Abstract

A comprehensive theoretical model for the long-wavelength micro-electro-mechanical-tunable high-contrast-grating vertical-cavity surface-emitting lasers is presented. Our band structure model calculates the optical gain and spontaneous emission of the InGaAlAs quantum well active region. The grating reflectivity and the cavity resonance condition are investigated through optical modeling. Correlating the results with the electrostatic model for the micro-electro-mechanical system, we accurately predict the measurements on the voltage-contolled lasing wavelength. Furthermore, our calculated temperature-dependent wavelength-tunable light output vs. current (L-I) curves show excellent agreement with experiment.

© 2014 Optical Society of America

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  1. K. Iga, “Surface-emitting laser-its birth and generation of new optoelectronics field,” IEEE J. Sel. Top. Quantum Electron. 6, 1201–1215 (2000).
    [CrossRef]
  2. M.-C. Amann, W. Hofmann, “InP-based long-wavelength VCSELs and VCSEL arrays,” IEEE J. Sel. Top. Quantum Electron. 15, 861–868 (2009).
    [CrossRef]
  3. P. A. Martin, “Near-infrared diode laser spectroscopy in chemical process and environmental air monitoring,” Chem. Soc. Rev. 31, 201–210 (2002).
    [CrossRef] [PubMed]
  4. D. I. Babic, K. Streubel, R. P. Mirin, N. M. Margalit, J. E. Bowers, E. L. Hu, D. E. Mars, L. Yang, K. Carey, “Room-temperature continuous-wave operation of 1.54-μm vertical-cavity lasers,” IEEE Photon. Technol. Lett. 7, 1225–1227 (1995).
    [CrossRef]
  5. C. J. Chang-Hasnain, “Tunable VCSEL,” IEEE J. Sel. Top. Quantum Electron. 6, 978–987 (2000).
    [CrossRef]
  6. N. Satyan, A. Vasilyev, G. Rakuljic, V. Leyva, A. Yariv, “Precise control of broadband frequency chirps using optoelectronic feedback,” Opt. Express 17, 15991–15999 (2009).
    [CrossRef] [PubMed]
  7. M. Y. Li, W. Yuen, G. S. Li, C. J. Chang-Hasnain, “Top-emitting micromechanical VCSEL with a 31.6-nm tuning range,” IEEE Photon. Technol. Lett. 10, 18–20 (1998).
    [CrossRef]
  8. M. C. Huang, Y. Zhou, C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics 1, 119–122 (2007).
    [CrossRef]
  9. C. Chase, Y. Rao, W. Hofmann, C. J. Chang-Hasnain, “1550 nm high contrast grating VCSEL,” Opt. Express 18, 15461–15466 (2010).
    [CrossRef] [PubMed]
  10. Y. Rao, W. J. Yang, C. Chase, M. C. Y. Huang, D. P. Worland, S. Khaleghi, M. R. Chitgarha, M. Ziyadi, A. E. Willner, C. J. Chang-Hasnain, “Long-wavelength VCSEL using high-contrast grating,” IEEE J. Sel. Top. Quantum Electron. 19, 1701311 (2013).
    [CrossRef]
  11. D. B. Young, J. W. Scott, F. H. Peters, M. G. Peters, M. L. Majewski, B. J. Thibeault, S. W. Corzine, L. A. Coldren, “Enhanced performance of offset-gain high-barrier vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 29, 2013–2022 (1993).
    [CrossRef]
  12. S. L. Chuang, Physics of Photonic Devices, 2 (Wiley, 2009), Chap. 4 and 9.
  13. G. L. Bir, G. E. Pikus, Symmetry and Strain-Induced Effects in Semiconductors (Wiley, 1974), Chap. 5.
  14. L. Condren, S. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995), Chap. 4.
  15. I. Vurgaftman, J. R. Meyer, L. R. Ram-Mohan, “Band parameters for IIIV compound semiconductors and their alloys,” J. Appl. Phys. 89, 5815 (2001).
    [CrossRef]
  16. Y. P. Varshni, “Temperature dependence of the energy gap in semiconductors,” Physica 34, 149–154 (1967).
    [CrossRef]
  17. J. Minch, S. H. Park, T. Keating, S. L. Chuang, “Theory and experiment of In1−xGaxAsyP1−y and In1−x−yGaxAlyAs long-wavelength strained quantum-well lasers,” IEEE J. Quantum Electron. 35, 771–782 (1999).
    [CrossRef]
  18. V. Karagodsky, F. G. Sedgwick, C. J. Chang-Hasnain, “Theoretical analysis of subwavelength high contrast grating reflectors,” Opt. Express 18, 16973–16988 (2010).
    [CrossRef] [PubMed]
  19. W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE, 1995), Chap. 2.
  20. M. Y. Li, C. J. Chang-Hasnain, “Tilt loss in wavelength tunable micromechanical vertical cavity lasers,” in CLEO: 1999, 457–458, May1999.
  21. S.-W. Chang, C.-Y. Lu, S. L. Chuang, T. D. Germann, U. W. Pohl, D. Bimberg, “Theory of metal-cavity surface-emitting microlasers and comparison with experiment,” IEEE J. Sel. Top. Quantum Electron. 17, 1681–1692 (2011).
    [CrossRef]
  22. J. W. Scott, D. B. Young, B. J. Thibeault, M. G. Peters, L. A. Coldren, “Design of index-guided vertical-cavity lasers for low temperature-sensitivity, sub-milliamp thresholds, and single-mode operation,” IEEE J. Sel. Top. Quantum Electron. 1, 638–648 (1995).
    [CrossRef]
  23. P. V. Mena, J. J. Morikuni, S.-M. Kang, A. V. Harton, K. W. Wyatt, “A comprehensive circuit-level model of vertical-cavity surface-emitting lasers,” J. Lightwave Technol. 17, 2612–2632 (1999).
    [CrossRef]

