Abstract

This is a continuation of our previous work [Opt. Express 16, 9155 (2008)]. In this paper we investigate the effect of nonuniform pumping on the modal properties of surface-emitting chirped circular grating lasers. By numerically solving the coupled-mode equations and matching the boundaries we compare and discuss the threshold pump levels and frequency detuning factors for three pumping profiles: uniform, Gaussian, and annular. Depending on the overlap of the pumping and modal profiles, Gaussian pumping results in the lowest threshold pump levels except for the fundamental mode of ring Bragg resonator laser, and annular pumping provides larger threshold discrimination between the fundamental and first-order modes of circular DFB and ring Bragg resonator lasers, which is favorable for single-mode operation in these lasers. We also study the far-field patterns of the fundamental modes of circular DFB, disk-, and ring-Bragg resonator lasers. Circular DFB and ring Bragg resonator lasers have the first-order dominating peak, while disk Bragg resonator laser exhibits the zeroth-order dominating peak.

© 2009 Optical Society of America

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  1. J. Scheuer and A. Yariv, "Coupled-Waves Approach to the Design and Analysis of Bragg and Photonic Crystal Annular Resonators," IEEE J. Quantum Electron. 39, 1555-1562 (2003).
    [CrossRef]
  2. J. Scheuer and A. Yariv, "Annular Bragg defect mode resonators," J. Opt. Soc. Am. B 20, 2285-2291 (2003).
    [CrossRef]
  3. X. K. Sun and A. Yariv, "Surface-emitting circular DFB, disk-, and ring- Bragg resonator lasers with chirped gratings: a unified theory and comparative study," Opt. Express 16, 9155-9164 (2008).
    [CrossRef] [PubMed]
  4. C. Olson, P. L. Greene, G. W. Wicks, D. G. Hall, and S. Rishton, "High-order azimuthal spatial modes of concentric-circle-grating surface-emitting semiconductor lasers," Appl. Phys. Lett. 72, 1284-1286 (1998).
    [CrossRef]
  5. J. Scheuer, W. M. J. Green, G. A. DeRose, and A. Yariv, "InGaAsP Annular Bragg Lasers: Theory, Applications, and Modal Properties," IEEE J. Sel. Top. Quantum Electron. 11, 476-484 (2005).
    [CrossRef]
  6. C. Wu, T. Makino, M. Fallahi, R. G. A. Craig, G. Knight, I. Templeton, and C. Blaauw, "Novel Circular Grating Surface-Emitting Lasers with Emission from Center," Jpn. J. Appl. Phys.  33-Pt. 2, L427-L429 (1994).
    [CrossRef]
  7. K. J. Kasunic, E. M. Wright, and N. Peyghambarian, "Numerical modeling of inhomogeneously-pumped circular-grating DFB lasers," Proc. SPIE 2398, 125-134 (1995).
    [CrossRef]
  8. P. L. Greene and D. G. Hall, "Effects of Radiation on Circular-Grating DFB Lasers—Part II: Device and Pump-Beam Parameters," IEEE J. Quantum Electron. 37, 364-371 (2001).
    [CrossRef]
  9. G. A. Turnbull, A. Carleton, A. Tahraouhi, T. F. Krauss, I. D. W. Samuel, G. F. Barlow, and K. A. Shore, "Effect of gain localization in circular-grating distributed feedback lasers," Appl. Phys. Lett. 87, 201101 (2005).
    [CrossRef]
  10. A. M. Shams-Zadeh-Amiri, X. Li, and W.-P. Huang, "Above-Threshold Analysis of Second-Order Circular-Grating DFB Lasers," IEEE J. Quantum Electron. 36, 259-267 (2000).
    [CrossRef]
  11. G. F. Barlow, A. Shore, G. A. Turnbull, and I. D. W. Samuel, "Design and analysis of a low-threshold polymer circular-grating distributed-feedback laser," J. Opt. Soc. Am. B 21, 2142-2150 (2004).
    [CrossRef]
  12. X. K. Sun, J. Scheuer, and A. Yariv, "Optimal design and reduced threshold in vertically emitting circular Bragg disk resonator lasers," IEEE J. Sel. Top. Quantum Electron. 13, 359-366 (2007).
    [CrossRef]
  13. X. K. Sun and A. Yariv, "Modal properties and modal control in vertically emitting annular Bragg lasers," Opt. Express 15, 17323-17333 (2007).
    [CrossRef] [PubMed]
  14. A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989).
  15. E. Hecht, Optics, 3rd ed. (Addison-Wesley, 1998).
  16. R. H. Jordan, D. G. Hall, O. King, G. Wicks, and S. Rishton, "Lasing behavior of circular grating surface-emitting semiconductor lasers," J. Opt. Soc. Am. B 14, 449-453 (1997).
    [CrossRef]
  17. 17. M. Fallahi, M. Dion, F. Chatenoud, I. M. Templeton, R. Barber, and J. Sedivy, "Low Threshold CW Operation of Circular-Grating Surface-Emitting DBR Lasers Using MQW and a Self-Aligned Process," IEEE Photon. Technol. Lett. 6, 1280-1282 (1994).
    [CrossRef]

