulators: Spectral, Athermal, and High-Speed Performance,” IEEE J. Sel. Top. Quantum Electron. 19(6), 127–137 (2013).
[Crossref]

Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, “A micrometre-scale Raman silicon laser with a microwatt threshold,” Nature 498(7455), 470–474 (2013).
[Crossref]

Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, “High-Q resonant modes in a photonic crystal heterostructure nanocavity and applicability to a Raman silicon laser,” Phys. Rev. B 88(23), 235313 (2013).
[Crossref]

2012 (1)

J. K. Doylend and A. P. Knights, “The evolution of silicon photonics as an enabling technology for optical interconnection,” Laser Photonics Rev. 6(4), 504–525 (2012).
[Crossref]

2011 (1)

2010 (2)

Y. Tanaka, S. Takayama, T. Asano, Y. Sato, and S. Noda, “A polarization diversity two-dimensional photonic-crystal device,” IEEE J. Sel. Top. Quantum Electron. 16(1), 70–76 (2010).
[Crossref]

X. Checoury, Z. Han, and P. Boucaud, “Stimulated Raman scattering in silicon photonic crystal waveguides under continuous excitation,” Phys. Rev. B 82(4), 041308 (2010).
[Crossref]

2009 (1)

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]

2008 (2)

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]

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]

2007 (4)

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]

H. Rong, S. Xu, Y. Kuo, V. Sih, O. Cohen, O. Raday, and M. Paniccia, “Low-threshold continuous-wave Raman silicon laser,” Nat. Photonics 1(4), 232–237 (2007).
[Crossref]

J. M. Shainline and J. Xu, “Silicon as an emissive optical medium,” Laser Photonics Rev. 1(4), 334–348 (2007).
[Crossref]

V. Sih, S. Xu, Y.-H. Kuo, H. Rong, M. Paniccia, O. Cohen, and O. Raday, “Raman amplification of 40 Gb/s data in low-loss silicon waveguides,” Opt. Express 15(2), 357–362 (2007).
[Crossref]

2006 (4)

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]

H. Takano, B. S. Song, T. Asano, and S. Noda, “Highly effective in-plane channel-drop filters in two-dimensional heterostructure photonic-crystal slab,” Jpn. J. Appl. Phys. 45(8A), 6078–6086 (2006).
[Crossref]

H. H. Jiun, I. Ahmad, A. Jalar, and G. Omar, “Effect of Laminated Wafer Toward Dicing Process and Alternative Double Pass Sawing Method to Reduce Chipping,” IEEE Trans. Electron. Packag. Manuf. 29(1), 17–24 (2006).
[Crossref]

B. Jalali, V. Raghunathan, D. Dimitropoulos, and O. Boyraz, “Raman-based silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(3), 412–421 (2006).
[Crossref]

2005 (3)

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]

R. Jones, H. Rong, A. Liu, A. Fang, M. Paniccia, D. Hak, and O. Cohen, “Net continuous wave optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 13(2), 519–525 (2005).
[Crossref]

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433(7027), 725–728 (2005).
[Crossref]

2004 (8)

2003 (2)

2002 (1)

2000 (1)

T. Iida, T. Itoh, D. Noguchi, and Y. Takano, “Residual lattice strain in thin silicon-on-insulator bonded wafers: Thermal behavior and formation mechanisms,” J. Appl. Phys. 87(2), 675–681 (2000).
[Crossref]

1989 (1)

R. Stengl, T. Tanm, and U. Gösele, “A Model for the Silicon Wafer Bonding Process,” Jpn. J. Appl. Phys. 28(Part 1), 1735–1741 (1989).
[Crossref]

1988 (1)

W. P. Maszara, G. Goetz, A. Caviglia, and J. B. McKitterick, “Bonding of silicon wafers for silicon-on-insulator,” J. Appl. Phys. 64(10), 4943–4950 (1988).
[Crossref]

Abe, H.

Ahmad, I.

H. H. Jiun, I. Ahmad, A. Jalar, and G. Omar, “Effect of Laminated Wafer Toward Dicing Process and Alternative Double Pass Sawing Method to Reduce Chipping,” IEEE Trans. Electron. Packag. Manuf. 29(1), 17–24 (2006).
[Crossref]

Akahane, Y.

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]

Almeida, V.

Arakawa, Y.

R. Katsumi, Y. Ota, M. Kakuda, S. Iwamoto, and Y. Arakawa, “Transfer-printed single-photon sources coupled to wire waveguides,” Optica 5(6), 691–694 (2018).
[Crossref]

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R. Jones, H. Rong, A. Liu, A. Fang, M. Paniccia, D. Hak, and O. Cohen, “Net continuous wave optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 13(2), 519–525 (2005).
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H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433(7027), 725–728 (2005).
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A. Liu, H. Rong, M. Paniccia, O. Cohen, and D. Hak, “Net optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 12(18), 4261–4268 (2004).
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Han, Z.

