Abstract

We report the fabrication and the performance of phase-locked VCSEL arrays emitting near 1310 nm wavelength. The arrays were fabricated using double wafer fusion by patterning a tunnel junction layer, which serves to define the individual single mode array elements. Phase-locking in both one-dimensional and two-dimensional array configurations was confirmed by means of far field and spectral measurements as well as theoretical modeling. CW output powers of more than 12 mW were achieved.

© 2009 Optical Society of America

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  1. A. Furukawa, S. Sasaki, M. Hoshi, A. Matsuzono, K. Moritoh, and T. Baba, "High-power single-mode verticalcavity surface-emitting lasers with triangular holey structure," Appl. Phys. Lett. 85, 5161-5163 (2004).
    [CrossRef]
  2. M. W. Wiemer, R. I. Aldaz, D. A. B. Miller, and J. S. Harris, "A Single Transverse-Mode Monolithically Integrated Long Vertical-Cavity Surface-Emitting Laser," IEEE Photon. Technol. Lett. 17, 1366-1368 (2005).
    [CrossRef]
  3. A. Mircea, A. Caliman, V. Iakovlev, A. Mereuta, G. Suruceanu, C. A. Berseth, P. Royo, A. Syrbu, and E. Kapon, "CavityMode - Gain Peak Tradeoff for 1320 nmWafer-Fused VCSELs with 3mWSingle-Mode Emission Power and 10Gb/s Modulation Speed up to 70◦C," IEEE Photon. Technol. Lett. 19, 121-123 (2007).
    [CrossRef]
  4. I. Kardosh, F. Demaria, F. Rinaldi, S. Menzel, and R. Michalzik, "High-Power Single Transverse Mode Vertical-Cavity Surface-Emitting Lasers With Monolithically Integrated Curved Dielectric Mirrors," IEEE Photon. Technol. Lett. 20, 2084-2086 (2008).
    [CrossRef]
  5. M. Grabherr, M. Miller, R. Jäger, R. Michalzik, U. Martin, H. J. Unhold, and K. J. Ebeling, "High-Power VCSEL’s: Single Devices and Densely Packed 2-D-Arrays," IEEE J. Sel. Top. Quantum Electron. 5, 495-502 (1999).
    [CrossRef]
  6. R. Shau, M. Ortsiefer, J. Rosskopf, G. Böhm, F. Köhler, and M. C. Amann, "Vertical-cavity surface-emitting laser diodes at 1.55μm with large output power and high operation temperature," Electron. Lett. 37, 1295-1296 (2001).
    [CrossRef]
  7. M. Achtenhagen, A. Hardy, and E. Kapon, "Mode discrimination in vertical-cavity surface-emitting lasers including Bragg reflectors and limiting apertures," Opt. Eng. 44, 104202 1-6 (2005).
    [CrossRef]
  8. M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florenz, and J. Wullert, "Two-dimensional phaselocked arrays of vertical-cavity semiconductor lasers by mirror reflectivity modulation," Appl. Phys. Lett. 58, 804-806 (1991).
    [CrossRef]
  9. M. Orenstein, E. Kapon, J. P. Harbison, L. T. Florenz, and N. G. Stoffel, "Large two-dimensional arrays of phase-locked vertical cavity surface emitting lasers," Appl. Phys. Lett. 60, 1335-1337 (1992).
    [CrossRef]
  10. H. J. Yoo, A. Scherer, J. P. Harbison, L. T. Florenz, E. G. Paek, B. P. Van der Gaag, J. R. Hayes, A. Von Lehmen, E. Kapon, and Y. S. Kwon, "Fabrication of a two-dimensional phased array of vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 56, 1198-1200 (1990).
    [CrossRef]
  11. J. J. Raftery, A. C. Lehman, A. J. Danner, P. O. Leisher, A. V. Giannopoulos, and K. D. Choquette, "In-phase evanescent coupling of two-dimensional arrays of defect cavities in photonic crystal vertical cavity surface emitting lasers," Appl. Phys. Lett. 89, 081119 1-3 (2006).
    [CrossRef]
  12. D. G. Deppe, J. P. van der Ziel, N. Chand, G. J. Zydzik, and S. N. G. Chu, "Phase-coupled two-dimensional AlxGa1−xAs-GaAs vertical-cavity surface-emitting laser array," Appl. Phys. Lett. 56, 2089-2091 (1990).
    [CrossRef]
  13. A.C. Lehman and K. D. Choquette, "One- and Two- Dimensional Coherently Coupled Implant-Defined Vertical-Cavity Laser Arrays," IEEE Photon. Technol. Lett. 19, 1421-1423 (2007).
    [CrossRef]
  14. A. C. Lehman, D. F. Siriani, and K. D. Choquette, "Two-dimensional electronic beam-steering with implantdefined coherent VCSEL arrays," Electron. Lett. 43, 1202-1203 (2007).
    [CrossRef]
  15. L. D. A. Lundeberg and E. Kapon, "Mode switching and beam steering in photonic crystal heterostructures implemented with vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 90, 241115 1-3 (2007).
    [CrossRef]
  16. A. Syrbu and E. Kapon, "Long-Wavelength VCSELs Power - efficient answer," Nature Photon.,  3, 27-29 (2009).
    [CrossRef]
  17. A. Mereuta, A. Syrbu, V. Iakovlev, A. Rudra, A. Caliman, G. Suruceanu, C. A. Berseth, E. Deichsel, and E. Kapon, "1.5μm VCSEL structure optimized for high-power and high-temperatrue operation," J. Crystal Growth 272, 520-525 (2004).
    [CrossRef]
  18. M. Arzberger, M. Lohner, G. Böhm, and M. C. Amann, "Low-resistivity p-side contacts for InP-based devices using buried InGaAs tunnel junction," Electron. Lett. 36, 87-88 (2000).
    [CrossRef]
  19. J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, Engelwood, Colorado, Third Edition, 2005).

