Abstract

We use a single-mode transfer equation model to study the performance of vertical-cavity surface-emitting distributed-feedback (DFB) and distributed-Bragg-reflector (DBR) semiconductor lasers above threshold. We find that DBR lasers exhibit less envelope spatial hole burning than both single and double phase-shifted DFB lasers and therefore may achieve more stable single-longitudinal-mode operation.

© 1989 Optical Society of America

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  1. N. W. Carlson, G. A. Evans, J. M. Hammer, M. Lurie, L. A. Carr, F. Z. Hawrylo, E. A. James, C. J. Kaiser, J. B. Kirk, W. F. Reichert, D. A. Truxal, J. R. Shealy, S. R. Chinn, P. S. Zory, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WO4.
  2. Z. L. Liau, J. N. Walpole, V. Diadiuk, in Digest of Meeting on Integrated and Guided-Wave Optics (Optical Society of America, Washington, D.C., 1988), paper WA1-1.
  3. S. Noda, K. Kojima, K. Kyuma, J. Ohta, K. Hamanaka, T. Nakayama, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WO1.
  4. S. H. Macomber, J. S. Mott, R. J. Noll, G. M. Gallatin, E. J. Gratrix, S. L. O’Dwyer, S. A. Lambert, Appl. Phys. Lett. 51, 472 (1987).
    [CrossRef]
  5. S. Kinoshita, K. Morito, F. Koyama, K. Iga, Electron. Lett. 24, 699 (1988).
    [CrossRef]
  6. A. Ibaraki, K. Kawashima, K. Furusawa, K. Ishikawa, T. Yamaguchi, T. Niina, in Proceedings of Eleventh International Semiconductor Laser Conference(Institute of Electrical and Electronics Engineers, New York, 1988), paper N-2.
  7. M. Ogura, W. Hsin, M.-C. Wu, S. Wang, J. R. Whinnery, S. C. Wang, J. J. Yang, Appl. Phys. Lett. 51, 1655 (1987).
    [CrossRef]
  8. D. Botez, L. M. Zinkiewicz, L. J. Mawst, T. J. Roth, in Proceedings of Eleventh International Semiconductor Laser Conference (Institute of Electrical and Electronics Engineers, New York, 1988), paper N-1.
  9. K. O. Hill, A. Watanabe, Appl. Opt. 14, 950 (1975).
    [CrossRef] [PubMed]
  10. H. A. Haus, Appl. Opt. 14, 2650 (1975).
    [CrossRef] [PubMed]
  11. P. Szczepanski, J. Appl. Phys. 63, 4854 (1988).
    [CrossRef]
  12. G. Björk, O. Nilsson, IEEE J. Lightwave Technol. LT-5, 140 (1987).
    [CrossRef]
  13. S. Wang, J. Appl. Phys. 44, 767 (1973).
    [CrossRef]
  14. International Mathematical and Statistical Library routine UMINF.
  15. M. Usami, S. Akiba, K. Utaka, IEEE J. Quantum Electron. QE-23, 815 (1987).
    [CrossRef]
  16. T. Kimura, A. Sugimura, Electron. Lett. 23, 1014 (1987).
    [CrossRef]
  17. G. P. Agrawal, J. E. Geusic, P. J. Anthony, Appl. Phys. Lett. 53, 178 (1988).
    [CrossRef]
  18. J. Kinoshita, K. Matsumoto, in Proceedings of Eleventh International Semiconductor Laser Conference (Institute of Electrical and Electronics Engineers, New York, 1988), paper H-4.

