Abstract

Radial Bragg distributed-feedback (DFB) lasers are designed and studied using the transfer matrix method, allowing an accurate analysis beyond the coupled-mode equations approach (small perturbations). Compared with conventional circular grating DFB lasers, incorporating periodic gratings, lower threshold levels, and enhanced mode discrimination are achieved by employing an optimal design strategy for the radial Bragg reflector.

© 2007 Optical Society of America

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  1. C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley, 1999).
  2. B. E. Little, "Second-order filtering and sensing with partially coupled traveling waves in a single resonator," Opt. Lett. 23, 1570-1572 (1998).
  3. C. Y. Chao and L. J. Guo, "Biochemical sensors based on polymer microrings with sharp asymmetrical resonance," Appl. Phys. Lett. 83, 1527-1529 (2003).
    [CrossRef]
  4. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
    [CrossRef]
  5. T. Yoshie, O. B. Shchekin, H. Chen, D. G. Deppe, and A. Scherer, "Planar photonic crystal nanolasers (II): low-threshold quantum dot lasers," IEICE Trans. Electron. E87-C, 300-307 (2004).
  6. Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature (London) 425, 944-947 (2003).
    [CrossRef]
  7. M. Notomi, A. Shinya, S. Mitsugi, E. Kuramochi, and H. Y. Ryu, "Waveguides, resonators and their coupled elements in photonic crystal slabs," Opt. Express 12, 1551-1561 (2004).
    [CrossRef]
  8. M. Loncar, M. Hochberg, and A. Scherer, "High quality factors and room-temperature lasing in a modified single-defect photonic crystal cavity," Opt. Lett. 29, 721-723 (2004).
    [CrossRef]
  9. H. Altug and J. Vuckovic, "Experimental demonstration of the slow group velocity of light in two-dimensional coupled photonic crystal microcavity arrays," Appl. Phys. Lett. 86, 111102 (2005).
    [CrossRef]
  10. K. Nozaki, T. Ide, J. Hashimoto, T. Baba, and W.-H. Zheng, "Photonic crystal point-shift nanolaser with ultimate small modal volume," Electron. Lett. 41, 843-845 (2005).
  11. J. Scheuer, W. M. J. Green, G. DeRose, and A. Yariv, "Lasing from a circular Bragg nanocavity with an ultra-small modal volume," Appl. Phys. Lett. 86, 251101 (2005).
    [CrossRef]
  12. Y. Fink, J. N. Winn, F. Shanhui, C. Chiping, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
    [CrossRef]
  13. S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, "Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers," Opt. Express 9, 748-779 (2001).
  14. 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]
  15. J. Scheuer and A. Yariv, "Annular Bragg defect mode resonators," J. Opt. Soc. Am. B 20, 2285-2291 (2003).
  16. J. Scheuer, W. M. J. Green, G. DeRose, and A. Yariv, "Low-threshold two-dimensional annular Bragg lasers," Opt. Lett. 29, 2641-2643 (2004).
    [CrossRef]
  17. J. Scheuer and A. Yariv, "Circular photonic crystal resonators," Phys. Rev. E 70, 036603 (2004).
    [CrossRef]
  18. J. Scheuer, W. M. J. Green, G. DeRose, and A. Yariv, "InGaAsP annular Bragg lasers: theory, applications and modal properties," IEEE J. Sel. Top. Quantum Electron. 11, 476-484 (2005).
    [CrossRef]
  19. T. Erdogan and D. G. Hall, "Circularly symmetric distributed feedback semiconductor laser: an analysis," J. Appl. Phys. 68, 1435-1444 (1990).
    [CrossRef]
  20. T. Erdogan and D. G. Hall, "Circularly symmetric distributed feedback laser: coupled mode treatment of TE vector fields," IEEE J. Quantum Electron. 28, 612-623 (1992).
    [CrossRef]
  21. X. M. Gong, A. K. Chan, and H. F. Taylor, "Lateral mode discrimination in surface emitting DBR lasers with cylindrical symmetry," IEEE J. Quantum Electron. 30, 1212-1218 (1994).
    [CrossRef]
  22. T. Makino and C. Wu, "Circular grating DFB and DBR semiconductor lasers: threshold current analysis," Opt. Commun. 90, 297-300 (1992).
    [CrossRef]
  23. C. Wu, T. Makino, S. I. Najafi, R. Maciejko, M. Svilans, J. Glinski, and M. Fallahi, "Threshold gain and threshold current analysis of circular grating DFB and DBR lasers," IEEE J. Quantum Electron. 29, 2596-2606 (1993).
    [CrossRef]
  24. K. J. Kasunic and M. Fallahi, "Gain saturation in circular-grating distributed-feedback semiconductor lasers," J. Opt. Soc. Am. B 14, 2147-2152 (1997).
  25. P. L. Greene and D. G. Hall, "Effects of radiation on circular-grating DFB lasers. Part I. Coupled-mode equations," IEEE J. Quantum Electron. 37, 353-364 (2001).
    [CrossRef]
  26. C. Wu, M. Svilans, M. Fallahi, T. Makino, J. Glinski, C. Maritan and C. Blaauw, "Optically pumped surface-emitting DFB GaInAsP/InP lasers with circular grating," Electron. Lett. 27, 1819-1820 (1991).
  27. C. Wu, T. Makino, R. Maciejko, S. I. Najafi, and M. Svilans, "Simplified coupled-wave equations for cylindrical waves in circular grating planar waveguides," J. Lightwave Technol. 10, 1575-1589 (1992).
    [CrossRef]
  28. A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford Press, 1997).
  29. P. Yeh, A. Yariv, and E. Marom, "Theory of Bragg fiber," J. Opt. Soc. Am. 68, 1196-1201 (1978).
  30. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984).
  31. G. N. Watson, Theory of Bessel Functions, 2nd ed. (Cambridge U. Press, 1952).