2009 (1)

A. Syrbu and E. Kapon, "Long-Wavelength VCSELs Power - efficient answer," Nature Photon.,  3, 27-29 (2009).
[CrossRef]

2008 (1)

I. Kardosh, F. Demaria, F. Rinaldi, S. Menzel, and R. Michalzik, "High-Power Single Transverse Mode Vertical-Cavity Surface-Emitting Lasers With Monolithically Integrated Curved Dielectric Mirrors," IEEE Photon. Technol. Lett. 20, 2084-2086 (2008).
[CrossRef]

2007 (3)

A. Mircea, A. Caliman, V. Iakovlev, A. Mereuta, G. Suruceanu, C. A. Berseth, P. Royo, A. Syrbu, and E. Kapon, "CavityMode - Gain Peak Tradeoff for 1320 nmWafer-Fused VCSELs with 3mWSingle-Mode Emission Power and 10Gb/s Modulation Speed up to 70◦C," IEEE Photon. Technol. Lett. 19, 121-123 (2007).
[CrossRef]

A.C. Lehman and K. D. Choquette, "One- and Two- Dimensional Coherently Coupled Implant-Defined Vertical-Cavity Laser Arrays," IEEE Photon. Technol. Lett. 19, 1421-1423 (2007).
[CrossRef]

A. C. Lehman, D. F. Siriani, and K. D. Choquette, "Two-dimensional electronic beam-steering with implantdefined coherent VCSEL arrays," Electron. Lett. 43, 1202-1203 (2007).
[CrossRef]

2006 (1)

J. J. Raftery, A. C. Lehman, A. J. Danner, P. O. Leisher, A. V. Giannopoulos, and K. D. Choquette, "In-phase evanescent coupling of two-dimensional arrays of defect cavities in photonic crystal vertical cavity surface emitting lasers," Appl. Phys. Lett. 89, 081119 1-3 (2006).
[CrossRef]

2005 (2)

M. Achtenhagen, A. Hardy, and E. Kapon, "Mode discrimination in vertical-cavity surface-emitting lasers including Bragg reflectors and limiting apertures," Opt. Eng. 44, 104202 1-6 (2005).
[CrossRef]

M. W. Wiemer, R. I. Aldaz, D. A. B. Miller, and J. S. Harris, "A Single Transverse-Mode Monolithically Integrated Long Vertical-Cavity Surface-Emitting Laser," IEEE Photon. Technol. Lett. 17, 1366-1368 (2005).
[CrossRef]

2004 (2)

A. Furukawa, S. Sasaki, M. Hoshi, A. Matsuzono, K. Moritoh, and T. Baba, "High-power single-mode verticalcavity surface-emitting lasers with triangular holey structure," Appl. Phys. Lett. 85, 5161-5163 (2004).
[CrossRef]

A. Mereuta, A. Syrbu, V. Iakovlev, A. Rudra, A. Caliman, G. Suruceanu, C. A. Berseth, E. Deichsel, and E. Kapon, "1.5μm VCSEL structure optimized for high-power and high-temperatrue operation," J. Crystal Growth 272, 520-525 (2004).
[CrossRef]

2001 (1)

R. Shau, M. Ortsiefer, J. Rosskopf, G. Böhm, F. Köhler, and M. C. Amann, "Vertical-cavity surface-emitting laser diodes at 1.55μm with large output power and high operation temperature," Electron. Lett. 37, 1295-1296 (2001).
[CrossRef]

2000 (1)

M. Arzberger, M. Lohner, G. Böhm, and M. C. Amann, "Low-resistivity p-side contacts for InP-based devices using buried InGaAs tunnel junction," Electron. Lett. 36, 87-88 (2000).
[CrossRef]

1999 (1)

M. Grabherr, M. Miller, R. Jäger, R. Michalzik, U. Martin, H. J. Unhold, and K. J. Ebeling, "High-Power VCSEL’s: Single Devices and Densely Packed 2-D-Arrays," IEEE J. Sel. Top. Quantum Electron. 5, 495-502 (1999).
[CrossRef]

1992 (1)

M. Orenstein, E. Kapon, J. P. Harbison, L. T. Florenz, and N. G. Stoffel, "Large two-dimensional arrays of phase-locked vertical cavity surface emitting lasers," Appl. Phys. Lett. 60, 1335-1337 (1992).
[CrossRef]

1991 (1)

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florenz, and J. Wullert, "Two-dimensional phaselocked arrays of vertical-cavity semiconductor lasers by mirror reflectivity modulation," Appl. Phys. Lett. 58, 804-806 (1991).
[CrossRef]

1990 (2)

H. J. Yoo, A. Scherer, J. P. Harbison, L. T. Florenz, E. G. Paek, B. P. Van der Gaag, J. R. Hayes, A. Von Lehmen, E. Kapon, and Y. S. Kwon, "Fabrication of a two-dimensional phased array of vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 56, 1198-1200 (1990).
[CrossRef]

D. G. Deppe, J. P. van der Ziel, N. Chand, G. J. Zydzik, and S. N. G. Chu, "Phase-coupled two-dimensional AlxGa1−xAs-GaAs vertical-cavity surface-emitting laser array," Appl. Phys. Lett. 56, 2089-2091 (1990).
[CrossRef]

Achtenhagen, M.

M. Achtenhagen, A. Hardy, and E. Kapon, "Mode discrimination in vertical-cavity surface-emitting lasers including Bragg reflectors and limiting apertures," Opt. Eng. 44, 104202 1-6 (2005).
[CrossRef]

Aldaz, R. I.

M. W. Wiemer, R. I. Aldaz, D. A. B. Miller, and J. S. Harris, "A Single Transverse-Mode Monolithically Integrated Long Vertical-Cavity Surface-Emitting Laser," IEEE Photon. Technol. Lett. 17, 1366-1368 (2005).
[CrossRef]

Amann, M. C.

R. Shau, M. Ortsiefer, J. Rosskopf, G. Böhm, F. Köhler, and M. C. Amann, "Vertical-cavity surface-emitting laser diodes at 1.55μm with large output power and high operation temperature," Electron. Lett. 37, 1295-1296 (2001).
[CrossRef]

M. Arzberger, M. Lohner, G. Böhm, and M. C. Amann, "Low-resistivity p-side contacts for InP-based devices using buried InGaAs tunnel junction," Electron. Lett. 36, 87-88 (2000).
[CrossRef]

Arzberger, M.