1988 (3)

S. Kinoshita, K. Morito, F. Koyama, K. Iga, Electron. Lett. 24, 699 (1988).
[CrossRef]

P. Szczepanski, J. Appl. Phys. 63, 4854 (1988).
[CrossRef]

G. P. Agrawal, J. E. Geusic, P. J. Anthony, Appl. Phys. Lett. 53, 178 (1988).
[CrossRef]

1987 (5)

M. Usami, S. Akiba, K. Utaka, IEEE J. Quantum Electron. QE-23, 815 (1987).
[CrossRef]

T. Kimura, A. Sugimura, Electron. Lett. 23, 1014 (1987).
[CrossRef]

G. Björk, O. Nilsson, IEEE J. Lightwave Technol. LT-5, 140 (1987).
[CrossRef]

M. Ogura, W. Hsin, M.-C. Wu, S. Wang, J. R. Whinnery, S. C. Wang, J. J. Yang, Appl. Phys. Lett. 51, 1655 (1987).
[CrossRef]

S. H. Macomber, J. S. Mott, R. J. Noll, G. M. Gallatin, E. J. Gratrix, S. L. O’Dwyer, S. A. Lambert, Appl. Phys. Lett. 51, 472 (1987).
[CrossRef]

1975 (2)

1973 (1)

S. Wang, J. Appl. Phys. 44, 767 (1973).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, J. E. Geusic, P. J. Anthony, Appl. Phys. Lett. 53, 178 (1988).
[CrossRef]

Akiba, S.

M. Usami, S. Akiba, K. Utaka, IEEE J. Quantum Electron. QE-23, 815 (1987).
[CrossRef]

Anthony, P. J.

G. P. Agrawal, J. E. Geusic, P. J. Anthony, Appl. Phys. Lett. 53, 178 (1988).
[CrossRef]

Björk, G.

G. Björk, O. Nilsson, IEEE J. Lightwave Technol. LT-5, 140 (1987).
[CrossRef]

Botez, D.

D. Botez, L. M. Zinkiewicz, L. J. Mawst, T. J. Roth, in Proceedings of Eleventh International Semiconductor Laser Conference (Institute of Electrical and Electronics Engineers, New York, 1988), paper N-1.

Carlson, N. W.

N. W. Carlson, G. A. Evans, J. M. Hammer, M. Lurie, L. A. Carr, F. Z. Hawrylo, E. A. James, C. J. Kaiser, J. B. Kirk, W. F. Reichert, D. A. Truxal, J. R. Shealy, S. R. Chinn, P. S. Zory, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WO4.

Carr, L. A.

N. W. Carlson, G. A. Evans, J. M. Hammer, M. Lurie, L. A. Carr, F. Z. Hawrylo, E. A. James, C. J. Kaiser, J. B. Kirk, W. F. Reichert, D. A. Truxal, J. R. Shealy, S. R. Chinn, P. S. Zory, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WO4.

Chinn, S. R.

N. W. Carlson, G. A. Evans, J. M. Hammer, M. Lurie, L. A. Carr, F. Z. Hawrylo, E. A. James, C. J. Kaiser, J. B. Kirk, W. F. Reichert, D. A. Truxal, J. R. Shealy, S. R. Chinn, P. S. Zory, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WO4.

Diadiuk, V.

Z. L. Liau, J. N. Walpole, V. Diadiuk, in Digest of Meeting on Integrated and Guided-Wave Optics (Optical Society of America, Washington, D.C., 1988), paper WA1-1.

Evans, G. A.

N. W. Carlson, G. A. Evans, J. M. Hammer, M. Lurie, L. A. Carr, F. Z. Hawrylo, E. A. James, C. J. Kaiser, J. B. Kirk, W. F. Reichert, D. A. Truxal, J. R. Shealy, S. R. Chinn, P. S. Zory, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WO4.

Furusawa, K.

A. Ibaraki, K. Kawashima, K. Furusawa, K. Ishikawa, T. Yamaguchi, T. Niina, in Proceedings of Eleventh International Semiconductor Laser Conference(Institute of Electrical and Electronics Engineers, New York, 1988), paper N-2.

Gallatin, G. M.

S. H. Macomber, J. S. Mott, R. J. Noll, G. M. Gallatin, E. J. Gratrix, S. L. O’Dwyer, S. A. Lambert, Appl. Phys. Lett. 51, 472 (1987).
[CrossRef]

Geusic, J. E.

G. P. Agrawal, J. E. Geusic, P. J. Anthony, Appl. Phys. Lett. 53, 178 (1988).
[CrossRef]

Gratrix, E. J.

S. H. Macomber, J. S. Mott, R. J. Noll, G. M. Gallatin, E. J. Gratrix, S. L. O’Dwyer, S. A. Lambert, Appl. Phys. Lett. 51, 472 (1987).
[CrossRef]

Hamanaka, K.