X. Checoury, Z. Han, and P. Boucaud, “Stimulated Raman scattering in silicon photonic crystal waveguides under continuous excitation,” Phys. Rev. B 82(4), 041308 (2010).
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Y.-H. Hsiao, S. Iwamoto, and Y. Arakawa, “Spontaneous and stimulated Raman scattering in silica-cladded silicon photonic crystal waveguides,” Jpn. J. Appl. Phys. 54(4S), 04DG02 (2015).
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Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, “High-Q resonant modes in a photonic crystal heterostructure nanocavity and applicability to a Raman silicon laser,” Phys. Rev. B 88(23), 235313 (2013).
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Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, “A micrometre-scale Raman silicon laser with a microwatt threshold,” Nature 498(7455), 470–474 (2013).
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T. Matsumoto, S. Maeda, H. Dang, T. Uchida, K. Ota, Y. Hirano, H. Sayama, T. Iwamatsu, T. Ipposhi, H. Oda, S. Maegawa, Y. Inoue, and T. Nishimura, “Novel SOI wafer engineering using low stress and high mobility CMOSFET with <100>-channel for embedded RF/analog applications,” Tech. Dig. of IEDM, 663–666 (2002).

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R. Katsumi, Y. Ota, M. Kakuda, S. Iwamoto, and Y. Arakawa, “Transfer-printed single-photon sources coupled to wire waveguides,” Optica 5(6), 691–694 (2018).
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Katsumi, R.

Kishimoto, K.

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H. Rong, S. Xu, Y. Kuo, V. Sih, O. Cohen, O. Raday, and M. Paniccia, “Low-threshold continuous-wave Raman silicon laser,” Nat. Photonics 1(4), 232–237 (2007).
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Kurihara, J.

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M. Kuwabara, S. Noda, and Y. Takahashi, “Ultrahigh-Q photonic nanocavity devices on a dual thickness SOI substrate operating at both 1.31- and 1.55-µm telecommunication wavelength bands,” Laser Photonics Rev. 13(2), 1800258 (2019).
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[Crossref]

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433(7027), 725–728 (2005).
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A. Liu, H. Rong, M. Paniccia, O. Cohen, and D. Hak, “Net optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 12(18), 4261–4268 (2004).
[Crossref]

H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak, “Raman gain and nonlinear optical absorption measurements in a low-loss silicon waveguide,” Appl. Phys. Lett. 85(12), 2196–2198 (2004).
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T. Matsumoto, S. Maeda, H. Dang, T. Uchida, K. Ota, Y. Hirano, H. Sayama, T. Iwamatsu, T. Ipposhi, H. Oda, S. Maegawa, Y. Inoue, and T. Nishimura, “Novel SOI wafer engineering using low stress and high mobility CMOSFET with <100>-channel for embedded RF/analog applications,” Tech. Dig. of IEDM, 663–666 (2002).

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W. P. Maszara, G. Goetz, A. Caviglia, and J. B. McKitterick, “Bonding of silicon wafers for silicon-on-insulator,” J. Appl. Phys. 64(10), 4943–4950 (1988).
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K. K. Mehta, J. S. Orcutt, O. Tehar-Zahav, Z. Sternberg, R. Bafrali, R. Meade, and R. J. Ram, “High-Q CMOS-integrated photonic crystal microcavity devices,” Sci. Rep. 4(1), 4077 (2015).
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H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak, “Raman gain and nonlinear optical absorption measurements in a low-loss silicon waveguide,” Appl. Phys. Lett. 85(12), 2196–2198 (2004).
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Nishimura, T.

T. Matsumoto, S. Maeda, H. Dang, T. Uchida, K. Ota, Y. Hirano, H. Sayama, T. Iwamatsu, T. Ipposhi, H. Oda, S. Maegawa, Y. Inoue, and T. Nishimura, “Novel SOI wafer engineering using low stress and high mobility CMOSFET with <100>-channel for embedded RF/analog applications,” Tech. Dig. of IEDM, 663–666 (2002).

Noda, S.