M. Arzberger, M. Lohner, G. Böhm, and M. C. Amann, "Low-resistivity p-side contacts for InP-based devices using buried InGaAs tunnel junction," Electron. Lett. 36, 87-88 (2000).
[CrossRef]

Baba, T.

A. Furukawa, S. Sasaki, M. Hoshi, A. Matsuzono, K. Moritoh, and T. Baba, "High-power single-mode verticalcavity surface-emitting lasers with triangular holey structure," Appl. Phys. Lett. 85, 5161-5163 (2004).
[CrossRef]

Berseth, C. A.

A. Mircea, A. Caliman, V. Iakovlev, A. Mereuta, G. Suruceanu, C. A. Berseth, P. Royo, A. Syrbu, and E. Kapon, "CavityMode - Gain Peak Tradeoff for 1320 nmWafer-Fused VCSELs with 3mWSingle-Mode Emission Power and 10Gb/s Modulation Speed up to 70◦C," IEEE Photon. Technol. Lett. 19, 121-123 (2007).
[CrossRef]

A. Mereuta, A. Syrbu, V. Iakovlev, A. Rudra, A. Caliman, G. Suruceanu, C. A. Berseth, E. Deichsel, and E. Kapon, "1.5μm VCSEL structure optimized for high-power and high-temperatrue operation," J. Crystal Growth 272, 520-525 (2004).
[CrossRef]

Böhm, G.

R. Shau, M. Ortsiefer, J. Rosskopf, G. Böhm, F. Köhler, and M. C. Amann, "Vertical-cavity surface-emitting laser diodes at 1.55μm with large output power and high operation temperature," Electron. Lett. 37, 1295-1296 (2001).
[CrossRef]

M. Arzberger, M. Lohner, G. Böhm, and M. C. Amann, "Low-resistivity p-side contacts for InP-based devices using buried InGaAs tunnel junction," Electron. Lett. 36, 87-88 (2000).
[CrossRef]

Caliman, A.

A. Mircea, A. Caliman, V. Iakovlev, A. Mereuta, G. Suruceanu, C. A. Berseth, P. Royo, A. Syrbu, and E. Kapon, "CavityMode - Gain Peak Tradeoff for 1320 nmWafer-Fused VCSELs with 3mWSingle-Mode Emission Power and 10Gb/s Modulation Speed up to 70◦C," IEEE Photon. Technol. Lett. 19, 121-123 (2007).
[CrossRef]

A. Mereuta, A. Syrbu, V. Iakovlev, A. Rudra, A. Caliman, G. Suruceanu, C. A. Berseth, E. Deichsel, and E. Kapon, "1.5μm VCSEL structure optimized for high-power and high-temperatrue operation," J. Crystal Growth 272, 520-525 (2004).
[CrossRef]

Chand, N.

D. G. Deppe, J. P. van der Ziel, N. Chand, G. J. Zydzik, and S. N. G. Chu, "Phase-coupled two-dimensional AlxGa1−xAs-GaAs vertical-cavity surface-emitting laser array," Appl. Phys. Lett. 56, 2089-2091 (1990).
[CrossRef]

Choquette, K. D.

A.C. Lehman and K. D. Choquette, "One- and Two- Dimensional Coherently Coupled Implant-Defined Vertical-Cavity Laser Arrays," IEEE Photon. Technol. Lett. 19, 1421-1423 (2007).
[CrossRef]

A. C. Lehman, D. F. Siriani, and K. D. Choquette, "Two-dimensional electronic beam-steering with implantdefined coherent VCSEL arrays," Electron. Lett. 43, 1202-1203 (2007).
[CrossRef]

J. J. Raftery, A. C. Lehman, A. J. Danner, P. O. Leisher, A. V. Giannopoulos, and K. D. Choquette, "In-phase evanescent coupling of two-dimensional arrays of defect cavities in photonic crystal vertical cavity surface emitting lasers," Appl. Phys. Lett. 89, 081119 1-3 (2006).
[CrossRef]

Chu, S. N. G.

D. G. Deppe, J. P. van der Ziel, N. Chand, G. J. Zydzik, and S. N. G. Chu, "Phase-coupled two-dimensional AlxGa1−xAs-GaAs vertical-cavity surface-emitting laser array," Appl. Phys. Lett. 56, 2089-2091 (1990).
[CrossRef]

Danner, A. J.

J. J. Raftery, A. C. Lehman, A. J. Danner, P. O. Leisher, A. V. Giannopoulos, and K. D. Choquette, "In-phase evanescent coupling of two-dimensional arrays of defect cavities in photonic crystal vertical cavity surface emitting lasers," Appl. Phys. Lett. 89, 081119 1-3 (2006).
[CrossRef]

Deichsel, E.

A. Mereuta, A. Syrbu, V. Iakovlev, A. Rudra, A. Caliman, G. Suruceanu, C. A. Berseth, E. Deichsel, and E. Kapon, "1.5μm VCSEL structure optimized for high-power and high-temperatrue operation," J. Crystal Growth 272, 520-525 (2004).
[CrossRef]

Demaria, F.

I. Kardosh, F. Demaria, F. Rinaldi, S. Menzel, and R. Michalzik, "High-Power Single Transverse Mode Vertical-Cavity Surface-Emitting Lasers With Monolithically Integrated Curved Dielectric Mirrors," IEEE Photon. Technol. Lett. 20, 2084-2086 (2008).
[CrossRef]

Deppe, D. G.

D. G. Deppe, J. P. van der Ziel, N. Chand, G. J. Zydzik, and S. N. G. Chu, "Phase-coupled two-dimensional AlxGa1−xAs-GaAs vertical-cavity surface-emitting laser array," Appl. Phys. Lett. 56, 2089-2091 (1990).
[CrossRef]

Ebeling, K. J.

M. Grabherr, M. Miller, R. Jäger, R. Michalzik, U. Martin, H. J. Unhold, and K. J. Ebeling, "High-Power VCSEL’s: Single Devices and Densely Packed 2-D-Arrays," IEEE J. Sel. Top. Quantum Electron. 5, 495-502 (1999).
[CrossRef]

Florenz, L. T.