2013 (1)

Y. Rao, W. J. Yang, C. Chase, M. C. Y. Huang, D. P. Worland, S. Khaleghi, M. R. Chitgarha, M. Ziyadi, A. E. Willner, C. J. Chang-Hasnain, “Long-wavelength VCSEL using high-contrast grating,” IEEE J. Sel. Top. Quantum Electron. 19, 1701311 (2013).
[CrossRef]

2011 (1)

S.-W. Chang, C.-Y. Lu, S. L. Chuang, T. D. Germann, U. W. Pohl, D. Bimberg, “Theory of metal-cavity surface-emitting microlasers and comparison with experiment,” IEEE J. Sel. Top. Quantum Electron. 17, 1681–1692 (2011).
[CrossRef]

2010 (2)

2009 (2)

N. Satyan, A. Vasilyev, G. Rakuljic, V. Leyva, A. Yariv, “Precise control of broadband frequency chirps using optoelectronic feedback,” Opt. Express 17, 15991–15999 (2009).
[CrossRef] [PubMed]

M.-C. Amann, W. Hofmann, “InP-based long-wavelength VCSELs and VCSEL arrays,” IEEE J. Sel. Top. Quantum Electron. 15, 861–868 (2009).
[CrossRef]

2007 (1)

M. C. Huang, Y. Zhou, C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics 1, 119–122 (2007).
[CrossRef]

2002 (1)

P. A. Martin, “Near-infrared diode laser spectroscopy in chemical process and environmental air monitoring,” Chem. Soc. Rev. 31, 201–210 (2002).
[CrossRef] [PubMed]

2001 (1)

I. Vurgaftman, J. R. Meyer, L. R. Ram-Mohan, “Band parameters for IIIV compound semiconductors and their alloys,” J. Appl. Phys. 89, 5815 (2001).
[CrossRef]

2000 (2)

K. Iga, “Surface-emitting laser-its birth and generation of new optoelectronics field,” IEEE J. Sel. Top. Quantum Electron. 6, 1201–1215 (2000).
[CrossRef]

C. J. Chang-Hasnain, “Tunable VCSEL,” IEEE J. Sel. Top. Quantum Electron. 6, 978–987 (2000).
[CrossRef]

1999 (2)

J. Minch, S. H. Park, T. Keating, S. L. Chuang, “Theory and experiment of In1−xGaxAsyP1−y and In1−x−yGaxAlyAs long-wavelength strained quantum-well lasers,” IEEE J. Quantum Electron. 35, 771–782 (1999).
[CrossRef]

P. V. Mena, J. J. Morikuni, S.-M. Kang, A. V. Harton, K. W. Wyatt, “A comprehensive circuit-level model of vertical-cavity surface-emitting lasers,” J. Lightwave Technol. 17, 2612–2632 (1999).
[CrossRef]

1998 (1)

M. Y. Li, W. Yuen, G. S. Li, C. J. Chang-Hasnain, “Top-emitting micromechanical VCSEL with a 31.6-nm tuning range,” IEEE Photon. Technol. Lett. 10, 18–20 (1998).
[CrossRef]

1995 (2)

D. I. Babic, K. Streubel, R. P. Mirin, N. M. Margalit, J. E. Bowers, E. L. Hu, D. E. Mars, L. Yang, K. Carey, “Room-temperature continuous-wave operation of 1.54-μm vertical-cavity lasers,” IEEE Photon. Technol. Lett. 7, 1225–1227 (1995).
[CrossRef]

J. W. Scott, D. B. Young, B. J. Thibeault, M. G. Peters, L. A. Coldren, “Design of index-guided vertical-cavity lasers for low temperature-sensitivity, sub-milliamp thresholds, and single-mode operation,” IEEE J. Sel. Top. Quantum Electron. 1, 638–648 (1995).
[CrossRef]

1993 (1)

D. B. Young, J. W. Scott, F. H. Peters, M. G. Peters, M. L. Majewski, B. J. Thibeault, S. W. Corzine, L. A. Coldren, “Enhanced performance of offset-gain high-barrier vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 29, 2013–2022 (1993).
[CrossRef]

1967 (1)

Y. P. Varshni, “Temperature dependence of the energy gap in semiconductors,” Physica 34, 149–154 (1967).
[CrossRef]

Amann, M.-C.

M.-C. Amann, W. Hofmann, “InP-based long-wavelength VCSELs and VCSEL arrays,” IEEE J. Sel. Top. Quantum Electron. 15, 861–868 (2009).
[CrossRef]

Babic, D. I.

