Abstract

A novel power-series method to solve the coupled-wave equations is introduced. The method is used to calculate the threshold gain margins of a complex-coupled distributed-feedback laser as functions of the ratio of gain coupling to index coupling (|κg|/|κn|) and of the phase difference between the index and the gain gratings. For coupling coefficient |κ|l < 0.9, the laser shows a mode degeneracy at specific values of the ratio |κg|/|κn| for cleaved facets. At phase differences π/2 and 3π/2 between the gain and the index gratings, an antireflection-coated complex-coupled laser becomes multimode, and a different mode starts to lase. The effect of facet reflectivity (both magnitude and phase) on the gain margin of a complex-coupled DFB laser is also investigated. Although the gain margin varies slowly with the magnitude of the facet’s reflectivity, it shows large variations as a function of the phase. Spatial hole burning was found to be minimum at phase difference nπ, n = 0, 1 … , and maximum at phase differences π/2 and 3π/2.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Kogelnik, C. V. Shank, “Coupled wave theory of distributed-feedback lasers,” J. Appl. Phys. 43, 2327–2335 (1972).
    [CrossRef]
  2. S. R. Chinn, “Effect of mirror reflectivity in a distributed-feedback laser,” IEEE J. Quantum Electron. QE-9, 570–574 (1973).
  3. W. Streifer, R. D. Burnham, D. R. Scifres, “Effect of external reflectors on longitudinal modes of distributed feedback lasers,” IEEE J. Quantum Electron. QE-11, 154–161 (1975).
    [CrossRef]
  4. H. Soda, Y. Kotaki, H. Sudo, H. Ishikawa, S. Yamakoshi, H. Imai, “Stability in single longitudinal mode operation in GaInAsP/InP phase adjusted lasers,” IEEE J. Quantum Electron. QE-23, 804–814 (1987).
    [CrossRef]
  5. J. E. A. Whiteway, B. Garrett, G. H. B. Thompson, A. J. Collar, C. J. Armistead, M. J. Fice, “The static and dynamic characteristics of single and multiple phase-shifted DFB laser structures,” IEEE J. Quantum Electron. 28, 1277–1293 (1992).
    [CrossRef]
  6. K. O. Hill, “Aperiodic distributed-parameter waveguides for integrated optics,” Appl. Opt. 13, 1753–1756 (1974).
    [CrossRef]
  7. Y. Luo, Y. Nakano, K. Tada, T. Inoue, H. Hosomatsu, H. Iwaoka, “Purely gain coupled distributed feedback lasers,” Appl. Phys. Lett. 56, 1620–1622 (1990).
    [CrossRef]
  8. G. Morthier, P. Vankwikelberge, K. David, R. Baets, “Improved performance of AR-coated DFB lasers by the introduction of gain coupling,” IEEE Photon. Technol. Lett. 2, 170–172 (1990).
    [CrossRef]
  9. K. David, D. Morthier, P. Vankwikelberge, R. Baets, T. Wolf, B. Borchert, “Gain-coupled DFB lasers versus index-coupled and phase-shifted DFB lasers: a comparison based on spatial hole burning corrected yield,” IEEE J. Quantum Electron. 27, 1714–1722 (1991).
    [CrossRef]
  10. F. Randone, I. Montrosset, “Analysis and simulation of gain-coupled distributed feedback lasers,” IEEE J. Quantum Electron. 31, 1964–1973 (1995).
    [CrossRef]
  11. B. Jonsson, A. Lowery, H. Olesen, B. Tromborg, “Instabilities and nonlinear L-I characteristics in complex-coupled DFB lasers with antiphase gain and index grating,” IEEE J. Quantum Electron. 32, 839–850 (1996).
    [CrossRef]
  12. J. Hong, T. Makino, H. Lu, G. P. Li, “Effect of in-phase and antiphase gain coupling on high-speed properties of MQW DFB lasers,” IEEE Photon. Technol. Lett. 7, 956–958 (1995).
    [CrossRef]
  13. J. Chen, A. Champagne, R. Maciejko, T. Makino, “Improvement of single-mode gain margin in gain-coupled DFB lasers,” IEEE J. Quantum Electron. 33, 33–40 (1997).
    [CrossRef]
  14. K. Kwon, “Effect of grating phase difference on single-mode yield in complex-coupled DFB lasers with gain and index grating,” IEEE J. Quantum Electron. 32, 1937–1949 (1996).
    [CrossRef]
  15. P. Vankwikelberge, G. Morthier, R. Baets, “CLADISS-A longitudinal model for the analysis of the static, dynamic, and stochastic behavior of diode lasers with distributed feedback,” IEEE J. Quantum Electron. 26, 1728–1741 (1990).
    [CrossRef]
  16. A. J. Lowery, D. Novak, “Performance comparison of gain-coupled and index-coupled DFB semiconductor lasers,” IEEE J. Quantum Electron. 30, 2051–2063 (1994).
    [CrossRef]
  17. K. B. Kahen, “Analysis of distributed-feedback lasers using a recursive Green’s functional approach,” IEEE J. Quantum Electron. 29, 368–373 (1993).
    [CrossRef]
  18. A. Suzuki, K. Tada, “Theory and experiment on distributed-feedback lasers with chirped grating,” in Guided-Wave Optical and Surface Acoustic Wave Devices, Systems and Applications, C. S. Tsai, ed., Proc. SPIE239, 10–18 (1980).
    [CrossRef]
  19. P. Zhou, G. S. Lee, “Phase-shifted distributed-feedback laser with linearly chirped grating for narrow linewidth and high-power operation,” Appl. Phys. Lett. 58, 331–333 (1991).
    [CrossRef]
  20. G. Morthier, P. Vankwikelberge, Handbook of Distributed Feedback Laser Diodes (Artech House, Norwood, Mass., 1997), Chap. 3.
  21. P. Zhou, G. S. Lee, “Mode selection and spatial hole burning suppression of a chirped grating distributed feedback laser,” Appl. Phys. Lett. 56, 1400–1402 (1990).
    [CrossRef]