M. Orenstein, E. Kapon, J. P. Harbison, L. T. Florenz, and N. G. Stoffel, "Large two-dimensional arrays of phase-locked vertical cavity surface emitting lasers," Appl. Phys. Lett. 60, 1335-1337 (1992).
[CrossRef]

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florenz, and J. Wullert, "Two-dimensional phaselocked arrays of vertical-cavity semiconductor lasers by mirror reflectivity modulation," Appl. Phys. Lett. 58, 804-806 (1991).
[CrossRef]

H. J. Yoo, A. Scherer, J. P. Harbison, L. T. Florenz, E. G. Paek, B. P. Van der Gaag, J. R. Hayes, A. Von Lehmen, E. Kapon, and Y. S. Kwon, "Fabrication of a two-dimensional phased array of vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 56, 1198-1200 (1990).
[CrossRef]

Furukawa, A.

A. Furukawa, S. Sasaki, M. Hoshi, A. Matsuzono, K. Moritoh, and T. Baba, "High-power single-mode verticalcavity surface-emitting lasers with triangular holey structure," Appl. Phys. Lett. 85, 5161-5163 (2004).
[CrossRef]

Giannopoulos, A. V.

J. J. Raftery, A. C. Lehman, A. J. Danner, P. O. Leisher, A. V. Giannopoulos, and K. D. Choquette, "In-phase evanescent coupling of two-dimensional arrays of defect cavities in photonic crystal vertical cavity surface emitting lasers," Appl. Phys. Lett. 89, 081119 1-3 (2006).
[CrossRef]

Grabherr, M.

M. Grabherr, M. Miller, R. Jäger, R. Michalzik, U. Martin, H. J. Unhold, and K. J. Ebeling, "High-Power VCSEL’s: Single Devices and Densely Packed 2-D-Arrays," IEEE J. Sel. Top. Quantum Electron. 5, 495-502 (1999).
[CrossRef]

Harbison, J. P.

M. Orenstein, E. Kapon, J. P. Harbison, L. T. Florenz, and N. G. Stoffel, "Large two-dimensional arrays of phase-locked vertical cavity surface emitting lasers," Appl. Phys. Lett. 60, 1335-1337 (1992).
[CrossRef]

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florenz, and J. Wullert, "Two-dimensional phaselocked arrays of vertical-cavity semiconductor lasers by mirror reflectivity modulation," Appl. Phys. Lett. 58, 804-806 (1991).
[CrossRef]

H. J. Yoo, A. Scherer, J. P. Harbison, L. T. Florenz, E. G. Paek, B. P. Van der Gaag, J. R. Hayes, A. Von Lehmen, E. Kapon, and Y. S. Kwon, "Fabrication of a two-dimensional phased array of vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 56, 1198-1200 (1990).
[CrossRef]

Hardy, A.

M. Achtenhagen, A. Hardy, and E. Kapon, "Mode discrimination in vertical-cavity surface-emitting lasers including Bragg reflectors and limiting apertures," Opt. Eng. 44, 104202 1-6 (2005).
[CrossRef]

Harris, J. S.

M. W. Wiemer, R. I. Aldaz, D. A. B. Miller, and J. S. Harris, "A Single Transverse-Mode Monolithically Integrated Long Vertical-Cavity Surface-Emitting Laser," IEEE Photon. Technol. Lett. 17, 1366-1368 (2005).
[CrossRef]

Hayes, J. R.

H. J. Yoo, A. Scherer, J. P. Harbison, L. T. Florenz, E. G. Paek, B. P. Van der Gaag, J. R. Hayes, A. Von Lehmen, E. Kapon, and Y. S. Kwon, "Fabrication of a two-dimensional phased array of vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 56, 1198-1200 (1990).
[CrossRef]

Hoshi, M.

A. Furukawa, S. Sasaki, M. Hoshi, A. Matsuzono, K. Moritoh, and T. Baba, "High-power single-mode verticalcavity surface-emitting lasers with triangular holey structure," Appl. Phys. Lett. 85, 5161-5163 (2004).
[CrossRef]

Iakovlev, V.

A. Mircea, A. Caliman, V. Iakovlev, A. Mereuta, G. Suruceanu, C. A. Berseth, P. Royo, A. Syrbu, and E. Kapon, "CavityMode - Gain Peak Tradeoff for 1320 nmWafer-Fused VCSELs with 3mWSingle-Mode Emission Power and 10Gb/s Modulation Speed up to 70◦C," IEEE Photon. Technol. Lett. 19, 121-123 (2007).
[CrossRef]

A. Mereuta, A. Syrbu, V. Iakovlev, A. Rudra, A. Caliman, G. Suruceanu, C. A. Berseth, E. Deichsel, and E. Kapon, "1.5μm VCSEL structure optimized for high-power and high-temperatrue operation," J. Crystal Growth 272, 520-525 (2004).
[CrossRef]

Jäger, R.

M. Grabherr, M. Miller, R. Jäger, R. Michalzik, U. Martin, H. J. Unhold, and K. J. Ebeling, "High-Power VCSEL’s: Single Devices and Densely Packed 2-D-Arrays," IEEE J. Sel. Top. Quantum Electron. 5, 495-502 (1999).
[CrossRef]

Kapon, E.

A. Syrbu and E. Kapon, "Long-Wavelength VCSELs Power - efficient answer," Nature Photon.,  3, 27-29 (2009).
[CrossRef]

A. Mircea, A. Caliman, V. Iakovlev, A. Mereuta, G. Suruceanu, C. A. Berseth, P. Royo, A. Syrbu, and E. Kapon, "CavityMode - Gain Peak Tradeoff for 1320 nmWafer-Fused VCSELs with 3mWSingle-Mode Emission Power and 10Gb/s Modulation Speed up to 70◦C," IEEE Photon. Technol. Lett. 19, 121-123 (2007).
[CrossRef]

M. Achtenhagen, A. Hardy, and E. Kapon, "Mode discrimination in vertical-cavity surface-emitting lasers including Bragg reflectors and limiting apertures," Opt. Eng. 44, 104202 1-6 (2005).
[CrossRef]