D. I. Babic, K. Streubel, R. P. Mirin, N. M. Margalit, J. E. Bowers, E. L. Hu, D. E. Mars, L. Yang, K. Carey, “Room-temperature continuous-wave operation of 1.54-μm vertical-cavity lasers,” IEEE Photon. Technol. Lett. 7, 1225–1227 (1995).
[CrossRef]

Bimberg, D.

S.-W. Chang, C.-Y. Lu, S. L. Chuang, T. D. Germann, U. W. Pohl, D. Bimberg, “Theory of metal-cavity surface-emitting microlasers and comparison with experiment,” IEEE J. Sel. Top. Quantum Electron. 17, 1681–1692 (2011).
[CrossRef]

Bir, G. L.

G. L. Bir, G. E. Pikus, Symmetry and Strain-Induced Effects in Semiconductors (Wiley, 1974), Chap. 5.

Bowers, J. E.

D. I. Babic, K. Streubel, R. P. Mirin, N. M. Margalit, J. E. Bowers, E. L. Hu, D. E. Mars, L. Yang, K. Carey, “Room-temperature continuous-wave operation of 1.54-μm vertical-cavity lasers,” IEEE Photon. Technol. Lett. 7, 1225–1227 (1995).
[CrossRef]

Carey, K.

D. I. Babic, K. Streubel, R. P. Mirin, N. M. Margalit, J. E. Bowers, E. L. Hu, D. E. Mars, L. Yang, K. Carey, “Room-temperature continuous-wave operation of 1.54-μm vertical-cavity lasers,” IEEE Photon. Technol. Lett. 7, 1225–1227 (1995).
[CrossRef]

Chang, S.-W.

S.-W. Chang, C.-Y. Lu, S. L. Chuang, T. D. Germann, U. W. Pohl, D. Bimberg, “Theory of metal-cavity surface-emitting microlasers and comparison with experiment,” IEEE J. Sel. Top. Quantum Electron. 17, 1681–1692 (2011).
[CrossRef]

Chang-Hasnain, C. J.

Y. Rao, W. J. Yang, C. Chase, M. C. Y. Huang, D. P. Worland, S. Khaleghi, M. R. Chitgarha, M. Ziyadi, A. E. Willner, C. J. Chang-Hasnain, “Long-wavelength VCSEL using high-contrast grating,” IEEE J. Sel. Top. Quantum Electron. 19, 1701311 (2013).
[CrossRef]

C. Chase, Y. Rao, W. Hofmann, C. J. Chang-Hasnain, “1550 nm high contrast grating VCSEL,” Opt. Express 18, 15461–15466 (2010).
[CrossRef] [PubMed]

V. Karagodsky, F. G. Sedgwick, C. J. Chang-Hasnain, “Theoretical analysis of subwavelength high contrast grating reflectors,” Opt. Express 18, 16973–16988 (2010).
[CrossRef] [PubMed]

M. C. Huang, Y. Zhou, C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics 1, 119–122 (2007).
[CrossRef]

C. J. Chang-Hasnain, “Tunable VCSEL,” IEEE J. Sel. Top. Quantum Electron. 6, 978–987 (2000).
[CrossRef]

M. Y. Li, W. Yuen, G. S. Li, C. J. Chang-Hasnain, “Top-emitting micromechanical VCSEL with a 31.6-nm tuning range,” IEEE Photon. Technol. Lett. 10, 18–20 (1998).
[CrossRef]

M. Y. Li, C. J. Chang-Hasnain, “Tilt loss in wavelength tunable micromechanical vertical cavity lasers,” in CLEO: 1999, 457–458, May1999.

Chase, C.

Y. Rao, W. J. Yang, C. Chase, M. C. Y. Huang, D. P. Worland, S. Khaleghi, M. R. Chitgarha, M. Ziyadi, A. E. Willner, C. J. Chang-Hasnain, “Long-wavelength VCSEL using high-contrast grating,” IEEE J. Sel. Top. Quantum Electron. 19, 1701311 (2013).
[CrossRef]

C. Chase, Y. Rao, W. Hofmann, C. J. Chang-Hasnain, “1550 nm high contrast grating VCSEL,” Opt. Express 18, 15461–15466 (2010).
[CrossRef] [PubMed]

Chew, W. C.

W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE, 1995), Chap. 2.

Chitgarha, M. R.

Y. Rao, W. J. Yang, C. Chase, M. C. Y. Huang, D. P. Worland, S. Khaleghi, M. R. Chitgarha, M. Ziyadi, A. E. Willner, C. J. Chang-Hasnain, “Long-wavelength VCSEL using high-contrast grating,” IEEE J. Sel. Top. Quantum Electron. 19, 1701311 (2013).
[CrossRef]

Chuang, S. L.

S.-W. Chang, C.-Y. Lu, S. L. Chuang, T. D. Germann, U. W. Pohl, D. Bimberg, “Theory of metal-cavity surface-emitting microlasers and comparison with experiment,” IEEE J. Sel. Top. Quantum Electron. 17, 1681–1692 (2011).
[CrossRef]

J. Minch, S. H. Park, T. Keating, S. L. Chuang, “Theory and experiment of In1−xGaxAsyP1−y and In1−x−yGaxAlyAs long-wavelength strained quantum-well lasers,” IEEE J. Quantum Electron. 35, 771–782 (1999).
[CrossRef]

S. L. Chuang, Physics of Photonic Devices, 2 (Wiley, 2009), Chap. 4 and 9.

Coldren, L. A.