M. Kuwabara, S. Noda, and Y. Takahashi, “Ultrahigh-Q photonic nanocavity devices on a dual thickness SOI substrate operating at both 1.31- and 1.55-µm telecommunication wavelength bands,” Laser Photonics Rev. 13(2), 1800258 (2019).
[Crossref]

D. Yamashita, Y. Takahashi, J. Kurihara, T. Asano, and S. Noda, “Lasing dynamics of optically-pumped ultralow-threshold Raman silicon nanocavity lasers,” Phys. Rev. Appl. 10(2), 024039 (2018).
[Crossref]

T. Asano and S. Noda, “Optimization of photonic crystal nanocavities based on deep learning,” Opt. Express 26(25), 32704–32716 (2018).
[Crossref]

D. Yamashita, T. Asano, S. Noda, and Y. Takahashi, “Strongly asymmetric wavelength dependence of optical gain in nanocavity-based Raman silicon lasers,” Optica 5(10), 1256–1263 (2018).
[Crossref]

T. Ihara, Y. Takahashi, S. Noda, and Y. Kanemitsu, “Enhanced radiative recombination rate for electron-hole droplets in a silicon photonic crystal nanocavity,” Phys. Rev. B 96(3), 035303 (2017).
[Crossref]

K. Maeno, Y. Takahashi, T. Nakamura, T. Asano, and S. Noda, “Analysis of high-Q photonic crystal L3 nanocavities designed by visualization of the leaky components,” Opt. Express 25(1), 367–376 (2017).
[Crossref]

K. Ashida, M. Okano, M. Ohtsuka, M. Seki, N. Yokoyama, K. Koshino, M. Mori, T. Asano, S. Noda, and Y. Takahashi, “Ultrahigh-Q photonic crystal nanocavities fabricated by CMOS process technologies,” Opt. Express 25(15), 18165–18174 (2017).
[Crossref]

T. Asano, Y. Ochi, Y. Takahashi, K. Kishimoto, and S. Noda, “Photonic crystal nanocavity with a Q factor exceeding eleven million,” Opt. Express 25(3), 1769–1777 (2017).
[Crossref]

D. Yamashita, Y. Takahashi, T. Asano, and S. Noda, “Raman shift and strain effect in high-Q photonic crystal silicon nanocavity,” Opt. Express 23(4), 3951–3959 (2015).
[Crossref]

Y. Takahashi, T. Asano, D. Yamashita, and S. Noda, “Ultra-compact 32-channel drop filter with 100 GHz spacing,” Opt. Express 22(4), 4692–4698 (2014).
[Crossref]

H. Sekoguchi, Y. Takahashi, T. Asano, and S. Noda, “Photonic crystal nanocavity with a Q-factor of ∼9 million,” Opt. Express 22(1), 916–924 (2014).
[Crossref]

Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, “A micrometre-scale Raman silicon laser with a microwatt threshold,” Nature 498(7455), 470–474 (2013).
[Crossref]

Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, “High-Q resonant modes in a photonic crystal heterostructure nanocavity and applicability to a Raman silicon laser,” Phys. Rev. B 88(23), 235313 (2013).
[Crossref]

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]

Y. Tanaka, S. Takayama, T. Asano, Y. Sato, and S. Noda, “A polarization diversity two-dimensional photonic-crystal device,” IEEE J. Sel. Top. Quantum Electron. 16(1), 70–76 (2010).
[Crossref]

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]

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]

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]

H. Takano, B. S. Song, T. Asano, and S. Noda, “Highly effective in-plane channel-drop filters in two-dimensional heterostructure photonic-crystal slab,” Jpn. J. Appl. Phys. 45(8A), 6078–6086 (2006).
[Crossref]

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]

Y. Yamauchi, M. Okano, S. Noda, and Y. Takahashi, “High-Q Nanocavity-Based Raman Laser Fabricated on a (100) SOI Substrate with a 45-Degree-Rotated Top Silicon Layer,” Proceedings of Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR) (2018), paper Th1H.2.

J. Kurihara, D. Yamashita, N. Tanaka, T. Asano, S. Noda, and Y. Takahashi, “Detrimental Fluctuation of Frequency Spacing Between the Two High-Quality Resonant Modes in a Raman Silicon Nanocavity Laser,” Submitted to IEEE J. Select. Top. Quant. Electron.

Y. Inui, Y. Takahashi, T. Asano, and S. Noda, in Autumn Meeting Japan Society of Applied Physics, Abstract (The Japan Society of Applied Physics, 2012), 14p-B1-6.

D. Yamashita, Y. Takahashi, T. Asano, and S. Noda, “A Sub-microwatt Threshold Raman Silicon Laser Using a High-Q Nanocavity,” Proceedings of Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR) (2015), paper 28J2_3.

Noguchi, D.

T. Iida, T. Itoh, D. Noguchi, and Y. Takano, “Residual lattice strain in thin silicon-on-insulator bonded wafers: Thermal behavior and formation mechanisms,” J. Appl. Phys. 87(2), 675–681 (2000).
[Crossref]

Ochi, Y.

Oda, H.

T. Matsumoto, S. Maeda, H. Dang, T. Uchida, K. Ota, Y. Hirano, H. Sayama, T. Iwamatsu, T. Ipposhi, H. Oda, S. Maegawa, Y. Inoue, and T. Nishimura, “Novel SOI wafer engineering using low stress and high mobility CMOSFET with <100>-channel for embedded RF/analog applications,” Tech. Dig. of IEDM, 663–666 (2002).