2005 (4)

H. Altug and J. Vuckovic, "Experimental demonstration of the slow group velocity of light in two-dimensional coupled photonic crystal microcavity arrays," Appl. Phys. Lett. 86, 111102 (2005).
[CrossRef]

K. Nozaki, T. Ide, J. Hashimoto, T. Baba, and W.-H. Zheng, "Photonic crystal point-shift nanolaser with ultimate small modal volume," Electron. Lett. 41, 843-845 (2005).

J. Scheuer, W. M. J. Green, G. DeRose, and A. Yariv, "Lasing from a circular Bragg nanocavity with an ultra-small modal volume," Appl. Phys. Lett. 86, 251101 (2005).
[CrossRef]

J. Scheuer, W. M. J. Green, G. 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 (5)

2003 (4)

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

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

C. Y. Chao and L. J. Guo, "Biochemical sensors based on polymer microrings with sharp asymmetrical resonance," Appl. Phys. Lett. 83, 1527-1529 (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]

2001 (2)

1999 (1)

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef]

1998 (2)

Y. Fink, J. N. Winn, F. Shanhui, C. Chiping, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef]

B. E. Little, "Second-order filtering and sensing with partially coupled traveling waves in a single resonator," Opt. Lett. 23, 1570-1572 (1998).

1997 (1)

1994 (1)

X. M. Gong, A. K. Chan, and H. F. Taylor, "Lateral mode discrimination in surface emitting DBR lasers with cylindrical symmetry," IEEE J. Quantum Electron. 30, 1212-1218 (1994).
[CrossRef]

1993 (1)

C. Wu, T. Makino, S. I. Najafi, R. Maciejko, M. Svilans, J. Glinski, and M. Fallahi, "Threshold gain and threshold current analysis of circular grating DFB and DBR lasers," IEEE J. Quantum Electron. 29, 2596-2606 (1993).
[CrossRef]

1992 (3)

C. Wu, T. Makino, R. Maciejko, S. I. Najafi, and M. Svilans, "Simplified coupled-wave equations for cylindrical waves in circular grating planar waveguides," J. Lightwave Technol. 10, 1575-1589 (1992).
[CrossRef]

T. Makino and C. Wu, "Circular grating DFB and DBR semiconductor lasers: threshold current analysis," Opt. Commun. 90, 297-300 (1992).
[CrossRef]

T. Erdogan and D. G. Hall, "Circularly symmetric distributed feedback laser: coupled mode treatment of TE vector fields," IEEE J. Quantum Electron. 28, 612-623 (1992).
[CrossRef]

1991 (1)

C. Wu, M. Svilans, M. Fallahi, T. Makino, J. Glinski, C. Maritan and C. Blaauw, "Optically pumped surface-emitting DFB GaInAsP/InP lasers with circular grating," Electron. Lett. 27, 1819-1820 (1991).