J. W. Scott, D. B. Young, B. J. Thibeault, M. G. Peters, L. A. Coldren, “Design of index-guided vertical-cavity lasers for low temperature-sensitivity, sub-milliamp thresholds, and single-mode operation,” IEEE J. Sel. Top. Quantum Electron. 1, 638–648 (1995).
[CrossRef]

D. B. Young, J. W. Scott, F. H. Peters, M. G. Peters, M. L. Majewski, B. J. Thibeault, S. W. Corzine, L. A. Coldren, “Enhanced performance of offset-gain high-barrier vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 29, 2013–2022 (1993).
[CrossRef]

Condren, L.

L. Condren, S. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995), Chap. 4.

Corzine, S.

L. Condren, S. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995), Chap. 4.

Corzine, S. W.

D. B. Young, J. W. Scott, F. H. Peters, M. G. Peters, M. L. Majewski, B. J. Thibeault, S. W. Corzine, L. A. Coldren, “Enhanced performance of offset-gain high-barrier vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 29, 2013–2022 (1993).
[CrossRef]

Germann, T. D.

S.-W. Chang, C.-Y. Lu, S. L. Chuang, T. D. Germann, U. W. Pohl, D. Bimberg, “Theory of metal-cavity surface-emitting microlasers and comparison with experiment,” IEEE J. Sel. Top. Quantum Electron. 17, 1681–1692 (2011).
[CrossRef]

Harton, A. V.

Hofmann, W.

C. Chase, Y. Rao, W. Hofmann, C. J. Chang-Hasnain, “1550 nm high contrast grating VCSEL,” Opt. Express 18, 15461–15466 (2010).
[CrossRef] [PubMed]

M.-C. Amann, W. Hofmann, “InP-based long-wavelength VCSELs and VCSEL arrays,” IEEE J. Sel. Top. Quantum Electron. 15, 861–868 (2009).
[CrossRef]

Hu, E. L.

D. I. Babic, K. Streubel, R. P. Mirin, N. M. Margalit, J. E. Bowers, E. L. Hu, D. E. Mars, L. Yang, K. Carey, “Room-temperature continuous-wave operation of 1.54-μm vertical-cavity lasers,” IEEE Photon. Technol. Lett. 7, 1225–1227 (1995).
[CrossRef]

Huang, M. C.

M. C. Huang, Y. Zhou, C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics 1, 119–122 (2007).
[CrossRef]

Huang, M. C. Y.

Y. Rao, W. J. Yang, C. Chase, M. C. Y. Huang, D. P. Worland, S. Khaleghi, M. R. Chitgarha, M. Ziyadi, A. E. Willner, C. J. Chang-Hasnain, “Long-wavelength VCSEL using high-contrast grating,” IEEE J. Sel. Top. Quantum Electron. 19, 1701311 (2013).
[CrossRef]

Iga, K.

K. Iga, “Surface-emitting laser-its birth and generation of new optoelectronics field,” IEEE J. Sel. Top. Quantum Electron. 6, 1201–1215 (2000).
[CrossRef]

Kang, S.-M.

Karagodsky, V.

Keating, T.

J. Minch, S. H. Park, T. Keating, S. L. Chuang, “Theory and experiment of In1−xGaxAsyP1−y and In1−x−yGaxAlyAs long-wavelength strained quantum-well lasers,” IEEE J. Quantum Electron. 35, 771–782 (1999).
[CrossRef]

Khaleghi, S.

Y. Rao, W. J. Yang, C. Chase, M. C. Y. Huang, D. P. Worland, S. Khaleghi, M. R. Chitgarha, M. Ziyadi, A. E. Willner, C. J. Chang-Hasnain, “Long-wavelength VCSEL using high-contrast grating,” IEEE J. Sel. Top. Quantum Electron. 19, 1701311 (2013).
[CrossRef]

Leyva, V.

Li, G. S.

M. Y. Li, W. Yuen, G. S. Li, C. J. Chang-Hasnain, “Top-emitting micromechanical VCSEL with a 31.6-nm tuning range,” IEEE Photon. Technol. Lett. 10, 18–20 (1998).
[CrossRef]

Li, M. Y.

M. Y. Li, W. Yuen, G. S. Li, C. J. Chang-Hasnain, “Top-emitting micromechanical VCSEL with a 31.6-nm tuning range,” IEEE Photon. Technol. Lett. 10, 18–20 (1998).
[CrossRef]

M. Y. Li, C. J. Chang-Hasnain, “Tilt loss in wavelength tunable micromechanical vertical cavity lasers,” in CLEO: 1999, 457–458, May1999.

Lu, C.-Y.

S.-W. Chang, C.-Y. Lu, S. L. Chuang, T. D. Germann, U. W. Pohl, D. Bimberg, “Theory of metal-cavity surface-emitting microlasers and comparison with experiment,” IEEE J. Sel. Top. Quantum Electron. 17, 1681–1692 (2011).
[CrossRef]

Majewski, M. L.