2008 (1)

2007 (2)

X. K. Sun, J. Scheuer, and A. Yariv, "Optimal design and reduced threshold in vertically emitting circular Bragg disk resonator lasers," IEEE J. Sel. Top. Quantum Electron. 13, 359-366 (2007).
[CrossRef]

X. K. Sun and A. Yariv, "Modal properties and modal control in vertically emitting annular Bragg lasers," Opt. Express 15, 17323-17333 (2007).
[CrossRef] [PubMed]

2005 (2)

G. A. Turnbull, A. Carleton, A. Tahraouhi, T. F. Krauss, I. D. W. Samuel, G. F. Barlow, and K. A. Shore, "Effect of gain localization in circular-grating distributed feedback lasers," Appl. Phys. Lett. 87, 201101 (2005).
[CrossRef]

J. Scheuer, W. M. J. Green, G. A. DeRose, and A. Yariv, "InGaAsP Annular Bragg Lasers: Theory, Applications, and Modal Properties," IEEE J. Sel. Top. Quantum Electron. 11, 476-484 (2005).
[CrossRef]

2004 (1)

2003 (2)

J. Scheuer and A. Yariv, "Coupled-Waves Approach to the Design and Analysis of Bragg and Photonic Crystal Annular Resonators," IEEE J. Quantum Electron. 39, 1555-1562 (2003).
[CrossRef]

J. Scheuer and A. Yariv, "Annular Bragg defect mode resonators," J. Opt. Soc. Am. B 20, 2285-2291 (2003).
[CrossRef]

2001 (1)

P. L. Greene and D. G. Hall, "Effects of Radiation on Circular-Grating DFB Lasers—Part II: Device and Pump-Beam Parameters," IEEE J. Quantum Electron. 37, 364-371 (2001).
[CrossRef]

2000 (1)

A. M. Shams-Zadeh-Amiri, X. Li, and W.-P. Huang, "Above-Threshold Analysis of Second-Order Circular-Grating DFB Lasers," IEEE J. Quantum Electron. 36, 259-267 (2000).
[CrossRef]

1998 (1)

C. Olson, P. L. Greene, G. W. Wicks, D. G. Hall, and S. Rishton, "High-order azimuthal spatial modes of concentric-circle-grating surface-emitting semiconductor lasers," Appl. Phys. Lett. 72, 1284-1286 (1998).
[CrossRef]

1997 (1)

1995 (1)

K. J. Kasunic, E. M. Wright, and N. Peyghambarian, "Numerical modeling of inhomogeneously-pumped circular-grating DFB lasers," Proc. SPIE 2398, 125-134 (1995).
[CrossRef]

1994 (2)

C. Wu, T. Makino, M. Fallahi, R. G. A. Craig, G. Knight, I. Templeton, and C. Blaauw, "Novel Circular Grating Surface-Emitting Lasers with Emission from Center," Jpn. J. Appl. Phys.  33-Pt. 2, L427-L429 (1994).
[CrossRef]

17. M. Fallahi, M. Dion, F. Chatenoud, I. M. Templeton, R. Barber, and J. Sedivy, "Low Threshold CW Operation of Circular-Grating Surface-Emitting DBR Lasers Using MQW and a Self-Aligned Process," IEEE Photon. Technol. Lett. 6, 1280-1282 (1994).
[CrossRef]

Barber, R.