A. Mereuta, A. Syrbu, V. Iakovlev, A. Rudra, A. Caliman, G. Suruceanu, C. A. Berseth, E. Deichsel, and E. Kapon, "1.5μm VCSEL structure optimized for high-power and high-temperatrue operation," J. Crystal Growth 272, 520-525 (2004).
[CrossRef]

M. Orenstein, E. Kapon, J. P. Harbison, L. T. Florenz, and N. G. Stoffel, "Large two-dimensional arrays of phase-locked vertical cavity surface emitting lasers," Appl. Phys. Lett. 60, 1335-1337 (1992).
[CrossRef]

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florenz, and J. Wullert, "Two-dimensional phaselocked arrays of vertical-cavity semiconductor lasers by mirror reflectivity modulation," Appl. Phys. Lett. 58, 804-806 (1991).
[CrossRef]

H. J. Yoo, A. Scherer, J. P. Harbison, L. T. Florenz, E. G. Paek, B. P. Van der Gaag, J. R. Hayes, A. Von Lehmen, E. Kapon, and Y. S. Kwon, "Fabrication of a two-dimensional phased array of vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 56, 1198-1200 (1990).
[CrossRef]

Kardosh, I.

I. Kardosh, F. Demaria, F. Rinaldi, S. Menzel, and R. Michalzik, "High-Power Single Transverse Mode Vertical-Cavity Surface-Emitting Lasers With Monolithically Integrated Curved Dielectric Mirrors," IEEE Photon. Technol. Lett. 20, 2084-2086 (2008).
[CrossRef]

Köhler, F.

R. Shau, M. Ortsiefer, J. Rosskopf, G. Böhm, F. Köhler, and M. C. Amann, "Vertical-cavity surface-emitting laser diodes at 1.55μm with large output power and high operation temperature," Electron. Lett. 37, 1295-1296 (2001).
[CrossRef]

Kwon, Y. S.

H. J. Yoo, A. Scherer, J. P. Harbison, L. T. Florenz, E. G. Paek, B. P. Van der Gaag, J. R. Hayes, A. Von Lehmen, E. Kapon, and Y. S. Kwon, "Fabrication of a two-dimensional phased array of vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 56, 1198-1200 (1990).
[CrossRef]

Lehman, A. C.

A. C. Lehman, D. F. Siriani, and K. D. Choquette, "Two-dimensional electronic beam-steering with implantdefined coherent VCSEL arrays," Electron. Lett. 43, 1202-1203 (2007).
[CrossRef]

J. J. Raftery, A. C. Lehman, A. J. Danner, P. O. Leisher, A. V. Giannopoulos, and K. D. Choquette, "In-phase evanescent coupling of two-dimensional arrays of defect cavities in photonic crystal vertical cavity surface emitting lasers," Appl. Phys. Lett. 89, 081119 1-3 (2006).
[CrossRef]

Lehman, A.C.

A.C. Lehman and K. D. Choquette, "One- and Two- Dimensional Coherently Coupled Implant-Defined Vertical-Cavity Laser Arrays," IEEE Photon. Technol. Lett. 19, 1421-1423 (2007).
[CrossRef]

Leisher, P. O.

J. J. Raftery, A. C. Lehman, A. J. Danner, P. O. Leisher, A. V. Giannopoulos, and K. D. Choquette, "In-phase evanescent coupling of two-dimensional arrays of defect cavities in photonic crystal vertical cavity surface emitting lasers," Appl. Phys. Lett. 89, 081119 1-3 (2006).
[CrossRef]

Lohner, M.

M. Arzberger, M. Lohner, G. Böhm, and M. C. Amann, "Low-resistivity p-side contacts for InP-based devices using buried InGaAs tunnel junction," Electron. Lett. 36, 87-88 (2000).
[CrossRef]

Martin, U.

M. Grabherr, M. Miller, R. Jäger, R. Michalzik, U. Martin, H. J. Unhold, and K. J. Ebeling, "High-Power VCSEL’s: Single Devices and Densely Packed 2-D-Arrays," IEEE J. Sel. Top. Quantum Electron. 5, 495-502 (1999).
[CrossRef]

Matsuzono, A.

A. Furukawa, S. Sasaki, M. Hoshi, A. Matsuzono, K. Moritoh, and T. Baba, "High-power single-mode verticalcavity surface-emitting lasers with triangular holey structure," Appl. Phys. Lett. 85, 5161-5163 (2004).
[CrossRef]

Menzel, S.

I. Kardosh, F. Demaria, F. Rinaldi, S. Menzel, and R. Michalzik, "High-Power Single Transverse Mode Vertical-Cavity Surface-Emitting Lasers With Monolithically Integrated Curved Dielectric Mirrors," IEEE Photon. Technol. Lett. 20, 2084-2086 (2008).
[CrossRef]

Mereuta, A.

A. Mircea, A. Caliman, V. Iakovlev, A. Mereuta, G. Suruceanu, C. A. Berseth, P. Royo, A. Syrbu, and E. Kapon, "CavityMode - Gain Peak Tradeoff for 1320 nmWafer-Fused VCSELs with 3mWSingle-Mode Emission Power and 10Gb/s Modulation Speed up to 70◦C," IEEE Photon. Technol. Lett. 19, 121-123 (2007).
[CrossRef]

A. Mereuta, A. Syrbu, V. Iakovlev, A. Rudra, A. Caliman, G. Suruceanu, C. A. Berseth, E. Deichsel, and E. Kapon, "1.5μm VCSEL structure optimized for high-power and high-temperatrue operation," J. Crystal Growth 272, 520-525 (2004).
[CrossRef]

Michalzik, R.

I. Kardosh, F. Demaria, F. Rinaldi, S. Menzel, and R. Michalzik, "High-Power Single Transverse Mode Vertical-Cavity Surface-Emitting Lasers With Monolithically Integrated Curved Dielectric Mirrors," IEEE Photon. Technol. Lett. 20, 2084-2086 (2008).
[CrossRef]

M. Grabherr, M. Miller, R. Jäger, R. Michalzik, U. Martin, H. J. Unhold, and K. J. Ebeling, "High-Power VCSEL’s: Single Devices and Densely Packed 2-D-Arrays," IEEE J. Sel. Top. Quantum Electron. 5, 495-502 (1999).
[CrossRef]

Miller, D. A. B.