D. B. Young, J. W. Scott, F. H. Peters, M. G. Peters, M. L. Majewski, B. J. Thibeault, S. W. Corzine, L. A. Coldren, “Enhanced performance of offset-gain high-barrier vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 29, 2013–2022 (1993).
[CrossRef]

Margalit, N. M.

D. I. Babic, K. Streubel, R. P. Mirin, N. M. Margalit, J. E. Bowers, E. L. Hu, D. E. Mars, L. Yang, K. Carey, “Room-temperature continuous-wave operation of 1.54-μm vertical-cavity lasers,” IEEE Photon. Technol. Lett. 7, 1225–1227 (1995).
[CrossRef]

Mars, D. E.

D. I. Babic, K. Streubel, R. P. Mirin, N. M. Margalit, J. E. Bowers, E. L. Hu, D. E. Mars, L. Yang, K. Carey, “Room-temperature continuous-wave operation of 1.54-μm vertical-cavity lasers,” IEEE Photon. Technol. Lett. 7, 1225–1227 (1995).
[CrossRef]

Martin, P. A.

P. A. Martin, “Near-infrared diode laser spectroscopy in chemical process and environmental air monitoring,” Chem. Soc. Rev. 31, 201–210 (2002).
[CrossRef] [PubMed]

Mena, P. V.

Meyer, J. R.

I. Vurgaftman, J. R. Meyer, L. R. Ram-Mohan, “Band parameters for IIIV compound semiconductors and their alloys,” J. Appl. Phys. 89, 5815 (2001).
[CrossRef]

Minch, J.

J. Minch, S. H. Park, T. Keating, S. L. Chuang, “Theory and experiment of In1−xGaxAsyP1−y and In1−x−yGaxAlyAs long-wavelength strained quantum-well lasers,” IEEE J. Quantum Electron. 35, 771–782 (1999).
[CrossRef]

Mirin, R. P.

D. I. Babic, K. Streubel, R. P. Mirin, N. M. Margalit, J. E. Bowers, E. L. Hu, D. E. Mars, L. Yang, K. Carey, “Room-temperature continuous-wave operation of 1.54-μm vertical-cavity lasers,” IEEE Photon. Technol. Lett. 7, 1225–1227 (1995).
[CrossRef]

Morikuni, J. J.

Park, S. H.

J. Minch, S. H. Park, T. Keating, S. L. Chuang, “Theory and experiment of In1−xGaxAsyP1−y and In1−x−yGaxAlyAs long-wavelength strained quantum-well lasers,” IEEE J. Quantum Electron. 35, 771–782 (1999).
[CrossRef]

Peters, F. H.

D. B. Young, J. W. Scott, F. H. Peters, M. G. Peters, M. L. Majewski, B. J. Thibeault, S. W. Corzine, L. A. Coldren, “Enhanced performance of offset-gain high-barrier vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 29, 2013–2022 (1993).
[CrossRef]

Peters, M. G.

J. W. Scott, D. B. Young, B. J. Thibeault, M. G. Peters, L. A. Coldren, “Design of index-guided vertical-cavity lasers for low temperature-sensitivity, sub-milliamp thresholds, and single-mode operation,” IEEE J. Sel. Top. Quantum Electron. 1, 638–648 (1995).
[CrossRef]

D. B. Young, J. W. Scott, F. H. Peters, M. G. Peters, M. L. Majewski, B. J. Thibeault, S. W. Corzine, L. A. Coldren, “Enhanced performance of offset-gain high-barrier vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 29, 2013–2022 (1993).
[CrossRef]

Pikus, G. E.

G. L. Bir, G. E. Pikus, Symmetry and Strain-Induced Effects in Semiconductors (Wiley, 1974), Chap. 5.

Pohl, U. W.

S.-W. Chang, C.-Y. Lu, S. L. Chuang, T. D. Germann, U. W. Pohl, D. Bimberg, “Theory of metal-cavity surface-emitting microlasers and comparison with experiment,” IEEE J. Sel. Top. Quantum Electron. 17, 1681–1692 (2011).
[CrossRef]

Rakuljic, G.

Ram-Mohan, L. R.

I. Vurgaftman, J. R. Meyer, L. R. Ram-Mohan, “Band parameters for IIIV compound semiconductors and their alloys,” J. Appl. Phys. 89, 5815 (2001).
[CrossRef]

Rao, Y.

Y. Rao, W. J. Yang, C. Chase, M. C. Y. Huang, D. P. Worland, S. Khaleghi, M. R. Chitgarha, M. Ziyadi, A. E. Willner, C. J. Chang-Hasnain, “Long-wavelength VCSEL using high-contrast grating,” IEEE J. Sel. Top. Quantum Electron. 19, 1701311 (2013).
[CrossRef]

C. Chase, Y. Rao, W. Hofmann, C. J. Chang-Hasnain, “1550 nm high contrast grating VCSEL,” Opt. Express 18, 15461–15466 (2010).
[CrossRef] [PubMed]

Satyan, N.

Scott, J. W.

J. W. Scott, D. B. Young, B. J. Thibeault, M. G. Peters, L. A. Coldren, “Design of index-guided vertical-cavity lasers for low temperature-sensitivity, sub-milliamp thresholds, and single-mode operation,” IEEE J. Sel. Top. Quantum Electron. 1, 638–648 (1995).
[CrossRef]

D. B. Young, J. W. Scott, F. H. Peters, M. G. Peters, M. L. Majewski, B. J. Thibeault, S. W. Corzine, L. A. Coldren, “Enhanced performance of offset-gain high-barrier vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 29, 2013–2022 (1993).
[CrossRef]

Sedgwick, F. G.