S. Noda, K. Kojima, K. Kyuma, J. Ohta, K. Hamanaka, T. Nakayama, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WO1.

Hammer, J. M.

N. W. Carlson, G. A. Evans, J. M. Hammer, M. Lurie, L. A. Carr, F. Z. Hawrylo, E. A. James, C. J. Kaiser, J. B. Kirk, W. F. Reichert, D. A. Truxal, J. R. Shealy, S. R. Chinn, P. S. Zory, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WO4.

Haus, H. A.

Hawrylo, F. Z.

N. W. Carlson, G. A. Evans, J. M. Hammer, M. Lurie, L. A. Carr, F. Z. Hawrylo, E. A. James, C. J. Kaiser, J. B. Kirk, W. F. Reichert, D. A. Truxal, J. R. Shealy, S. R. Chinn, P. S. Zory, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WO4.

Hill, K. O.

Hsin, W.

M. Ogura, W. Hsin, M.-C. Wu, S. Wang, J. R. Whinnery, S. C. Wang, J. J. Yang, Appl. Phys. Lett. 51, 1655 (1987).
[CrossRef]

Ibaraki, A.

A. Ibaraki, K. Kawashima, K. Furusawa, K. Ishikawa, T. Yamaguchi, T. Niina, in Proceedings of Eleventh International Semiconductor Laser Conference(Institute of Electrical and Electronics Engineers, New York, 1988), paper N-2.

Iga, K.

S. Kinoshita, K. Morito, F. Koyama, K. Iga, Electron. Lett. 24, 699 (1988).
[CrossRef]

Ishikawa, K.

A. Ibaraki, K. Kawashima, K. Furusawa, K. Ishikawa, T. Yamaguchi, T. Niina, in Proceedings of Eleventh International Semiconductor Laser Conference(Institute of Electrical and Electronics Engineers, New York, 1988), paper N-2.

James, E. A.

N. W. Carlson, G. A. Evans, J. M. Hammer, M. Lurie, L. A. Carr, F. Z. Hawrylo, E. A. James, C. J. Kaiser, J. B. Kirk, W. F. Reichert, D. A. Truxal, J. R. Shealy, S. R. Chinn, P. S. Zory, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WO4.

Kaiser, C. J.

N. W. Carlson, G. A. Evans, J. M. Hammer, M. Lurie, L. A. Carr, F. Z. Hawrylo, E. A. James, C. J. Kaiser, J. B. Kirk, W. F. Reichert, D. A. Truxal, J. R. Shealy, S. R. Chinn, P. S. Zory, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WO4.

Kawashima, K.

A. Ibaraki, K. Kawashima, K. Furusawa, K. Ishikawa, T. Yamaguchi, T. Niina, in Proceedings of Eleventh International Semiconductor Laser Conference(Institute of Electrical and Electronics Engineers, New York, 1988), paper N-2.

Kimura, T.

T. Kimura, A. Sugimura, Electron. Lett. 23, 1014 (1987).
[CrossRef]

Kinoshita, J.

J. Kinoshita, K. Matsumoto, in Proceedings of Eleventh International Semiconductor Laser Conference (Institute of Electrical and Electronics Engineers, New York, 1988), paper H-4.

Kinoshita, S.

S. Kinoshita, K. Morito, F. Koyama, K. Iga, Electron. Lett. 24, 699 (1988).
[CrossRef]

Kirk, J. B.

N. W. Carlson, G. A. Evans, J. M. Hammer, M. Lurie, L. A. Carr, F. Z. Hawrylo, E. A. James, C. J. Kaiser, J. B. Kirk, W. F. Reichert, D. A. Truxal, J. R. Shealy, S. R. Chinn, P. S. Zory, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WO4.

Kojima, K.

S. Noda, K. Kojima, K. Kyuma, J. Ohta, K. Hamanaka, T. Nakayama, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WO1.

Koyama, F.

S. Kinoshita, K. Morito, F. Koyama, K. Iga, Electron. Lett. 24, 699 (1988).
[CrossRef]

Kyuma, K.