M. W. Wiemer, R. I. Aldaz, D. A. B. Miller, and J. S. Harris, "A Single Transverse-Mode Monolithically Integrated Long Vertical-Cavity Surface-Emitting Laser," IEEE Photon. Technol. Lett. 17, 1366-1368 (2005).
[CrossRef]

Miller, M.

M. Grabherr, M. Miller, R. Jäger, R. Michalzik, U. Martin, H. J. Unhold, and K. J. Ebeling, "High-Power VCSEL’s: Single Devices and Densely Packed 2-D-Arrays," IEEE J. Sel. Top. Quantum Electron. 5, 495-502 (1999).
[CrossRef]

Mircea, A.

A. Mircea, A. Caliman, V. Iakovlev, A. Mereuta, G. Suruceanu, C. A. Berseth, P. Royo, A. Syrbu, and E. Kapon, "CavityMode - Gain Peak Tradeoff for 1320 nmWafer-Fused VCSELs with 3mWSingle-Mode Emission Power and 10Gb/s Modulation Speed up to 70◦C," IEEE Photon. Technol. Lett. 19, 121-123 (2007).
[CrossRef]

Moritoh, K.

A. Furukawa, S. Sasaki, M. Hoshi, A. Matsuzono, K. Moritoh, and T. Baba, "High-power single-mode verticalcavity surface-emitting lasers with triangular holey structure," Appl. Phys. Lett. 85, 5161-5163 (2004).
[CrossRef]

Orenstein, M.

M. Orenstein, E. Kapon, J. P. Harbison, L. T. Florenz, and N. G. Stoffel, "Large two-dimensional arrays of phase-locked vertical cavity surface emitting lasers," Appl. Phys. Lett. 60, 1335-1337 (1992).
[CrossRef]

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florenz, and J. Wullert, "Two-dimensional phaselocked arrays of vertical-cavity semiconductor lasers by mirror reflectivity modulation," Appl. Phys. Lett. 58, 804-806 (1991).
[CrossRef]

Ortsiefer, M.

R. Shau, M. Ortsiefer, J. Rosskopf, G. Böhm, F. Köhler, and M. C. Amann, "Vertical-cavity surface-emitting laser diodes at 1.55μm with large output power and high operation temperature," Electron. Lett. 37, 1295-1296 (2001).
[CrossRef]

Paek, E. G.

H. J. Yoo, A. Scherer, J. P. Harbison, L. T. Florenz, E. G. Paek, B. P. Van der Gaag, J. R. Hayes, A. Von Lehmen, E. Kapon, and Y. S. Kwon, "Fabrication of a two-dimensional phased array of vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 56, 1198-1200 (1990).
[CrossRef]

Raftery, J. J.

J. J. Raftery, A. C. Lehman, A. J. Danner, P. O. Leisher, A. V. Giannopoulos, and K. D. Choquette, "In-phase evanescent coupling of two-dimensional arrays of defect cavities in photonic crystal vertical cavity surface emitting lasers," Appl. Phys. Lett. 89, 081119 1-3 (2006).
[CrossRef]

Rinaldi, F.

I. Kardosh, F. Demaria, F. Rinaldi, S. Menzel, and R. Michalzik, "High-Power Single Transverse Mode Vertical-Cavity Surface-Emitting Lasers With Monolithically Integrated Curved Dielectric Mirrors," IEEE Photon. Technol. Lett. 20, 2084-2086 (2008).
[CrossRef]

Rosskopf, J.

R. Shau, M. Ortsiefer, J. Rosskopf, G. Böhm, F. Köhler, and M. C. Amann, "Vertical-cavity surface-emitting laser diodes at 1.55μm with large output power and high operation temperature," Electron. Lett. 37, 1295-1296 (2001).
[CrossRef]

Royo, P.

A. Mircea, A. Caliman, V. Iakovlev, A. Mereuta, G. Suruceanu, C. A. Berseth, P. Royo, A. Syrbu, and E. Kapon, "CavityMode - Gain Peak Tradeoff for 1320 nmWafer-Fused VCSELs with 3mWSingle-Mode Emission Power and 10Gb/s Modulation Speed up to 70◦C," IEEE Photon. Technol. Lett. 19, 121-123 (2007).
[CrossRef]

Rudra, A.

A. Mereuta, A. Syrbu, V. Iakovlev, A. Rudra, A. Caliman, G. Suruceanu, C. A. Berseth, E. Deichsel, and E. Kapon, "1.5μm VCSEL structure optimized for high-power and high-temperatrue operation," J. Crystal Growth 272, 520-525 (2004).
[CrossRef]

Sasaki, S.

A. Furukawa, S. Sasaki, M. Hoshi, A. Matsuzono, K. Moritoh, and T. Baba, "High-power single-mode verticalcavity surface-emitting lasers with triangular holey structure," Appl. Phys. Lett. 85, 5161-5163 (2004).
[CrossRef]

Scherer, A.

H. J. Yoo, A. Scherer, J. P. Harbison, L. T. Florenz, E. G. Paek, B. P. Van der Gaag, J. R. Hayes, A. Von Lehmen, E. Kapon, and Y. S. Kwon, "Fabrication of a two-dimensional phased array of vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 56, 1198-1200 (1990).
[CrossRef]

Shau, R.

R. Shau, M. Ortsiefer, J. Rosskopf, G. Böhm, F. Köhler, and M. C. Amann, "Vertical-cavity surface-emitting laser diodes at 1.55μm with large output power and high operation temperature," Electron. Lett. 37, 1295-1296 (2001).
[CrossRef]

Siriani, D. F.

A. C. Lehman, D. F. Siriani, and K. D. Choquette, "Two-dimensional electronic beam-steering with implantdefined coherent VCSEL arrays," Electron. Lett. 43, 1202-1203 (2007).
[CrossRef]

Stoffel, N. G.