Streubel, K.

D. I. Babic, K. Streubel, R. P. Mirin, N. M. Margalit, J. E. Bowers, E. L. Hu, D. E. Mars, L. Yang, K. Carey, “Room-temperature continuous-wave operation of 1.54-μm vertical-cavity lasers,” IEEE Photon. Technol. Lett. 7, 1225–1227 (1995).
[CrossRef]

Thibeault, B. J.

J. W. Scott, D. B. Young, B. J. Thibeault, M. G. Peters, L. A. Coldren, “Design of index-guided vertical-cavity lasers for low temperature-sensitivity, sub-milliamp thresholds, and single-mode operation,” IEEE J. Sel. Top. Quantum Electron. 1, 638–648 (1995).
[CrossRef]

D. B. Young, J. W. Scott, F. H. Peters, M. G. Peters, M. L. Majewski, B. J. Thibeault, S. W. Corzine, L. A. Coldren, “Enhanced performance of offset-gain high-barrier vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 29, 2013–2022 (1993).
[CrossRef]

Varshni, Y. P.

Y. P. Varshni, “Temperature dependence of the energy gap in semiconductors,” Physica 34, 149–154 (1967).
[CrossRef]

Vasilyev, A.

Vurgaftman, I.

I. Vurgaftman, J. R. Meyer, L. R. Ram-Mohan, “Band parameters for IIIV compound semiconductors and their alloys,” J. Appl. Phys. 89, 5815 (2001).
[CrossRef]

Willner, A. E.

Y. Rao, W. J. Yang, C. Chase, M. C. Y. Huang, D. P. Worland, S. Khaleghi, M. R. Chitgarha, M. Ziyadi, A. E. Willner, C. J. Chang-Hasnain, “Long-wavelength VCSEL using high-contrast grating,” IEEE J. Sel. Top. Quantum Electron. 19, 1701311 (2013).
[CrossRef]

Worland, D. P.

Y. Rao, W. J. Yang, C. Chase, M. C. Y. Huang, D. P. Worland, S. Khaleghi, M. R. Chitgarha, M. Ziyadi, A. E. Willner, C. J. Chang-Hasnain, “Long-wavelength VCSEL using high-contrast grating,” IEEE J. Sel. Top. Quantum Electron. 19, 1701311 (2013).
[CrossRef]

Wyatt, K. W.

Yang, L.

D. I. Babic, K. Streubel, R. P. Mirin, N. M. Margalit, J. E. Bowers, E. L. Hu, D. E. Mars, L. Yang, K. Carey, “Room-temperature continuous-wave operation of 1.54-μm vertical-cavity lasers,” IEEE Photon. Technol. Lett. 7, 1225–1227 (1995).
[CrossRef]

Yang, W. J.

Y. Rao, W. J. Yang, C. Chase, M. C. Y. Huang, D. P. Worland, S. Khaleghi, M. R. Chitgarha, M. Ziyadi, A. E. Willner, C. J. Chang-Hasnain, “Long-wavelength VCSEL using high-contrast grating,” IEEE J. Sel. Top. Quantum Electron. 19, 1701311 (2013).
[CrossRef]

Yariv, A.

Young, D. B.

J. W. Scott, D. B. Young, B. J. Thibeault, M. G. Peters, L. A. Coldren, “Design of index-guided vertical-cavity lasers for low temperature-sensitivity, sub-milliamp thresholds, and single-mode operation,” IEEE J. Sel. Top. Quantum Electron. 1, 638–648 (1995).
[CrossRef]

D. B. Young, J. W. Scott, F. H. Peters, M. G. Peters, M. L. Majewski, B. J. Thibeault, S. W. Corzine, L. A. Coldren, “Enhanced performance of offset-gain high-barrier vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 29, 2013–2022 (1993).
[CrossRef]

Yuen, W.

M. Y. Li, W. Yuen, G. S. Li, C. J. Chang-Hasnain, “Top-emitting micromechanical VCSEL with a 31.6-nm tuning range,” IEEE Photon. Technol. Lett. 10, 18–20 (1998).
[CrossRef]

Zhou, Y.

M. C. Huang, Y. Zhou, C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics 1, 119–122 (2007).
[CrossRef]

Ziyadi, M.