S. Noda, K. Kojima, K. Kyuma, J. Ohta, K. Hamanaka, T. Nakayama, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WO1.

Lambert, S. A.

S. H. Macomber, J. S. Mott, R. J. Noll, G. M. Gallatin, E. J. Gratrix, S. L. O’Dwyer, S. A. Lambert, Appl. Phys. Lett. 51, 472 (1987).
[CrossRef]

Liau, Z. L.

Z. L. Liau, J. N. Walpole, V. Diadiuk, in Digest of Meeting on Integrated and Guided-Wave Optics (Optical Society of America, Washington, D.C., 1988), paper WA1-1.

Lurie, M.

N. W. Carlson, G. A. Evans, J. M. Hammer, M. Lurie, L. A. Carr, F. Z. Hawrylo, E. A. James, C. J. Kaiser, J. B. Kirk, W. F. Reichert, D. A. Truxal, J. R. Shealy, S. R. Chinn, P. S. Zory, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WO4.

Macomber, S. H.

S. H. Macomber, J. S. Mott, R. J. Noll, G. M. Gallatin, E. J. Gratrix, S. L. O’Dwyer, S. A. Lambert, Appl. Phys. Lett. 51, 472 (1987).
[CrossRef]

Matsumoto, K.

J. Kinoshita, K. Matsumoto, in Proceedings of Eleventh International Semiconductor Laser Conference (Institute of Electrical and Electronics Engineers, New York, 1988), paper H-4.

Mawst, L. J.

D. Botez, L. M. Zinkiewicz, L. J. Mawst, T. J. Roth, in Proceedings of Eleventh International Semiconductor Laser Conference (Institute of Electrical and Electronics Engineers, New York, 1988), paper N-1.

Morito, K.

S. Kinoshita, K. Morito, F. Koyama, K. Iga, Electron. Lett. 24, 699 (1988).
[CrossRef]

Mott, J. S.

S. H. Macomber, J. S. Mott, R. J. Noll, G. M. Gallatin, E. J. Gratrix, S. L. O’Dwyer, S. A. Lambert, Appl. Phys. Lett. 51, 472 (1987).
[CrossRef]

Nakayama, T.

S. Noda, K. Kojima, K. Kyuma, J. Ohta, K. Hamanaka, T. Nakayama, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WO1.

Niina, T.

A. Ibaraki, K. Kawashima, K. Furusawa, K. Ishikawa, T. Yamaguchi, T. Niina, in Proceedings of Eleventh International Semiconductor Laser Conference(Institute of Electrical and Electronics Engineers, New York, 1988), paper N-2.

Nilsson, O.

G. Björk, O. Nilsson, IEEE J. Lightwave Technol. LT-5, 140 (1987).
[CrossRef]

Noda, S.

S. Noda, K. Kojima, K. Kyuma, J. Ohta, K. Hamanaka, T. Nakayama, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WO1.

Noll, R. J.

S. H. Macomber, J. S. Mott, R. J. Noll, G. M. Gallatin, E. J. Gratrix, S. L. O’Dwyer, S. A. Lambert, Appl. Phys. Lett. 51, 472 (1987).
[CrossRef]

O’Dwyer, S. L.

S. H. Macomber, J. S. Mott, R. J. Noll, G. M. Gallatin, E. J. Gratrix, S. L. O’Dwyer, S. A. Lambert, Appl. Phys. Lett. 51, 472 (1987).
[CrossRef]

Ogura, M.

M. Ogura, W. Hsin, M.-C. Wu, S. Wang, J. R. Whinnery, S. C. Wang, J. J. Yang, Appl. Phys. Lett. 51, 1655 (1987).
[CrossRef]

Ohta, J.

S. Noda, K. Kojima, K. Kyuma, J. Ohta, K. Hamanaka, T. Nakayama, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WO1.

Reichert, W. F.

N. W. Carlson, G. A. Evans, J. M. Hammer, M. Lurie, L. A. Carr, F. Z. Hawrylo, E. A. James, C. J. Kaiser, J. B. Kirk, W. F. Reichert, D. A. Truxal, J. R. Shealy, S. R. Chinn, P. S. Zory, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WO4.