17. M. Fallahi, M. Dion, F. Chatenoud, I. M. Templeton, R. Barber, and J. Sedivy, "Low Threshold CW Operation of Circular-Grating Surface-Emitting DBR Lasers Using MQW and a Self-Aligned Process," IEEE Photon. Technol. Lett. 6, 1280-1282 (1994).
[CrossRef]

Barlow, G. F.

G. A. Turnbull, A. Carleton, A. Tahraouhi, T. F. Krauss, I. D. W. Samuel, G. F. Barlow, and K. A. Shore, "Effect of gain localization in circular-grating distributed feedback lasers," Appl. Phys. Lett. 87, 201101 (2005).
[CrossRef]

G. F. Barlow, A. Shore, G. A. Turnbull, and I. D. W. Samuel, "Design and analysis of a low-threshold polymer circular-grating distributed-feedback laser," J. Opt. Soc. Am. B 21, 2142-2150 (2004).
[CrossRef]

Blaauw, C.

C. Wu, T. Makino, M. Fallahi, R. G. A. Craig, G. Knight, I. Templeton, and C. Blaauw, "Novel Circular Grating Surface-Emitting Lasers with Emission from Center," Jpn. J. Appl. Phys.  33-Pt. 2, L427-L429 (1994).
[CrossRef]

Carleton, A.

G. A. Turnbull, A. Carleton, A. Tahraouhi, T. F. Krauss, I. D. W. Samuel, G. F. Barlow, and K. A. Shore, "Effect of gain localization in circular-grating distributed feedback lasers," Appl. Phys. Lett. 87, 201101 (2005).
[CrossRef]

Chatenoud, F.

17. M. Fallahi, M. Dion, F. Chatenoud, I. M. Templeton, R. Barber, and J. Sedivy, "Low Threshold CW Operation of Circular-Grating Surface-Emitting DBR Lasers Using MQW and a Self-Aligned Process," IEEE Photon. Technol. Lett. 6, 1280-1282 (1994).
[CrossRef]

Craig, R. G. A.

C. Wu, T. Makino, M. Fallahi, R. G. A. Craig, G. Knight, I. Templeton, and C. Blaauw, "Novel Circular Grating Surface-Emitting Lasers with Emission from Center," Jpn. J. Appl. Phys.  33-Pt. 2, L427-L429 (1994).
[CrossRef]

DeRose, G. A.

J. Scheuer, W. M. J. Green, G. A. DeRose, and A. Yariv, "InGaAsP Annular Bragg Lasers: Theory, Applications, and Modal Properties," IEEE J. Sel. Top. Quantum Electron. 11, 476-484 (2005).
[CrossRef]

Dion, M.

17. M. Fallahi, M. Dion, F. Chatenoud, I. M. Templeton, R. Barber, and J. Sedivy, "Low Threshold CW Operation of Circular-Grating Surface-Emitting DBR Lasers Using MQW and a Self-Aligned Process," IEEE Photon. Technol. Lett. 6, 1280-1282 (1994).
[CrossRef]

Fallahi, M.

17. M. Fallahi, M. Dion, F. Chatenoud, I. M. Templeton, R. Barber, and J. Sedivy, "Low Threshold CW Operation of Circular-Grating Surface-Emitting DBR Lasers Using MQW and a Self-Aligned Process," IEEE Photon. Technol. Lett. 6, 1280-1282 (1994).
[CrossRef]

C. Wu, T. Makino, M. Fallahi, R. G. A. Craig, G. Knight, I. Templeton, and C. Blaauw, "Novel Circular Grating Surface-Emitting Lasers with Emission from Center," Jpn. J. Appl. Phys.  33-Pt. 2, L427-L429 (1994).
[CrossRef]

Green, W. M. J.