1990 (1)

T. Erdogan and D. G. Hall, "Circularly symmetric distributed feedback semiconductor laser: an analysis," J. Appl. Phys. 68, 1435-1444 (1990).
[CrossRef]

1978 (1)

Appl. Phys. Lett. (3)

C. Y. Chao and L. J. Guo, "Biochemical sensors based on polymer microrings with sharp asymmetrical resonance," Appl. Phys. Lett. 83, 1527-1529 (2003).
[CrossRef]

H. Altug and J. Vuckovic, "Experimental demonstration of the slow group velocity of light in two-dimensional coupled photonic crystal microcavity arrays," Appl. Phys. Lett. 86, 111102 (2005).
[CrossRef]

J. Scheuer, W. M. J. Green, G. DeRose, and A. Yariv, "Lasing from a circular Bragg nanocavity with an ultra-small modal volume," Appl. Phys. Lett. 86, 251101 (2005).
[CrossRef]

Electron. Lett. (2)

K. Nozaki, T. Ide, J. Hashimoto, T. Baba, and W.-H. Zheng, "Photonic crystal point-shift nanolaser with ultimate small modal volume," Electron. Lett. 41, 843-845 (2005).

C. Wu, M. Svilans, M. Fallahi, T. Makino, J. Glinski, C. Maritan and C. Blaauw, "Optically pumped surface-emitting DFB GaInAsP/InP lasers with circular grating," Electron. Lett. 27, 1819-1820 (1991).

IEEE J. Quantum Electron. (5)

T. Erdogan and D. G. Hall, "Circularly symmetric distributed feedback laser: coupled mode treatment of TE vector fields," IEEE J. Quantum Electron. 28, 612-623 (1992).
[CrossRef]

X. M. Gong, A. K. Chan, and H. F. Taylor, "Lateral mode discrimination in surface emitting DBR lasers with cylindrical symmetry," IEEE J. Quantum Electron. 30, 1212-1218 (1994).
[CrossRef]

C. Wu, T. Makino, S. I. Najafi, R. Maciejko, M. Svilans, J. Glinski, and M. Fallahi, "Threshold gain and threshold current analysis of circular grating DFB and DBR lasers," IEEE J. Quantum Electron. 29, 2596-2606 (1993).
[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 I. Coupled-mode equations," IEEE J. Quantum Electron. 37, 353-364 (2001).
[CrossRef]

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

J. Scheuer, W. M. J. Green, G. DeRose, and A. Yariv, "InGaAsP annular Bragg lasers: theory, applications and modal properties," IEEE J. Sel. Top. Quantum Electron. 11, 476-484 (2005).
[CrossRef]

IEICE Trans. Electron. (1)

T. Yoshie, O. B. Shchekin, H. Chen, D. G. Deppe, and A. Scherer, "Planar photonic crystal nanolasers (II): low-threshold quantum dot lasers," IEICE Trans. Electron. E87-C, 300-307 (2004).

J. Appl. Phys. (1)

T. Erdogan and D. G. Hall, "Circularly symmetric distributed feedback semiconductor laser: an analysis," J. Appl. Phys. 68, 1435-1444 (1990).
[CrossRef]

J. Lightwave Technol. (1)

C. Wu, T. Makino, R. Maciejko, S. I. Najafi, and M. Svilans, "Simplified coupled-wave equations for cylindrical waves in circular grating planar waveguides," J. Lightwave Technol. 10, 1575-1589 (1992).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (2)

Nature (London) (1)

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

Opt. Commun. (1)

T. Makino and C. Wu, "Circular grating DFB and DBR semiconductor lasers: threshold current analysis," Opt. Commun. 90, 297-300 (1992).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. E (1)

J. Scheuer and A. Yariv, "Circular photonic crystal resonators," Phys. Rev. E 70, 036603 (2004).
[CrossRef]

Science (2)

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef]

Y. Fink, J. N. Winn, F. Shanhui, C. Chiping, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef]

Other (4)

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley, 1999).

A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford Press, 1997).

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984).

G. N. Watson, Theory of Bessel Functions, 2nd ed. (Cambridge U. Press, 1952).

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