M. Orenstein, E. Kapon, J. P. Harbison, L. T. Florenz, and N. G. Stoffel, "Large two-dimensional arrays of phase-locked vertical cavity surface emitting lasers," Appl. Phys. Lett. 60, 1335-1337 (1992).
[CrossRef]

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florenz, and J. Wullert, "Two-dimensional phaselocked arrays of vertical-cavity semiconductor lasers by mirror reflectivity modulation," Appl. Phys. Lett. 58, 804-806 (1991).
[CrossRef]

Suruceanu, G.

A. Mircea, A. Caliman, V. Iakovlev, A. Mereuta, G. Suruceanu, C. A. Berseth, P. Royo, A. Syrbu, and E. Kapon, "CavityMode - Gain Peak Tradeoff for 1320 nmWafer-Fused VCSELs with 3mWSingle-Mode Emission Power and 10Gb/s Modulation Speed up to 70◦C," IEEE Photon. Technol. Lett. 19, 121-123 (2007).
[CrossRef]

A. Mereuta, A. Syrbu, V. Iakovlev, A. Rudra, A. Caliman, G. Suruceanu, C. A. Berseth, E. Deichsel, and E. Kapon, "1.5μm VCSEL structure optimized for high-power and high-temperatrue operation," J. Crystal Growth 272, 520-525 (2004).
[CrossRef]

Syrbu, A.

A. Syrbu and E. Kapon, "Long-Wavelength VCSELs Power - efficient answer," Nature Photon.,  3, 27-29 (2009).
[CrossRef]

A. Mircea, A. Caliman, V. Iakovlev, A. Mereuta, G. Suruceanu, C. A. Berseth, P. Royo, A. Syrbu, and E. Kapon, "CavityMode - Gain Peak Tradeoff for 1320 nmWafer-Fused VCSELs with 3mWSingle-Mode Emission Power and 10Gb/s Modulation Speed up to 70◦C," IEEE Photon. Technol. Lett. 19, 121-123 (2007).
[CrossRef]

A. Mereuta, A. Syrbu, V. Iakovlev, A. Rudra, A. Caliman, G. Suruceanu, C. A. Berseth, E. Deichsel, and E. Kapon, "1.5μm VCSEL structure optimized for high-power and high-temperatrue operation," J. Crystal Growth 272, 520-525 (2004).
[CrossRef]

Unhold, H. J.

M. Grabherr, M. Miller, R. Jäger, R. Michalzik, U. Martin, H. J. Unhold, and K. J. Ebeling, "High-Power VCSEL’s: Single Devices and Densely Packed 2-D-Arrays," IEEE J. Sel. Top. Quantum Electron. 5, 495-502 (1999).
[CrossRef]

Van der Gaag, B. P.

H. J. Yoo, A. Scherer, J. P. Harbison, L. T. Florenz, E. G. Paek, B. P. Van der Gaag, J. R. Hayes, A. Von Lehmen, E. Kapon, and Y. S. Kwon, "Fabrication of a two-dimensional phased array of vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 56, 1198-1200 (1990).
[CrossRef]

van der Ziel, J. P.

D. G. Deppe, J. P. van der Ziel, N. Chand, G. J. Zydzik, and S. N. G. Chu, "Phase-coupled two-dimensional AlxGa1−xAs-GaAs vertical-cavity surface-emitting laser array," Appl. Phys. Lett. 56, 2089-2091 (1990).
[CrossRef]

Von Lehmen, A.

H. J. Yoo, A. Scherer, J. P. Harbison, L. T. Florenz, E. G. Paek, B. P. Van der Gaag, J. R. Hayes, A. Von Lehmen, E. Kapon, and Y. S. Kwon, "Fabrication of a two-dimensional phased array of vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 56, 1198-1200 (1990).
[CrossRef]

Wiemer, M. W.

M. W. Wiemer, R. I. Aldaz, D. A. B. Miller, and J. S. Harris, "A Single Transverse-Mode Monolithically Integrated Long Vertical-Cavity Surface-Emitting Laser," IEEE Photon. Technol. Lett. 17, 1366-1368 (2005).
[CrossRef]

Wullert, J.

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florenz, and J. Wullert, "Two-dimensional phaselocked arrays of vertical-cavity semiconductor lasers by mirror reflectivity modulation," Appl. Phys. Lett. 58, 804-806 (1991).
[CrossRef]

Yoo, H. J.

H. J. Yoo, A. Scherer, J. P. Harbison, L. T. Florenz, E. G. Paek, B. P. Van der Gaag, J. R. Hayes, A. Von Lehmen, E. Kapon, and Y. S. Kwon, "Fabrication of a two-dimensional phased array of vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 56, 1198-1200 (1990).
[CrossRef]

Zydzik, G. J.

D. G. Deppe, J. P. van der Ziel, N. Chand, G. J. Zydzik, and S. N. G. Chu, "Phase-coupled two-dimensional AlxGa1−xAs-GaAs vertical-cavity surface-emitting laser array," Appl. Phys. Lett. 56, 2089-2091 (1990).
[CrossRef]

Appl. Phys. Lett. (6)

A. Furukawa, S. Sasaki, M. Hoshi, A. Matsuzono, K. Moritoh, and T. Baba, "High-power single-mode verticalcavity surface-emitting lasers with triangular holey structure," Appl. Phys. Lett. 85, 5161-5163 (2004).
[CrossRef]

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florenz, and J. Wullert, "Two-dimensional phaselocked arrays of vertical-cavity semiconductor lasers by mirror reflectivity modulation," Appl. Phys. Lett. 58, 804-806 (1991).
[CrossRef]

M. Orenstein, E. Kapon, J. P. Harbison, L. T. Florenz, and N. G. Stoffel, "Large two-dimensional arrays of phase-locked vertical cavity surface emitting lasers," Appl. Phys. Lett. 60, 1335-1337 (1992).
[CrossRef]

H. J. Yoo, A. Scherer, J. P. Harbison, L. T. Florenz, E. G. Paek, B. P. Van der Gaag, J. R. Hayes, A. Von Lehmen, E. Kapon, and Y. S. Kwon, "Fabrication of a two-dimensional phased array of vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 56, 1198-1200 (1990).
[CrossRef]

J. J. Raftery, A. C. Lehman, A. J. Danner, P. O. Leisher, A. V. Giannopoulos, and K. D. Choquette, "In-phase evanescent coupling of two-dimensional arrays of defect cavities in photonic crystal vertical cavity surface emitting lasers," Appl. Phys. Lett. 89, 081119 1-3 (2006).
[CrossRef]