J. Scheuer, W. M. J. Green, G. A. DeRose, and A. Yariv, "InGaAsP Annular Bragg Lasers: Theory, Applications, and Modal Properties," IEEE J. Sel. Top. Quantum Electron. 11, 476-484 (2005).
[CrossRef]

Greene, P. L.

P. L. Greene and D. G. Hall, "Effects of Radiation on Circular-Grating DFB Lasers—Part II: Device and Pump-Beam Parameters," IEEE J. Quantum Electron. 37, 364-371 (2001).
[CrossRef]

C. Olson, P. L. Greene, G. W. Wicks, D. G. Hall, and S. Rishton, "High-order azimuthal spatial modes of concentric-circle-grating surface-emitting semiconductor lasers," Appl. Phys. Lett. 72, 1284-1286 (1998).
[CrossRef]

Hall, D. G.

P. L. Greene and D. G. Hall, "Effects of Radiation on Circular-Grating DFB Lasers—Part II: Device and Pump-Beam Parameters," IEEE J. Quantum Electron. 37, 364-371 (2001).
[CrossRef]

C. Olson, P. L. Greene, G. W. Wicks, D. G. Hall, and S. Rishton, "High-order azimuthal spatial modes of concentric-circle-grating surface-emitting semiconductor lasers," Appl. Phys. Lett. 72, 1284-1286 (1998).
[CrossRef]

R. H. Jordan, D. G. Hall, O. King, G. Wicks, and S. Rishton, "Lasing behavior of circular grating surface-emitting semiconductor lasers," J. Opt. Soc. Am. B 14, 449-453 (1997).
[CrossRef]

Huang, W.-P.

A. M. Shams-Zadeh-Amiri, X. Li, and W.-P. Huang, "Above-Threshold Analysis of Second-Order Circular-Grating DFB Lasers," IEEE J. Quantum Electron. 36, 259-267 (2000).
[CrossRef]

Jordan, R. H.

Kasunic, K. J.

K. J. Kasunic, E. M. Wright, and N. Peyghambarian, "Numerical modeling of inhomogeneously-pumped circular-grating DFB lasers," Proc. SPIE 2398, 125-134 (1995).
[CrossRef]

King, O.

Knight, G.

C. Wu, T. Makino, M. Fallahi, R. G. A. Craig, G. Knight, I. Templeton, and C. Blaauw, "Novel Circular Grating Surface-Emitting Lasers with Emission from Center," Jpn. J. Appl. Phys.  33-Pt. 2, L427-L429 (1994).
[CrossRef]

Krauss, T. F.

G. A. Turnbull, A. Carleton, A. Tahraouhi, T. F. Krauss, I. D. W. Samuel, G. F. Barlow, and K. A. Shore, "Effect of gain localization in circular-grating distributed feedback lasers," Appl. Phys. Lett. 87, 201101 (2005).
[CrossRef]

Li, X.

A. M. Shams-Zadeh-Amiri, X. Li, and W.-P. Huang, "Above-Threshold Analysis of Second-Order Circular-Grating DFB Lasers," IEEE J. Quantum Electron. 36, 259-267 (2000).
[CrossRef]

Makino, T.

C. Wu, T. Makino, M. Fallahi, R. G. A. Craig, G. Knight, I. Templeton, and C. Blaauw, "Novel Circular Grating Surface-Emitting Lasers with Emission from Center," Jpn. J. Appl. Phys.  33-Pt. 2, L427-L429 (1994).
[CrossRef]

Olson, C.

C. Olson, P. L. Greene, G. W. Wicks, D. G. Hall, and S. Rishton, "High-order azimuthal spatial modes of concentric-circle-grating surface-emitting semiconductor lasers," Appl. Phys. Lett. 72, 1284-1286 (1998).
[CrossRef]

Peyghambarian, N.