Roth, T. J.

D. Botez, L. M. Zinkiewicz, L. J. Mawst, T. J. Roth, in Proceedings of Eleventh International Semiconductor Laser Conference (Institute of Electrical and Electronics Engineers, New York, 1988), paper N-1.

Shealy, J. R.

N. W. Carlson, G. A. Evans, J. M. Hammer, M. Lurie, L. A. Carr, F. Z. Hawrylo, E. A. James, C. J. Kaiser, J. B. Kirk, W. F. Reichert, D. A. Truxal, J. R. Shealy, S. R. Chinn, P. S. Zory, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WO4.

Sugimura, A.

T. Kimura, A. Sugimura, Electron. Lett. 23, 1014 (1987).
[CrossRef]

Szczepanski, P.

P. Szczepanski, J. Appl. Phys. 63, 4854 (1988).
[CrossRef]

Truxal, D. A.

N. W. Carlson, G. A. Evans, J. M. Hammer, M. Lurie, L. A. Carr, F. Z. Hawrylo, E. A. James, C. J. Kaiser, J. B. Kirk, W. F. Reichert, D. A. Truxal, J. R. Shealy, S. R. Chinn, P. S. Zory, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WO4.

Usami, M.

M. Usami, S. Akiba, K. Utaka, IEEE J. Quantum Electron. QE-23, 815 (1987).
[CrossRef]

Utaka, K.

M. Usami, S. Akiba, K. Utaka, IEEE J. Quantum Electron. QE-23, 815 (1987).
[CrossRef]

Walpole, J. N.

Z. L. Liau, J. N. Walpole, V. Diadiuk, in Digest of Meeting on Integrated and Guided-Wave Optics (Optical Society of America, Washington, D.C., 1988), paper WA1-1.

Wang, S.

M. Ogura, W. Hsin, M.-C. Wu, S. Wang, J. R. Whinnery, S. C. Wang, J. J. Yang, Appl. Phys. Lett. 51, 1655 (1987).
[CrossRef]

S. Wang, J. Appl. Phys. 44, 767 (1973).
[CrossRef]

Wang, S. C.

M. Ogura, W. Hsin, M.-C. Wu, S. Wang, J. R. Whinnery, S. C. Wang, J. J. Yang, Appl. Phys. Lett. 51, 1655 (1987).
[CrossRef]

Watanabe, A.

Whinnery, J. R.

M. Ogura, W. Hsin, M.-C. Wu, S. Wang, J. R. Whinnery, S. C. Wang, J. J. Yang, Appl. Phys. Lett. 51, 1655 (1987).
[CrossRef]

Wu, M.-C.

M. Ogura, W. Hsin, M.-C. Wu, S. Wang, J. R. Whinnery, S. C. Wang, J. J. Yang, Appl. Phys. Lett. 51, 1655 (1987).
[CrossRef]

Yamaguchi, T.

A. Ibaraki, K. Kawashima, K. Furusawa, K. Ishikawa, T. Yamaguchi, T. Niina, in Proceedings of Eleventh International Semiconductor Laser Conference(Institute of Electrical and Electronics Engineers, New York, 1988), paper N-2.

Yang, J. J.

M. Ogura, W. Hsin, M.-C. Wu, S. Wang, J. R. Whinnery, S. C. Wang, J. J. Yang, Appl. Phys. Lett. 51, 1655 (1987).
[CrossRef]

Zinkiewicz, L. M.

D. Botez, L. M. Zinkiewicz, L. J. Mawst, T. J. Roth, in Proceedings of Eleventh International Semiconductor Laser Conference (Institute of Electrical and Electronics Engineers, New York, 1988), paper N-1.

Zory, P. S.

N. W. Carlson, G. A. Evans, J. M. Hammer, M. Lurie, L. A. Carr, F. Z. Hawrylo, E. A. James, C. J. Kaiser, J. B. Kirk, W. F. Reichert, D. A. Truxal, J. R. Shealy, S. R. Chinn, P. S. Zory, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WO4.