D. G. Deppe, J. P. van der Ziel, N. Chand, G. J. Zydzik, and S. N. G. Chu, "Phase-coupled two-dimensional AlxGa1−xAs-GaAs vertical-cavity surface-emitting laser array," Appl. Phys. Lett. 56, 2089-2091 (1990).
[CrossRef]

Electron. Lett. (3)

R. Shau, M. Ortsiefer, J. Rosskopf, G. Böhm, F. Köhler, and M. C. Amann, "Vertical-cavity surface-emitting laser diodes at 1.55μm with large output power and high operation temperature," Electron. Lett. 37, 1295-1296 (2001).
[CrossRef]

A. C. Lehman, D. F. Siriani, and K. D. Choquette, "Two-dimensional electronic beam-steering with implantdefined coherent VCSEL arrays," Electron. Lett. 43, 1202-1203 (2007).
[CrossRef]

M. Arzberger, M. Lohner, G. Böhm, and M. C. Amann, "Low-resistivity p-side contacts for InP-based devices using buried InGaAs tunnel junction," Electron. Lett. 36, 87-88 (2000).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

M. Grabherr, M. Miller, R. Jäger, R. Michalzik, U. Martin, H. J. Unhold, and K. J. Ebeling, "High-Power VCSEL’s: Single Devices and Densely Packed 2-D-Arrays," IEEE J. Sel. Top. Quantum Electron. 5, 495-502 (1999).
[CrossRef]

IEEE Photon. Technol. Lett. (4)

A.C. Lehman and K. D. Choquette, "One- and Two- Dimensional Coherently Coupled Implant-Defined Vertical-Cavity Laser Arrays," IEEE Photon. Technol. Lett. 19, 1421-1423 (2007).
[CrossRef]

M. W. Wiemer, R. I. Aldaz, D. A. B. Miller, and J. S. Harris, "A Single Transverse-Mode Monolithically Integrated Long Vertical-Cavity Surface-Emitting Laser," IEEE Photon. Technol. Lett. 17, 1366-1368 (2005).
[CrossRef]

A. Mircea, A. Caliman, V. Iakovlev, A. Mereuta, G. Suruceanu, C. A. Berseth, P. Royo, A. Syrbu, and E. Kapon, "CavityMode - Gain Peak Tradeoff for 1320 nmWafer-Fused VCSELs with 3mWSingle-Mode Emission Power and 10Gb/s Modulation Speed up to 70◦C," IEEE Photon. Technol. Lett. 19, 121-123 (2007).
[CrossRef]

I. Kardosh, F. Demaria, F. Rinaldi, S. Menzel, and R. Michalzik, "High-Power Single Transverse Mode Vertical-Cavity Surface-Emitting Lasers With Monolithically Integrated Curved Dielectric Mirrors," IEEE Photon. Technol. Lett. 20, 2084-2086 (2008).
[CrossRef]

J. Crystal Growth (1)

A. Mereuta, A. Syrbu, V. Iakovlev, A. Rudra, A. Caliman, G. Suruceanu, C. A. Berseth, E. Deichsel, and E. Kapon, "1.5μm VCSEL structure optimized for high-power and high-temperatrue operation," J. Crystal Growth 272, 520-525 (2004).
[CrossRef]

Nature Photon. (1)

A. Syrbu and E. Kapon, "Long-Wavelength VCSELs Power - efficient answer," Nature Photon.,  3, 27-29 (2009).
[CrossRef]

Opt. Eng. (1)

M. Achtenhagen, A. Hardy, and E. Kapon, "Mode discrimination in vertical-cavity surface-emitting lasers including Bragg reflectors and limiting apertures," Opt. Eng. 44, 104202 1-6 (2005).
[CrossRef]

Other (2)

L. D. A. Lundeberg and E. Kapon, "Mode switching and beam steering in photonic crystal heterostructures implemented with vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 90, 241115 1-3 (2007).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, Engelwood, Colorado, Third Edition, 2005).

Cited By

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Figures (6)

Fig. 1.
Fig. 1.

(a) Cross section through the VCSEL array structure. The carriers are locally injected through the tunnel junction apertures. (b) Top view of a 2×4 VCSEL array. For the devices discussed here, Λ = 8 μm and d = 6 μm.

Fig. 2.
Fig. 2.

Light-current-voltage characteristics of (a) single VCSEL, (b) 1×4 array, (c) 1×8 array and (d) 2×4 array structure under continuous wave operation at 20°C. All devices emit near 1320 nm wavelength.

Fig. 3.
Fig. 3.

Average optical output power per pixel as a function of the average pumping current per array element for the devices of Fig. 2: single VCSEL (dotted curve), linear 1×4 array (dashed), 1×8 array (fine dashed), and 2×4 array (solid curve).

Fig. 4.
Fig. 4.

Near fields (left column), far fields (middle column), and emission spectra (right column) of a linear 1×4 array (Ith ≈ 5.5 mA), and of a single VCSEL (Ith ≈ 2mA) with the same tunnel junction aperture diameter (top row), measured at different diode currents using a variable attenuator in order to use the full sensitivity range of the camera. The bottom row shows the calculated far field pattern obtained using the measured near field intensity distributions close to the lasing threshold, i.e., at 5.5 mA and assuming out-of-phase electric fields in neighbouring pixels.

Fig. 5.
Fig. 5.

Near fields (left column), far fields (middle column), and emission spectra (right column) of a 1×8 VCSEL array (Ith ≈ 11mA). The bottom row shows the calculated far field pattern obtained using the measured near field intensity distributions close to the lasing threshold.

Fig. 6.
Fig. 6.

Near fields (left column), far fields (middle column), and spectra (right column) of a 2×4 VCSEL array (Ith ≈ 8mA). The bottom row shows the calculated far field pattern obtained using the measured near field intensity distributions close to the lasing threshold.

Equations (1)

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FF(θx,θy)=ejkzejk2z(x2+y2)jλz NF(η,ν)ej2πλ(sinθxη+sinθyν)dηdν

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