K. J. Kasunic, E. M. Wright, and N. Peyghambarian, "Numerical modeling of inhomogeneously-pumped circular-grating DFB lasers," Proc. SPIE 2398, 125-134 (1995).
[CrossRef]

Rishton, S.

C. Olson, P. L. Greene, G. W. Wicks, D. G. Hall, and S. Rishton, "High-order azimuthal spatial modes of concentric-circle-grating surface-emitting semiconductor lasers," Appl. Phys. Lett. 72, 1284-1286 (1998).
[CrossRef]

R. H. Jordan, D. G. Hall, O. King, G. Wicks, and S. Rishton, "Lasing behavior of circular grating surface-emitting semiconductor lasers," J. Opt. Soc. Am. B 14, 449-453 (1997).
[CrossRef]

Samuel, I. D. W.

G. A. Turnbull, A. Carleton, A. Tahraouhi, T. F. Krauss, I. D. W. Samuel, G. F. Barlow, and K. A. Shore, "Effect of gain localization in circular-grating distributed feedback lasers," Appl. Phys. Lett. 87, 201101 (2005).
[CrossRef]

G. F. Barlow, A. Shore, G. A. Turnbull, and I. D. W. Samuel, "Design and analysis of a low-threshold polymer circular-grating distributed-feedback laser," J. Opt. Soc. Am. B 21, 2142-2150 (2004).
[CrossRef]

Scheuer, J.

X. K. Sun, J. Scheuer, and A. Yariv, "Optimal design and reduced threshold in vertically emitting circular Bragg disk resonator lasers," IEEE J. Sel. Top. Quantum Electron. 13, 359-366 (2007).
[CrossRef]

J. Scheuer, W. M. J. Green, G. A. DeRose, and A. Yariv, "InGaAsP Annular Bragg Lasers: Theory, Applications, and Modal Properties," IEEE J. Sel. Top. Quantum Electron. 11, 476-484 (2005).
[CrossRef]

J. Scheuer and A. Yariv, "Coupled-Waves Approach to the Design and Analysis of Bragg and Photonic Crystal Annular Resonators," IEEE J. Quantum Electron. 39, 1555-1562 (2003).
[CrossRef]

J. Scheuer and A. Yariv, "Annular Bragg defect mode resonators," J. Opt. Soc. Am. B 20, 2285-2291 (2003).
[CrossRef]

Sedivy, J.

17. M. Fallahi, M. Dion, F. Chatenoud, I. M. Templeton, R. Barber, and J. Sedivy, "Low Threshold CW Operation of Circular-Grating Surface-Emitting DBR Lasers Using MQW and a Self-Aligned Process," IEEE Photon. Technol. Lett. 6, 1280-1282 (1994).
[CrossRef]

Shams-Zadeh-Amiri, A. M.

A. M. Shams-Zadeh-Amiri, X. Li, and W.-P. Huang, "Above-Threshold Analysis of Second-Order Circular-Grating DFB Lasers," IEEE J. Quantum Electron. 36, 259-267 (2000).
[CrossRef]

Shore, A.

Shore, K. A.

G. A. Turnbull, A. Carleton, A. Tahraouhi, T. F. Krauss, I. D. W. Samuel, G. F. Barlow, and K. A. Shore, "Effect of gain localization in circular-grating distributed feedback lasers," Appl. Phys. Lett. 87, 201101 (2005).
[CrossRef]

Sun, X. K.

Tahraouhi, A.

G. A. Turnbull, A. Carleton, A. Tahraouhi, T. F. Krauss, I. D. W. Samuel, G. F. Barlow, and K. A. Shore, "Effect of gain localization in circular-grating distributed feedback lasers," Appl. Phys. Lett. 87, 201101 (2005).
[CrossRef]

Templeton, I.