H. Sayama, Y. Nishida, H. Oda, T. Oishi, S. Shimizu, T. Kunikiyo, K. Sonoda, Y. Inoue, and M. Inuishi, “Effect of <100> channel direction for high performance SCE immune pMOSFET with less than 0.15 µm gate length,” Tech. Dig. of IEDM, 657–660 (1999).

Ohtsuka, M.

Oishi, T.

H. Sayama, Y. Nishida, H. Oda, T. Oishi, S. Shimizu, T. Kunikiyo, K. Sonoda, Y. Inoue, and M. Inuishi, “Effect of <100> channel direction for high performance SCE immune pMOSFET with less than 0.15 µm gate length,” Tech. Dig. of IEDM, 657–660 (1999).

Okano, M.

Omar, G.

H. H. Jiun, I. Ahmad, A. Jalar, and G. Omar, “Effect of Laminated Wafer Toward Dicing Process and Alternative Double Pass Sawing Method to Reduce Chipping,” IEEE Trans. Electron. Packag. Manuf. 29(1), 17–24 (2006).
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K. K. Mehta, J. S. Orcutt, O. Tehar-Zahav, Z. Sternberg, R. Bafrali, R. Meade, and R. J. Ram, “High-Q CMOS-integrated photonic crystal microcavity devices,” Sci. Rep. 4(1), 4077 (2015).
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Ota, K.

T. Matsumoto, S. Maeda, H. Dang, T. Uchida, K. Ota, Y. Hirano, H. Sayama, T. Iwamatsu, T. Ipposhi, H. Oda, S. Maegawa, Y. Inoue, and T. Nishimura, “Novel SOI wafer engineering using low stress and high mobility CMOSFET with <100>-channel for embedded RF/analog applications,” Tech. Dig. of IEDM, 663–666 (2002).

Ota, Y.

Otsuka, S.

H. C. Nguyen, N. Yazawa, S. Hashimoto, S. Otsuka, and T. Baba, “Sub-100 µm Photonic Crystal Si Optical Modulators: Spectral, Athermal, and High-Speed Performance,” IEEE J. Sel. Top. Quantum Electron. 19(6), 127–137 (2013).
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Palomo, P. M.

Paniccia, M.

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).
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H. Rong, S. Xu, Y. Kuo, V. Sih, O. Cohen, O. Raday, and M. Paniccia, “Low-threshold continuous-wave Raman silicon laser,” Nat. Photonics 1(4), 232–237 (2007).
[Crossref]

V. Sih, S. Xu, Y.-H. Kuo, H. Rong, M. Paniccia, O. Cohen, and O. Raday, “Raman amplification of 40 Gb/s data in low-loss silicon waveguides,” Opt. Express 15(2), 357–362 (2007).
[Crossref]

R. Jones, H. Rong, A. Liu, A. Fang, M. Paniccia, D. Hak, and O. Cohen, “Net continuous wave optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 13(2), 519–525 (2005).
[Crossref]

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433(7027), 725–728 (2005).
[Crossref]

A. Liu, H. Rong, M. Paniccia, O. Cohen, and D. Hak, “Net optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 12(18), 4261–4268 (2004).
[Crossref]

H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak, “Raman gain and nonlinear optical absorption measurements in a low-loss silicon waveguide,” Appl. Phys. Lett. 85(12), 2196–2198 (2004).
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Raday, O.

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]

H. Rong, S. Xu, Y. Kuo, V. Sih, O. Cohen, O. Raday, and M. Paniccia, “Low-threshold continuous-wave Raman silicon laser,” Nat. Photonics 1(4), 232–237 (2007).
[Crossref]

V. Sih, S. Xu, Y.-H. Kuo, H. Rong, M. Paniccia, O. Cohen, and O. Raday, “Raman amplification of 40 Gb/s data in low-loss silicon waveguides,” Opt. Express 15(2), 357–362 (2007).
[Crossref]

Raghunathan, V.

B. Jalali, V. Raghunathan, D. Dimitropoulos, and O. Boyraz, “Raman-based silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(3), 412–421 (2006).
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R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, “Observation of stimulated Raman amplification in silicon waveguides,” Opt. Express 11(15), 1731–1739 (2003).
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Ram, R. J.

K. K. Mehta, J. S. Orcutt, O. Tehar-Zahav, Z. Sternberg, R. Bafrali, R. Meade, and R. J. Ram, “High-Q CMOS-integrated photonic crystal microcavity devices,” Sci. Rep. 4(1), 4077 (2015).
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Randel, S.

Renner, H.

Rong, H.