1997 (1)

J. Chen, A. Champagne, R. Maciejko, T. Makino, “Improvement of single-mode gain margin in gain-coupled DFB lasers,” IEEE J. Quantum Electron. 33, 33–40 (1997).
[CrossRef]

1996 (2)

K. Kwon, “Effect of grating phase difference on single-mode yield in complex-coupled DFB lasers with gain and index grating,” IEEE J. Quantum Electron. 32, 1937–1949 (1996).
[CrossRef]

B. Jonsson, A. Lowery, H. Olesen, B. Tromborg, “Instabilities and nonlinear L-I characteristics in complex-coupled DFB lasers with antiphase gain and index grating,” IEEE J. Quantum Electron. 32, 839–850 (1996).
[CrossRef]

1995 (2)

J. Hong, T. Makino, H. Lu, G. P. Li, “Effect of in-phase and antiphase gain coupling on high-speed properties of MQW DFB lasers,” IEEE Photon. Technol. Lett. 7, 956–958 (1995).
[CrossRef]

F. Randone, I. Montrosset, “Analysis and simulation of gain-coupled distributed feedback lasers,” IEEE J. Quantum Electron. 31, 1964–1973 (1995).
[CrossRef]

1994 (1)

A. J. Lowery, D. Novak, “Performance comparison of gain-coupled and index-coupled DFB semiconductor lasers,” IEEE J. Quantum Electron. 30, 2051–2063 (1994).
[CrossRef]

1993 (1)

K. B. Kahen, “Analysis of distributed-feedback lasers using a recursive Green’s functional approach,” IEEE J. Quantum Electron. 29, 368–373 (1993).
[CrossRef]

1992 (1)

J. E. A. Whiteway, B. Garrett, G. H. B. Thompson, A. J. Collar, C. J. Armistead, M. J. Fice, “The static and dynamic characteristics of single and multiple phase-shifted DFB laser structures,” IEEE J. Quantum Electron. 28, 1277–1293 (1992).
[CrossRef]

1991 (2)

P. Zhou, G. S. Lee, “Phase-shifted distributed-feedback laser with linearly chirped grating for narrow linewidth and high-power operation,” Appl. Phys. Lett. 58, 331–333 (1991).
[CrossRef]

K. David, D. Morthier, P. Vankwikelberge, R. Baets, T. Wolf, B. Borchert, “Gain-coupled DFB lasers versus index-coupled and phase-shifted DFB lasers: a comparison based on spatial hole burning corrected yield,” IEEE J. Quantum Electron. 27, 1714–1722 (1991).
[CrossRef]

1990 (4)

P. Zhou, G. S. Lee, “Mode selection and spatial hole burning suppression of a chirped grating distributed feedback laser,” Appl. Phys. Lett. 56, 1400–1402 (1990).
[CrossRef]