C. Wu, T. Makino, M. Fallahi, R. G. A. Craig, G. Knight, I. Templeton, and C. Blaauw, "Novel Circular Grating Surface-Emitting Lasers with Emission from Center," Jpn. J. Appl. Phys.  33-Pt. 2, L427-L429 (1994).
[CrossRef]

Templeton, I. M.

17. M. Fallahi, M. Dion, F. Chatenoud, I. M. Templeton, R. Barber, and J. Sedivy, "Low Threshold CW Operation of Circular-Grating Surface-Emitting DBR Lasers Using MQW and a Self-Aligned Process," IEEE Photon. Technol. Lett. 6, 1280-1282 (1994).
[CrossRef]

Turnbull, G. A.

G. A. Turnbull, A. Carleton, A. Tahraouhi, T. F. Krauss, I. D. W. Samuel, G. F. Barlow, and K. A. Shore, "Effect of gain localization in circular-grating distributed feedback lasers," Appl. Phys. Lett. 87, 201101 (2005).
[CrossRef]

G. F. Barlow, A. Shore, G. A. Turnbull, and I. D. W. Samuel, "Design and analysis of a low-threshold polymer circular-grating distributed-feedback laser," J. Opt. Soc. Am. B 21, 2142-2150 (2004).
[CrossRef]

Wicks, G.

Wicks, G. W.

C. Olson, P. L. Greene, G. W. Wicks, D. G. Hall, and S. Rishton, "High-order azimuthal spatial modes of concentric-circle-grating surface-emitting semiconductor lasers," Appl. Phys. Lett. 72, 1284-1286 (1998).
[CrossRef]

Wright, E. M.

K. J. Kasunic, E. M. Wright, and N. Peyghambarian, "Numerical modeling of inhomogeneously-pumped circular-grating DFB lasers," Proc. SPIE 2398, 125-134 (1995).
[CrossRef]

Wu, C.

C. Wu, T. Makino, M. Fallahi, R. G. A. Craig, G. Knight, I. Templeton, and C. Blaauw, "Novel Circular Grating Surface-Emitting Lasers with Emission from Center," Jpn. J. Appl. Phys.  33-Pt. 2, L427-L429 (1994).
[CrossRef]

Yariv, A.

X. K. Sun and A. Yariv, "Surface-emitting circular DFB, disk-, and ring- Bragg resonator lasers with chirped gratings: a unified theory and comparative study," Opt. Express 16, 9155-9164 (2008).
[CrossRef] [PubMed]

X. K. Sun and A. Yariv, "Modal properties and modal control in vertically emitting annular Bragg lasers," Opt. Express 15, 17323-17333 (2007).
[CrossRef] [PubMed]

X. K. Sun, J. Scheuer, and A. Yariv, "Optimal design and reduced threshold in vertically emitting circular Bragg disk resonator lasers," IEEE J. Sel. Top. Quantum Electron. 13, 359-366 (2007).
[CrossRef]

J. Scheuer, W. M. J. Green, G. A. DeRose, and A. Yariv, "InGaAsP Annular Bragg Lasers: Theory, Applications, and Modal Properties," IEEE J. Sel. Top. Quantum Electron. 11, 476-484 (2005).
[CrossRef]

J. Scheuer and A. Yariv, "Annular Bragg defect mode resonators," J. Opt. Soc. Am. B 20, 2285-2291 (2003).
[CrossRef]

J. Scheuer and A. Yariv, "Coupled-Waves Approach to the Design and Analysis of Bragg and Photonic Crystal Annular Resonators," IEEE J. Quantum Electron. 39, 1555-1562 (2003).
[CrossRef]

Appl. Phys. Lett. (2)

C. Olson, P. L. Greene, G. W. Wicks, D. G. Hall, and S. Rishton, "High-order azimuthal spatial modes of concentric-circle-grating surface-emitting semiconductor lasers," Appl. Phys. Lett. 72, 1284-1286 (1998).
[CrossRef]