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]

H. Rong, S. Xu, Y. Kuo, V. Sih, O. Cohen, O. Raday, and M. Paniccia, “Low-threshold continuous-wave Raman silicon laser,” Nat. Photonics 1(4), 232–237 (2007).
[Crossref]

V. Sih, S. Xu, Y.-H. Kuo, H. Rong, M. Paniccia, O. Cohen, and O. Raday, “Raman amplification of 40 Gb/s data in low-loss silicon waveguides,” Opt. Express 15(2), 357–362 (2007).
[Crossref]

R. Jones, H. Rong, A. Liu, A. Fang, M. Paniccia, D. Hak, and O. Cohen, “Net continuous wave optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 13(2), 519–525 (2005).
[Crossref]

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433(7027), 725–728 (2005).
[Crossref]

A. Liu, H. Rong, M. Paniccia, O. Cohen, and D. Hak, “Net optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 12(18), 4261–4268 (2004).
[Crossref]

H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak, “Raman gain and nonlinear optical absorption measurements in a low-loss silicon waveguide,” Appl. Phys. Lett. 85(12), 2196–2198 (2004).
[Crossref]

Sato, Y.

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]

Y. Tanaka, S. Takayama, T. Asano, Y. Sato, and S. Noda, “A polarization diversity two-dimensional photonic-crystal device,” IEEE J. Sel. Top. Quantum Electron. 16(1), 70–76 (2010).
[Crossref]

Saurav, K.

Sayama, H.

T. Matsumoto, S. Maeda, H. Dang, T. Uchida, K. Ota, Y. Hirano, H. Sayama, T. Iwamatsu, T. Ipposhi, H. Oda, S. Maegawa, Y. Inoue, and T. Nishimura, “Novel SOI wafer engineering using low stress and high mobility CMOSFET with <100>-channel for embedded RF/analog applications,” Tech. Dig. of IEDM, 663–666 (2002).

H. Sayama, Y. Nishida, H. Oda, T. Oishi, S. Shimizu, T. Kunikiyo, K. Sonoda, Y. Inoue, and M. Inuishi, “Effect of <100> channel direction for high performance SCE immune pMOSFET with less than 0.15 µm gate length,” Tech. Dig. of IEDM, 657–660 (1999).

Seki, M.

Sekoguchi, H.

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Shimizu, S.

H. Sayama, Y. Nishida, H. Oda, T. Oishi, S. Shimizu, T. Kunikiyo, K. Sonoda, Y. Inoue, and M. Inuishi, “Effect of <100> channel direction for high performance SCE immune pMOSFET with less than 0.15 µm gate length,” Tech. Dig. of IEDM, 657–660 (1999).

Sih, V.

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]

H. Rong, S. Xu, Y. Kuo, V. Sih, O. Cohen, O. Raday, and M. Paniccia, “Low-threshold continuous-wave Raman silicon laser,” Nat. Photonics 1(4), 232–237 (2007).
[Crossref]

V. Sih, S. Xu, Y.-H. Kuo, H. Rong, M. Paniccia, O. Cohen, and O. Raday, “Raman amplification of 40 Gb/s data in low-loss silicon waveguides,” Opt. Express 15(2), 357–362 (2007).
[Crossref]

Song, B. S.

H. Takano, B. S. Song, T. Asano, and S. Noda, “Highly effective in-plane channel-drop filters in two-dimensional heterostructure photonic-crystal slab,” Jpn. J. Appl. Phys. 45(8A), 6078–6086 (2006).
[Crossref]

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]

Song, B.-S.

Sonoda, K.

H. Sayama, Y. Nishida, H. Oda, T. Oishi, S. Shimizu, T. Kunikiyo, K. Sonoda, Y. Inoue, and M. Inuishi, “Effect of <100> channel direction for high performance SCE immune pMOSFET with less than 0.15 µm gate length,” Tech. Dig. of IEDM, 657–660 (1999).

Stengl, R.

R. Stengl, T. Tanm, and U. Gösele, “A Model for the Silicon Wafer Bonding Process,” Jpn. J. Appl. Phys. 28(Part 1), 1735–1741 (1989).
[Crossref]

Sternberg, Z.

K. K. Mehta, J. S. Orcutt, O. Tehar-Zahav, Z. Sternberg, R. Bafrali, R. Meade, and R. J. Ram, “High-Q CMOS-integrated photonic crystal microcavity devices,” Sci. Rep. 4(1), 4077 (2015).
[Crossref]

Taguchi, Y.

Takahashi, Y.