Y. Rao, W. J. Yang, C. Chase, M. C. Y. Huang, D. P. Worland, S. Khaleghi, M. R. Chitgarha, M. Ziyadi, A. E. Willner, C. J. Chang-Hasnain, “Long-wavelength VCSEL using high-contrast grating,” IEEE J. Sel. Top. Quantum Electron. 19, 1701311 (2013).
[CrossRef]

Chem. Soc. Rev. (1)

P. A. Martin, “Near-infrared diode laser spectroscopy in chemical process and environmental air monitoring,” Chem. Soc. Rev. 31, 201–210 (2002).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (2)

D. B. Young, J. W. Scott, F. H. Peters, M. G. Peters, M. L. Majewski, B. J. Thibeault, S. W. Corzine, L. A. Coldren, “Enhanced performance of offset-gain high-barrier vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 29, 2013–2022 (1993).
[CrossRef]

J. Minch, S. H. Park, T. Keating, S. L. Chuang, “Theory and experiment of In1−xGaxAsyP1−y and In1−x−yGaxAlyAs long-wavelength strained quantum-well lasers,” IEEE J. Quantum Electron. 35, 771–782 (1999).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (6)

K. Iga, “Surface-emitting laser-its birth and generation of new optoelectronics field,” IEEE J. Sel. Top. Quantum Electron. 6, 1201–1215 (2000).
[CrossRef]

M.-C. Amann, W. Hofmann, “InP-based long-wavelength VCSELs and VCSEL arrays,” IEEE J. Sel. Top. Quantum Electron. 15, 861–868 (2009).
[CrossRef]

C. J. Chang-Hasnain, “Tunable VCSEL,” IEEE J. Sel. Top. Quantum Electron. 6, 978–987 (2000).
[CrossRef]

S.-W. Chang, C.-Y. Lu, S. L. Chuang, T. D. Germann, U. W. Pohl, D. Bimberg, “Theory of metal-cavity surface-emitting microlasers and comparison with experiment,” IEEE J. Sel. Top. Quantum Electron. 17, 1681–1692 (2011).
[CrossRef]

J. W. Scott, D. B. Young, B. J. Thibeault, M. G. Peters, L. A. Coldren, “Design of index-guided vertical-cavity lasers for low temperature-sensitivity, sub-milliamp thresholds, and single-mode operation,” IEEE J. Sel. Top. Quantum Electron. 1, 638–648 (1995).
[CrossRef]

Y. Rao, W. J. Yang, C. Chase, M. C. Y. Huang, D. P. Worland, S. Khaleghi, M. R. Chitgarha, M. Ziyadi, A. E. Willner, C. J. Chang-Hasnain, “Long-wavelength VCSEL using high-contrast grating,” IEEE J. Sel. Top. Quantum Electron. 19, 1701311 (2013).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

M. Y. Li, W. Yuen, G. S. Li, C. J. Chang-Hasnain, “Top-emitting micromechanical VCSEL with a 31.6-nm tuning range,” IEEE Photon. Technol. Lett. 10, 18–20 (1998).
[CrossRef]

D. I. Babic, K. Streubel, R. P. Mirin, N. M. Margalit, J. E. Bowers, E. L. Hu, D. E. Mars, L. Yang, K. Carey, “Room-temperature continuous-wave operation of 1.54-μm vertical-cavity lasers,” IEEE Photon. Technol. Lett. 7, 1225–1227 (1995).
[CrossRef]

J. Appl. Phys. (1)

I. Vurgaftman, J. R. Meyer, L. R. Ram-Mohan, “Band parameters for IIIV compound semiconductors and their alloys,” J. Appl. Phys. 89, 5815 (2001).
[CrossRef]

J. Lightwave Technol. (1)

Nat. Photonics (1)

M. C. Huang, Y. Zhou, C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics 1, 119–122 (2007).
[CrossRef]

Opt. Express (3)

Physica (1)

Y. P. Varshni, “Temperature dependence of the energy gap in semiconductors,” Physica 34, 149–154 (1967).
[CrossRef]

Other (5)

W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE, 1995), Chap. 2.

M. Y. Li, C. J. Chang-Hasnain, “Tilt loss in wavelength tunable micromechanical vertical cavity lasers,” in CLEO: 1999, 457–458, May1999.

S. L. Chuang, Physics of Photonic Devices, 2 (Wiley, 2009), Chap. 4 and 9.

G. L. Bir, G. E. Pikus, Symmetry and Strain-Induced Effects in Semiconductors (Wiley, 1974), Chap. 5.

L. Condren, S. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995), Chap. 4.

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Figures (13)

Fig. 1
Fig. 1

(a) Schematic of the high contrast grating tunable VCSEL. (b) Block diagram of the theoretical modeling procedure.

Fig. 2
Fig. 2

(a) TE-polarized material gain and (b) TE-polarized spontaneous emission rate calculated for InGaAlAs quantum wells at T = 283 K (solid), T = 313 K (dashed), and T = 343 K (dotted), with carrier densities n = 1.0×1018 cm−3 (blue), n = 1.8×1018 cm−3 (green), and n = 3.0 × 1018 cm−3 (red).

Fig. 3
Fig. 3

(a) Schematic of a HCG reflector with a normal incident plane wave. The complex reflection coefficient |r|e for the zero-order reflected wave is to be determined. (b) Calculation of the HCG reflection by mode matching method. Fields in each region are expanded by eigenmodes, and the reflection and transmission matrices R and T are determined at each interface. The generalized reflection matrix is obtained.

Fig. 4
Fig. 4

(a) Total electric field distribution calculated with the mode matching method for a 1550 nm normal incident plane wave reflected by a TE-HCG. The HCG parameters are: nr = 3.164, grating period Λ = 1070 nm, thickness tg = 195 nm, width w = 260 nm. (b) The reflectivity and (c) the phase of the complex reflection coefficient of a TE-HCG calculated using analytical mode matching method [18] (solid), numerical mode matching method (circle), and finite element method with COMSOL Multiphysics (cross). The green dashed line indicates λ = Λ.