Appl. Opt. (2)

Appl. Phys. Lett. (3)

M. Ogura, W. Hsin, M.-C. Wu, S. Wang, J. R. Whinnery, S. C. Wang, J. J. Yang, Appl. Phys. Lett. 51, 1655 (1987).
[CrossRef]

S. H. Macomber, J. S. Mott, R. J. Noll, G. M. Gallatin, E. J. Gratrix, S. L. O’Dwyer, S. A. Lambert, Appl. Phys. Lett. 51, 472 (1987).
[CrossRef]

G. P. Agrawal, J. E. Geusic, P. J. Anthony, Appl. Phys. Lett. 53, 178 (1988).
[CrossRef]

Electron. Lett. (2)

T. Kimura, A. Sugimura, Electron. Lett. 23, 1014 (1987).
[CrossRef]

S. Kinoshita, K. Morito, F. Koyama, K. Iga, Electron. Lett. 24, 699 (1988).
[CrossRef]

IEEE J. Lightwave Technol. (1)

G. Björk, O. Nilsson, IEEE J. Lightwave Technol. LT-5, 140 (1987).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Usami, S. Akiba, K. Utaka, IEEE J. Quantum Electron. QE-23, 815 (1987).
[CrossRef]

J. Appl. Phys. (2)

S. Wang, J. Appl. Phys. 44, 767 (1973).
[CrossRef]

P. Szczepanski, J. Appl. Phys. 63, 4854 (1988).
[CrossRef]

Other (7)

D. Botez, L. M. Zinkiewicz, L. J. Mawst, T. J. Roth, in Proceedings of Eleventh International Semiconductor Laser Conference (Institute of Electrical and Electronics Engineers, New York, 1988), paper N-1.

A. Ibaraki, K. Kawashima, K. Furusawa, K. Ishikawa, T. Yamaguchi, T. Niina, in Proceedings of Eleventh International Semiconductor Laser Conference(Institute of Electrical and Electronics Engineers, New York, 1988), paper N-2.

N. W. Carlson, G. A. Evans, J. M. Hammer, M. Lurie, L. A. Carr, F. Z. Hawrylo, E. A. James, C. J. Kaiser, J. B. Kirk, W. F. Reichert, D. A. Truxal, J. R. Shealy, S. R. Chinn, P. S. Zory, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WO4.

Z. L. Liau, J. N. Walpole, V. Diadiuk, in Digest of Meeting on Integrated and Guided-Wave Optics (Optical Society of America, Washington, D.C., 1988), paper WA1-1.

S. Noda, K. Kojima, K. Kyuma, J. Ohta, K. Hamanaka, T. Nakayama, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WO1.

International Mathematical and Statistical Library routine UMINF.

J. Kinoshita, K. Matsumoto, in Proceedings of Eleventh International Semiconductor Laser Conference (Institute of Electrical and Electronics Engineers, New York, 1988), paper H-4.

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Figures (4)

Fig. 1
Fig. 1

Power output versus the pumping parameter.

Fig. 2
Fig. 2

Single-phase-shift laser axial intensity distribution for (a) the Bragg mode and (b) the next-higher-order longitudinal mode.

Fig. 3
Fig. 3

Double-phase-shift laser axial intensity distribution for (a) the lowest-order and (b) the next-to-lowest-order axial modes.

Fig. 4
Fig. 4

Axial intensity distribution of the fundamental mode of a DBR laser.

Equations (7)

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

A i ( z i + l i ) = A i ( z i ) exp [ i β i l i + ( 1 / 2 ) g i ( A i , B i ) l i ] ,
B i ( z i + l i ) = B i ( z i ) exp [ - i β i l i - ( 1 / 2 ) g i ( A i , B i ) l i ] ,
g i ( A i , B i ) = g 0 / [ 1 + A i ( z i ) 2 + B i ( z i ) 2 ] ,
A j = F i j [ ( β i + β j ) 2 β j A i + ( β j - β i ) 2 β j B i ] ,
B j = F i j [ ( β j - β i ) 2 β j A i + ( β i + β j ) 2 β j B i ] ,
F i j = ( β j β i ) 1 / 2 H i j ( H i i H j j ) 1 / 2 ,
H i j = d x d y w i w j * ,

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