M. Kuwabara, S. Noda, and Y. Takahashi, “Ultrahigh-Q photonic nanocavity devices on a dual thickness SOI substrate operating at both 1.31- and 1.55-µm telecommunication wavelength bands,” Laser Photonics Rev. 13(2), 1800258 (2019).
[Crossref]

D. Yamashita, Y. Takahashi, J. Kurihara, T. Asano, and S. Noda, “Lasing dynamics of optically-pumped ultralow-threshold Raman silicon nanocavity lasers,” Phys. Rev. Appl. 10(2), 024039 (2018).
[Crossref]

K. Ashida, M. Okano, M. Ohtsuka, M. Seki, N. Yokoyama, K. Koshino, K. Yamada, and Y. Takahashi, “Photonic Crystal Nanocavities with an Average Q factor of 1.9 million Fabricated on a 300-mm-Wide SOI Wafer Using a CMOS-Compatible Process,” J. Lightwave Technol. 36(20), 4774–4782 (2018).
[Crossref]

D. Yamashita, T. Asano, S. Noda, and Y. Takahashi, “Strongly asymmetric wavelength dependence of optical gain in nanocavity-based Raman silicon lasers,” Optica 5(10), 1256–1263 (2018).
[Crossref]

T. Ihara, Y. Takahashi, S. Noda, and Y. Kanemitsu, “Enhanced radiative recombination rate for electron-hole droplets in a silicon photonic crystal nanocavity,” Phys. Rev. B 96(3), 035303 (2017).
[Crossref]

T. Asano, Y. Ochi, Y. Takahashi, K. Kishimoto, and S. Noda, “Photonic crystal nanocavity with a Q factor exceeding eleven million,” Opt. Express 25(3), 1769–1777 (2017).
[Crossref]

K. Maeno, Y. Takahashi, T. Nakamura, T. Asano, and S. Noda, “Analysis of high-Q photonic crystal L3 nanocavities designed by visualization of the leaky components,” Opt. Express 25(1), 367–376 (2017).
[Crossref]

K. Ashida, M. Okano, M. Ohtsuka, M. Seki, N. Yokoyama, K. Koshino, M. Mori, T. Asano, S. Noda, and Y. Takahashi, “Ultrahigh-Q photonic crystal nanocavities fabricated by CMOS process technologies,” Opt. Express 25(15), 18165–18174 (2017).
[Crossref]

D. Yamashita, Y. Takahashi, T. Asano, and S. Noda, “Raman shift and strain effect in high-Q photonic crystal silicon nanocavity,” Opt. Express 23(4), 3951–3959 (2015).
[Crossref]

H. Sekoguchi, Y. Takahashi, T. Asano, and S. Noda, “Photonic crystal nanocavity with a Q-factor of ∼9 million,” Opt. Express 22(1), 916–924 (2014).
[Crossref]

Y. Takahashi, T. Asano, D. Yamashita, and S. Noda, “Ultra-compact 32-channel drop filter with 100 GHz spacing,” Opt. Express 22(4), 4692–4698 (2014).
[Crossref]

Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, “High-Q resonant modes in a photonic crystal heterostructure nanocavity and applicability to a Raman silicon laser,” Phys. Rev. B 88(23), 235313 (2013).
[Crossref]

Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, “A micrometre-scale Raman silicon laser with a microwatt threshold,” Nature 498(7455), 470–474 (2013).
[Crossref]

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]

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]

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]

D. Yamashita, Y. Takahashi, T. Asano, and S. Noda, “A Sub-microwatt Threshold Raman Silicon Laser Using a High-Q Nanocavity,” Proceedings of Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR) (2015), paper 28J2_3.

J. Kurihara, D. Yamashita, N. Tanaka, T. Asano, S. Noda, and Y. Takahashi, “Detrimental Fluctuation of Frequency Spacing Between the Two High-Quality Resonant Modes in a Raman Silicon Nanocavity Laser,” Submitted to IEEE J. Select. Top. Quant. Electron.

Y. Yamauchi, M. Okano, S. Noda, and Y. Takahashi, “High-Q Nanocavity-Based Raman Laser Fabricated on a (100) SOI Substrate with a 45-Degree-Rotated Top Silicon Layer,” Proceedings of Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR) (2018), paper Th1H.2.

Y. Inui, Y. Takahashi, T. Asano, and S. Noda, in Autumn Meeting Japan Society of Applied Physics, Abstract (The Japan Society of Applied Physics, 2012), 14p-B1-6.

Takano, H.

H. Takano, B. S. Song, T. Asano, and S. Noda, “Highly effective in-plane channel-drop filters in two-dimensional heterostructure photonic-crystal slab,” Jpn. J. Appl. Phys. 45(8A), 6078–6086 (2006).
[Crossref]

Takano, Y.

T. Iida, T. Itoh, D. Noguchi, and Y. Takano, “Residual lattice strain in thin silicon-on-insulator bonded wafers: Thermal behavior and formation mechanisms,” J. Appl. Phys. 87(2), 675–681 (2000).
[Crossref]

Takayama, S.