Fig. 5
Fig. 5

The reflectivity of the top (blue) and bottom (black) mirrors calculated by the transfer matrix method, plotted with the reflectivity of HCG alone (red).

Fig. 6
Fig. 6

(a) The reflectivity of the top mirror with different air-gap thicknesses: d1 = 2.13 μm, d2 = 2.03 μm, d3 = 1.83 μm, d4 = 1.63 μm, and d5 = 1.53 μm. The circles indicate the corresponding resonance wavelengths at different air-gap thicknesses. (b) Total round-trip phase spectra in the Febry-Perot model with different air-gap thicknesses. The zero-crossing points of the total round-trip phase determine the resonance wavelengths.

Fig. 7
Fig. 7

(a) Cavity resonance wavelengths of the HCG VCSEL at different air-gap thicknesses controlled by the MEMS. (b) Cavity mirror loss αm and radiation quality factor Qrad as functions of the air-gap thickness.

Fig. 8
Fig. 8

Comparison between the theoretical and experimental L-I curves for a fixed-gap TE-HCG VCSEL at different temperatures.

Fig. 9
Fig. 9

(a) Material gain and (b) carrier density solved from the rate equations as functions of the injection current at different substrate temperatures.

Fig. 10
Fig. 10

(a) Calculated spontaneous emission rate (solid) and Auger recombination rate (dashed) as functions of the injection current at different substrate temperatures as labeled. (b) Relationship among the B coefficient, spontaneous emission rate, and the carrier density, all of which are solved from the rate equations at different substrate temperatures as labeled.

Fig. 11
Fig. 11

The stimulated emission current (green), spontaneous emission current (red), non-radiative recombination current (cyan), series leakage current (black), and shunt leakage current (blue) solved as functions of the injection current with substrate temperatures at (a) T = 288 K, (b) T = 308 K, (c) T = 328 K, and (d) T = 348 K.

Fig. 12
Fig. 12

(a) Schematic of the electrostatic model for MEMS controlling the air-gap thickness. (b) Theoretical and experimental resonance wavelengths vs. tuning voltage.

Fig. 13
Fig. 13

(a) Theoretical (dashed) and experimental (solid) L-I curves of a MEMS-controlled TE-HCG VCSEL with different tuning voltages. (b) Theoretical (circle) and experimental (square) peak output powers and threshold currents as functions of the MEMS tuning voltage.

Tables (1)

Tables Icon

Table 1 Parameters used in our theoretical model.

Equations (23)

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g ( h ¯ ω ) = π e 2 n r c ε 0 m 0 2 ω σ n , m 0 k t d k t π L z M n m σ ( k t ) [ f c n ( k t ) f v σ , m ( k t ) ] L ( k t , h ¯ ω ) r spon ( h ¯ ω ) = n r ω e 2 π h ¯ c 3 ε 0 m 0 2 σ n , m 0 k t d k t π L z M n m σ ( k t ) f c n ( k t ) [ 1 f v σ , m ( k t ) ] L ( k t , h ¯ ω )
Δ E g = Δ E BR ( n 2 D ) 1 / 3
E g ( T ) = E g ( T = 0 ) α T 2 T + β
R sp = 0 1 3 [ 2 × r spon TE ( h ¯ ω ) + r spon TM ( h ¯ ω ) ] d ( h ¯ ω ) .
R ˜ 12 = R 12 + T 21 ( I K 2 R 23 K 2 R 21 ) 1 K 2 R 23 K 2 T 12
K 2 = ( exp ( i k 1 z t g ) 0 0 exp ( i k 2 z t g ) )
ϕ total ( λ ) = ϕ top ( λ ) + ϕ cavity + bottom ( λ )
ϕ total ( λ r ) = 2 m π , m = integer .
n = n + i n = { n + i ( α i g ) λ 4 π , in QWs n + i α i λ 4 π , elsewhere
G total ( g ) = ln ( 1 | r top ( λ ) | 2 | r cavity + bottom ( λ , g ) | 2 ) | λ = λ r
G total ( g th ) = 0 .
α m = G th | α i = 0 = Γ g th | α i = 0 ,
1 τ p = v g ( α m + α i + α d ) = ω Q rad + ω Q mat + ω Q d
d n d t = η i I I l ( n , T a ) I sh ( I ) q V a R nr ( n ) R sp ( n , T a ) R st ( n , T a ) S d S d t = Γ R st ( n , T a ) S S τ p + Γ β sp R sp ( n , T a )
T a = T sub + R th ( V I P )
Δ λ = d λ d T Δ T
R nr ( n ) = v s A a V a n + C n 3
R st ( n , T a ) = v g g ( λ , n , T a )
I l ( n , T a ) = I l 0 exp ( ( F c F v ) E g , barrier k T a )
P = β c 1 h ¯ ω S V a Γ v g α m + β c 2 h ¯ ω R sp V a
B ( n , T ) = R sp ( n , T a ) n 2
k ( h 0 x 0 ) = m g , for V = 0 k ( h 0 x ) = m g + F E = m g + ε A V 2 2 x 2 , for V 0
x 2 ( x 0 x ) = ε A V 2 2 k .

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