Y. Luo, Y. Nakano, K. Tada, T. Inoue, H. Hosomatsu, H. Iwaoka, “Purely gain coupled distributed feedback lasers,” Appl. Phys. Lett. 56, 1620–1622 (1990).
[CrossRef]

G. Morthier, P. Vankwikelberge, K. David, R. Baets, “Improved performance of AR-coated DFB lasers by the introduction of gain coupling,” IEEE Photon. Technol. Lett. 2, 170–172 (1990).
[CrossRef]

P. Vankwikelberge, G. Morthier, R. Baets, “CLADISS-A longitudinal model for the analysis of the static, dynamic, and stochastic behavior of diode lasers with distributed feedback,” IEEE J. Quantum Electron. 26, 1728–1741 (1990).
[CrossRef]

1987 (1)

H. Soda, Y. Kotaki, H. Sudo, H. Ishikawa, S. Yamakoshi, H. Imai, “Stability in single longitudinal mode operation in GaInAsP/InP phase adjusted lasers,” IEEE J. Quantum Electron. QE-23, 804–814 (1987).
[CrossRef]

1975 (1)

W. Streifer, R. D. Burnham, D. R. Scifres, “Effect of external reflectors on longitudinal modes of distributed feedback lasers,” IEEE J. Quantum Electron. QE-11, 154–161 (1975).
[CrossRef]

1974 (1)

1973 (1)

S. R. Chinn, “Effect of mirror reflectivity in a distributed-feedback laser,” IEEE J. Quantum Electron. QE-9, 570–574 (1973).

1972 (1)

H. Kogelnik, C. V. Shank, “Coupled wave theory of distributed-feedback lasers,” J. Appl. Phys. 43, 2327–2335 (1972).
[CrossRef]

Armistead, C. J.

J. E. A. Whiteway, B. Garrett, G. H. B. Thompson, A. J. Collar, C. J. Armistead, M. J. Fice, “The static and dynamic characteristics of single and multiple phase-shifted DFB laser structures,” IEEE J. Quantum Electron. 28, 1277–1293 (1992).
[CrossRef]

Baets, R.

K. David, D. Morthier, P. Vankwikelberge, R. Baets, T. Wolf, B. Borchert, “Gain-coupled DFB lasers versus index-coupled and phase-shifted DFB lasers: a comparison based on spatial hole burning corrected yield,” IEEE J. Quantum Electron. 27, 1714–1722 (1991).
[CrossRef]

G. Morthier, P. Vankwikelberge, K. David, R. Baets, “Improved performance of AR-coated DFB lasers by the introduction of gain coupling,” IEEE Photon. Technol. Lett. 2, 170–172 (1990).
[CrossRef]

P. Vankwikelberge, G. Morthier, R. Baets, “CLADISS-A longitudinal model for the analysis of the static, dynamic, and stochastic behavior of diode lasers with distributed feedback,” IEEE J. Quantum Electron. 26, 1728–1741 (1990).
[CrossRef]

Borchert, B.

K. David, D. Morthier, P. Vankwikelberge, R. Baets, T. Wolf, B. Borchert, “Gain-coupled DFB lasers versus index-coupled and phase-shifted DFB lasers: a comparison based on spatial hole burning corrected yield,” IEEE J. Quantum Electron. 27, 1714–1722 (1991).
[CrossRef]

Burnham, R. D.

W. Streifer, R. D. Burnham, D. R. Scifres, “Effect of external reflectors on longitudinal modes of distributed feedback lasers,” IEEE J. Quantum Electron. QE-11, 154–161 (1975).
[CrossRef]

Champagne, A.

J. Chen, A. Champagne, R. Maciejko, T. Makino, “Improvement of single-mode gain margin in gain-coupled DFB lasers,” IEEE J. Quantum Electron. 33, 33–40 (1997).
[CrossRef]

Chen, J.

J. Chen, A. Champagne, R. Maciejko, T. Makino, “Improvement of single-mode gain margin in gain-coupled DFB lasers,” IEEE J. Quantum Electron. 33, 33–40 (1997).
[CrossRef]

Chinn, S. R.

S. R. Chinn, “Effect of mirror reflectivity in a distributed-feedback laser,” IEEE J. Quantum Electron. QE-9, 570–574 (1973).

Collar, A. J.