Y. Tanaka, S. Takayama, T. Asano, Y. Sato, and S. Noda, “A polarization diversity two-dimensional photonic-crystal device,” IEEE J. Sel. Top. Quantum Electron. 16(1), 70–76 (2010).
[Crossref]

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Takeuchi, M.

Tanabe, T.

Tanaka, N.

J. Kurihara, D. Yamashita, N. Tanaka, T. Asano, S. Noda, and Y. Takahashi, “Detrimental Fluctuation of Frequency Spacing Between the Two High-Quality Resonant Modes in a Raman Silicon Nanocavity Laser,” Submitted to IEEE J. Select. Top. Quant. Electron.

Tanaka, Y.

Y. Tanaka, S. Takayama, T. Asano, Y. Sato, and S. Noda, “A polarization diversity two-dimensional photonic-crystal device,” IEEE J. Sel. Top. Quantum Electron. 16(1), 70–76 (2010).
[Crossref]

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]

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]

Tanm, T.

R. Stengl, T. Tanm, and U. Gösele, “A Model for the Silicon Wafer Bonding Process,” Jpn. J. Appl. Phys. 28(Part 1), 1735–1741 (1989).
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W. H. Teh, D. S. Boning, and R. E. Welsch, “Multi-Strata Stealth Dicing Before Grinding for Singulation-Defects Elimination and Die Strength Enhancement: Experiment and Simulation,” IEEE Trans. Semicon. Manufact. 28(3), 408–423 (2015).
[Crossref]

Tehar-Zahav, O.

K. K. Mehta, J. S. Orcutt, O. Tehar-Zahav, Z. Sternberg, R. Bafrali, R. Meade, and R. J. Ram, “High-Q CMOS-integrated photonic crystal microcavity devices,” Sci. Rep. 4(1), 4077 (2015).
[Crossref]

Terada, Y.

Terawaki, R.

Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, “A micrometre-scale Raman silicon laser with a microwatt threshold,” Nature 498(7455), 470–474 (2013).
[Crossref]

Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, “High-Q resonant modes in a photonic crystal heterostructure nanocavity and applicability to a Raman silicon laser,” Phys. Rev. B 88(23), 235313 (2013).
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Thomas, N. L.

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Troppenz, U.

Tsang, H.

T. Liang and H. Tsang, “Nonlinear absorption and Raman scattering in silicon-on-insulator optical waveguides,” IEEE J. Sel. Top. Quantum Electron. 10(5), 1149–1153 (2004).
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T. Liang and H. Tsang, “Efficient Raman amplification in silicon-on-insulator waveguides,” Appl. Phys. Lett. 85(16), 3343–3345 (2004).
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T. Matsumoto, S. Maeda, H. Dang, T. Uchida, K. Ota, Y. Hirano, H. Sayama, T. Iwamatsu, T. Ipposhi, H. Oda, S. Maegawa, Y. Inoue, and T. Nishimura, “Novel SOI wafer engineering using low stress and high mobility CMOSFET with <100>-channel for embedded RF/analog applications,” Tech. Dig. of IEDM, 663–666 (2002).

Vlasov, Y.

Wang, Z.

Welsch, R. E.

W. H. Teh, D. S. Boning, and R. E. Welsch, “Multi-Strata Stealth Dicing Before Grinding for Singulation-Defects Elimination and Die Strength Enhancement: Experiment and Simulation,” IEEE Trans. Semicon. Manufact. 28(3), 408–423 (2015).
[Crossref]

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V. Sih, S. Xu, Y.-H. Kuo, H. Rong, M. Paniccia, O. Cohen, and O. Raday, “Raman amplification of 40 Gb/s data in low-loss silicon waveguides,” Opt. Express 15(2), 357–362 (2007).
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D. Yamashita, Y. Takahashi, J. Kurihara, T. Asano, and S. Noda, “Lasing dynamics of optically-pumped ultralow-threshold Raman silicon nanocavity lasers,” Phys. Rev. Appl. 10(2), 024039 (2018).
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Y. Takahashi, T. Asano, D. Yamashita, and S. Noda, “Ultra-compact 32-channel drop filter with 100 GHz spacing,” Opt. Express 22(4), 4692–4698 (2014).
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J. Kurihara, D. Yamashita, N. Tanaka, T. Asano, S. Noda, and Y. Takahashi, “Detrimental Fluctuation of Frequency Spacing Between the Two High-Quality Resonant Modes in a Raman Silicon Nanocavity Laser,” Submitted to IEEE J. Select. Top. Quant. Electron.

D. Yamashita, Y. Takahashi, T. Asano, and S. Noda, “A Sub-microwatt Threshold Raman Silicon Laser Using a High-Q Nanocavity,” Proceedings of Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR) (2015), paper 28J2_3.