G. A. Turnbull, A. Carleton, A. Tahraouhi, T. F. Krauss, I. D. W. Samuel, G. F. Barlow, and K. A. Shore, "Effect of gain localization in circular-grating distributed feedback lasers," Appl. Phys. Lett. 87, 201101 (2005).
[CrossRef]

IEEE J. Quantum Electron. (3)

A. M. Shams-Zadeh-Amiri, X. Li, and W.-P. Huang, "Above-Threshold Analysis of Second-Order Circular-Grating DFB Lasers," IEEE J. Quantum Electron. 36, 259-267 (2000).
[CrossRef]

J. Scheuer and A. Yariv, "Coupled-Waves Approach to the Design and Analysis of Bragg and Photonic Crystal Annular Resonators," IEEE J. Quantum Electron. 39, 1555-1562 (2003).
[CrossRef]

P. L. Greene and D. G. Hall, "Effects of Radiation on Circular-Grating DFB Lasers—Part II: Device and Pump-Beam Parameters," IEEE J. Quantum Electron. 37, 364-371 (2001).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

X. K. Sun, J. Scheuer, and A. Yariv, "Optimal design and reduced threshold in vertically emitting circular Bragg disk resonator lasers," IEEE J. Sel. Top. Quantum Electron. 13, 359-366 (2007).
[CrossRef]

J. Scheuer, W. M. J. Green, G. A. DeRose, and A. Yariv, "InGaAsP Annular Bragg Lasers: Theory, Applications, and Modal Properties," IEEE J. Sel. Top. Quantum Electron. 11, 476-484 (2005).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

17. M. Fallahi, M. Dion, F. Chatenoud, I. M. Templeton, R. Barber, and J. Sedivy, "Low Threshold CW Operation of Circular-Grating Surface-Emitting DBR Lasers Using MQW and a Self-Aligned Process," IEEE Photon. Technol. Lett. 6, 1280-1282 (1994).
[CrossRef]

J. Opt. Soc. Am. B (3)

Jpn. J. Appl. Phys. (1)

C. Wu, T. Makino, M. Fallahi, R. G. A. Craig, G. Knight, I. Templeton, and C. Blaauw, "Novel Circular Grating Surface-Emitting Lasers with Emission from Center," Jpn. J. Appl. Phys.  33-Pt. 2, L427-L429 (1994).
[CrossRef]

Opt. Express (2)

Proc. SPIE (1)

K. J. Kasunic, E. M. Wright, and N. Peyghambarian, "Numerical modeling of inhomogeneously-pumped circular-grating DFB lasers," Proc. SPIE 2398, 125-134 (1995).
[CrossRef]

Other (2)

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989).

E. Hecht, Optics, 3rd ed. (Addison-Wesley, 1998).

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Figures (4)

Fig. 1.
Fig. 1.

Surface-emitting chirped circular grating lasers: (a) Circular DFB laser; (b) Disk Bragg resonator laser; (c) Ring Bragg resonator laser. Laser radiation is coupled out of the resonators in vertical direction via the gratings.

Fig. 2.
Fig. 2.

Illustration of different gain distribution profiles: (a) uniform; (b) Gaussian; (c) annular.

Fig. 3.
Fig. 3.

Threshold pump level Pth and detuning factor δ of circular DFB, disk-, and ring- Bragg resonator lasers under uniform, Gaussian and annular pumping profiles.

Fig. 4.
Fig. 4.

Far-field intensity patterns of the fundamental modes of circular DFB, disk-, and ring-Bragg resonator lasers.

Equations (3)

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{dA(x)dx=u(x)A(x)vB(x)e2iδxdB(x)dx=u(x)B(x)+vA(x)e2iδx.
U(r)apertureΔEρψexp(ikrr)4πrrdreikr4πrapertureΔEρψexp(ik(rr̂))dr
=eikr4πr ψ=02πρ=0ρbΔE(ρ)exp[ikρsinθcos(ψϕ)]ρdρdψ=eikr2r 0ρbΔE (ρ) J0 (kρsinθ) ρ d ρ

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