J. E. A. Whiteway, B. Garrett, G. H. B. Thompson, A. J. Collar, C. J. Armistead, M. J. Fice, “The static and dynamic characteristics of single and multiple phase-shifted DFB laser structures,” IEEE J. Quantum Electron. 28, 1277–1293 (1992).
[CrossRef]

David, K.

K. David, D. Morthier, P. Vankwikelberge, R. Baets, T. Wolf, B. Borchert, “Gain-coupled DFB lasers versus index-coupled and phase-shifted DFB lasers: a comparison based on spatial hole burning corrected yield,” IEEE J. Quantum Electron. 27, 1714–1722 (1991).
[CrossRef]

G. Morthier, P. Vankwikelberge, K. David, R. Baets, “Improved performance of AR-coated DFB lasers by the introduction of gain coupling,” IEEE Photon. Technol. Lett. 2, 170–172 (1990).
[CrossRef]

Fice, M. J.

J. E. A. Whiteway, B. Garrett, G. H. B. Thompson, A. J. Collar, C. J. Armistead, M. J. Fice, “The static and dynamic characteristics of single and multiple phase-shifted DFB laser structures,” IEEE J. Quantum Electron. 28, 1277–1293 (1992).
[CrossRef]

Garrett, B.

J. E. A. Whiteway, B. Garrett, G. H. B. Thompson, A. J. Collar, C. J. Armistead, M. J. Fice, “The static and dynamic characteristics of single and multiple phase-shifted DFB laser structures,” IEEE J. Quantum Electron. 28, 1277–1293 (1992).
[CrossRef]

Hill, K. O.

Hong, J.

J. Hong, T. Makino, H. Lu, G. P. Li, “Effect of in-phase and antiphase gain coupling on high-speed properties of MQW DFB lasers,” IEEE Photon. Technol. Lett. 7, 956–958 (1995).
[CrossRef]

Hosomatsu, H.

Y. Luo, Y. Nakano, K. Tada, T. Inoue, H. Hosomatsu, H. Iwaoka, “Purely gain coupled distributed feedback lasers,” Appl. Phys. Lett. 56, 1620–1622 (1990).
[CrossRef]

Imai, H.

H. Soda, Y. Kotaki, H. Sudo, H. Ishikawa, S. Yamakoshi, H. Imai, “Stability in single longitudinal mode operation in GaInAsP/InP phase adjusted lasers,” IEEE J. Quantum Electron. QE-23, 804–814 (1987).
[CrossRef]

Inoue, T.

Y. Luo, Y. Nakano, K. Tada, T. Inoue, H. Hosomatsu, H. Iwaoka, “Purely gain coupled distributed feedback lasers,” Appl. Phys. Lett. 56, 1620–1622 (1990).
[CrossRef]

Ishikawa, H.

H. Soda, Y. Kotaki, H. Sudo, H. Ishikawa, S. Yamakoshi, H. Imai, “Stability in single longitudinal mode operation in GaInAsP/InP phase adjusted lasers,” IEEE J. Quantum Electron. QE-23, 804–814 (1987).
[CrossRef]

Iwaoka, H.

Y. Luo, Y. Nakano, K. Tada, T. Inoue, H. Hosomatsu, H. Iwaoka, “Purely gain coupled distributed feedback lasers,” Appl. Phys. Lett. 56, 1620–1622 (1990).
[CrossRef]

Jonsson, B.

B. Jonsson, A. Lowery, H. Olesen, B. Tromborg, “Instabilities and nonlinear L-I characteristics in complex-coupled DFB lasers with antiphase gain and index grating,” IEEE J. Quantum Electron. 32, 839–850 (1996).
[CrossRef]

Kahen, K. B.

K. B. Kahen, “Analysis of distributed-feedback lasers using a recursive Green’s functional approach,” IEEE J. Quantum Electron. 29, 368–373 (1993).
[CrossRef]

Kogelnik, H.

H. Kogelnik, C. V. Shank, “Coupled wave theory of distributed-feedback lasers,” J. Appl. Phys. 43, 2327–2335 (1972).
[CrossRef]

Kotaki, Y.

H. Soda, Y. Kotaki, H. Sudo, H. Ishikawa, S. Yamakoshi, H. Imai, “Stability in single longitudinal mode operation in GaInAsP/InP phase adjusted lasers,” IEEE J. Quantum Electron. QE-23, 804–814 (1987).
[CrossRef]

Kwon, K.