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Y. Takahashi, T. Asano, D. Yamashita, and S. Noda, “Ultra-compact 32-channel drop filter with 100 GHz spacing,” Opt. Express 22(4), 4692–4698 (2014).
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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).
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Phys. Rev. Appl. (1)

D. Yamashita, Y. Takahashi, J. Kurihara, T. Asano, and S. Noda, “Lasing dynamics of optically-pumped ultralow-threshold Raman silicon nanocavity lasers,” Phys. Rev. Appl. 10(2), 024039 (2018).
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Other (7)

Y. Yamauchi, M. Okano, S. Noda, and Y. Takahashi, “High-Q Nanocavity-Based Raman Laser Fabricated on a (100) SOI Substrate with a 45-Degree-Rotated Top Silicon Layer,” Proceedings of Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR) (2018), paper Th1H.2.

H. Sayama, Y. Nishida, H. Oda, T. Oishi, S. Shimizu, T. Kunikiyo, K. Sonoda, Y. Inoue, and M. Inuishi, “Effect of <100> channel direction for high performance SCE immune pMOSFET with less than 0.15 µm gate length,” Tech. Dig. of IEDM, 657–660 (1999).

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D. Yamashita, Y. Takahashi, T. Asano, and S. Noda, “A Sub-microwatt Threshold Raman Silicon Laser Using a High-Q Nanocavity,” Proceedings of Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR) (2015), paper 28J2_3.

J. Kurihara, D. Yamashita, N. Tanaka, T. Asano, S. Noda, and Y. Takahashi, “Detrimental Fluctuation of Frequency Spacing Between the Two High-Quality Resonant Modes in a Raman Silicon Nanocavity Laser,” Submitted to IEEE J. Select. Top. Quant. Electron.

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Figures (8)

Fig. 1.
Fig. 1. (a) Schematic of a heterostructure nanocavity. (b) Band diagram of the nanocavity. (c) The x- and y-components of the electric field distribution calculated for the pump nanocavity mode, Ex_pump and Ey_pump. (d) The components of the electric field distribution for the Stokes nanocavity mode, i.e., Ex_stokes and Ey_stokes. (e) Schematic of the in-plane Raman scattering for the cavity’s x-direction being parallel to the [100] direction of crystalline Si.
Fig. 2.
Fig. 2. (a) Structure of a conventional (100) SOI wafer. (b) Diagram of the conventional (100) SOI wafer. Red arrows represent the cleavable directions, [110] and [1–10]. (c) Diagram of the 45°-rotated (100) SOI wafer used in this study.
Fig. 3.
Fig. 3. (a) Schematic of φ-scan measurement of the in-plane XRD. (b) XRD φ-scan spectrum of Si (220) for the conventional SOI wafer and (c) that for the 45°-rotated SOI wafer.
Fig. 4.
Fig. 4. (a) SEM image of the fabricated laser sample. (b) SEM image of the cleaved facet. The inset is the corresponding image for the Raman Si laser on the conventional SOI wafer.
Fig. 5.
Fig. 5. (a) Resonance spectrum of the pump nanocavity mode. (b) Resonance spectrum of the Stokes nanocavity mode. (c) Raman laser output power as a function of the excitation power coupled into nanocavity that is fabricated on the 45°-rotated SOI wafer (filled circles). The open circles are the results for the [110]-aligned cavity fabricated on the conventional SOI wafer. The inset illustrates the excitation geometry. (d) Camera images of the nanocavity under three different excitation powers. The pump laser light is eliminated by inserting a long-pass filter with a cutoff wavelength of 1500 nm in front of the camera. (e) Camera image of the Stokes light emitted from the facet (on the transmission side) of the lower waveguide in the inset of (c). All images use the same intensity scale.
Fig. 6.
Fig. 6. (a) Surface topology of the air-bridged PC slab for the Raman laser on the 45°-rotated SOI wafer obtained by SWLI. (b) Corresponding image for the laser device on the conventional SOI wafer. (c) Results for the PC fabricated on the 45°-rotated SOI wafer: the left panel is the SWLI image of the PC slab close to the cleaved facet, the right is the corresponding profile of the PC slab along the center line of the slab. (d),(e) Results for two PC slabs fabricated on the conventional SOI.
Fig. 7.
Fig. 7. Experimental setup for investigation of the input/output characteristics of Raman lasers.
Fig. 8.
Fig. 8. Input-output relation of the Raman Si laser shown in Fig. 5(c) on a linear scale.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

R x = [ 0 0 0 0 0 1 0 1 0 ] , R y = [ 0 0 1 0 0 0 1 0 0 ] , R z = [ 0 1 0 1 0 0 0 0 0 ]
χ i j m n R k = x , y , z ( R k ) i j ( R k ) m n
| E x _ Stokes E y _ pump + E y _ Stokes E x _ pump | 2 d x d y d z

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