K. Kwon, “Effect of grating phase difference on single-mode yield in complex-coupled DFB lasers with gain and index grating,” IEEE J. Quantum Electron. 32, 1937–1949 (1996).
[CrossRef]

Lee, G. S.

P. Zhou, G. S. Lee, “Phase-shifted distributed-feedback laser with linearly chirped grating for narrow linewidth and high-power operation,” Appl. Phys. Lett. 58, 331–333 (1991).
[CrossRef]

P. Zhou, G. S. Lee, “Mode selection and spatial hole burning suppression of a chirped grating distributed feedback laser,” Appl. Phys. Lett. 56, 1400–1402 (1990).
[CrossRef]

Li, G. P.

J. Hong, T. Makino, H. Lu, G. P. Li, “Effect of in-phase and antiphase gain coupling on high-speed properties of MQW DFB lasers,” IEEE Photon. Technol. Lett. 7, 956–958 (1995).
[CrossRef]

Lowery, A.

B. Jonsson, A. Lowery, H. Olesen, B. Tromborg, “Instabilities and nonlinear L-I characteristics in complex-coupled DFB lasers with antiphase gain and index grating,” IEEE J. Quantum Electron. 32, 839–850 (1996).
[CrossRef]

Lowery, A. J.

A. J. Lowery, D. Novak, “Performance comparison of gain-coupled and index-coupled DFB semiconductor lasers,” IEEE J. Quantum Electron. 30, 2051–2063 (1994).
[CrossRef]

Lu, H.

J. Hong, T. Makino, H. Lu, G. P. Li, “Effect of in-phase and antiphase gain coupling on high-speed properties of MQW DFB lasers,” IEEE Photon. Technol. Lett. 7, 956–958 (1995).
[CrossRef]

Luo, Y.

Y. Luo, Y. Nakano, K. Tada, T. Inoue, H. Hosomatsu, H. Iwaoka, “Purely gain coupled distributed feedback lasers,” Appl. Phys. Lett. 56, 1620–1622 (1990).
[CrossRef]

Maciejko, R.

J. Chen, A. Champagne, R. Maciejko, T. Makino, “Improvement of single-mode gain margin in gain-coupled DFB lasers,” IEEE J. Quantum Electron. 33, 33–40 (1997).
[CrossRef]

Makino, T.

J. Chen, A. Champagne, R. Maciejko, T. Makino, “Improvement of single-mode gain margin in gain-coupled DFB lasers,” IEEE J. Quantum Electron. 33, 33–40 (1997).
[CrossRef]

J. Hong, T. Makino, H. Lu, G. P. Li, “Effect of in-phase and antiphase gain coupling on high-speed properties of MQW DFB lasers,” IEEE Photon. Technol. Lett. 7, 956–958 (1995).
[CrossRef]

Montrosset, I.

F. Randone, I. Montrosset, “Analysis and simulation of gain-coupled distributed feedback lasers,” IEEE J. Quantum Electron. 31, 1964–1973 (1995).
[CrossRef]

Morthier, D.

K. David, D. Morthier, P. Vankwikelberge, R. Baets, T. Wolf, B. Borchert, “Gain-coupled DFB lasers versus index-coupled and phase-shifted DFB lasers: a comparison based on spatial hole burning corrected yield,” IEEE J. Quantum Electron. 27, 1714–1722 (1991).
[CrossRef]

Morthier, G.

G. Morthier, P. Vankwikelberge, K. David, R. Baets, “Improved performance of AR-coated DFB lasers by the introduction of gain coupling,” IEEE Photon. Technol. Lett. 2, 170–172 (1990).
[CrossRef]

P. Vankwikelberge, G. Morthier, R. Baets, “CLADISS-A longitudinal model for the analysis of the static, dynamic, and stochastic behavior of diode lasers with distributed feedback,” IEEE J. Quantum Electron. 26, 1728–1741 (1990).
[CrossRef]

G. Morthier, P. Vankwikelberge, Handbook of Distributed Feedback Laser Diodes (Artech House, Norwood, Mass., 1997), Chap. 3.

Nakano, Y.

Y. Luo, Y. Nakano, K. Tada, T. Inoue, H. Hosomatsu, H. Iwaoka, “Purely gain coupled distributed feedback lasers,” Appl. Phys. Lett. 56, 1620–1622 (1990).
[CrossRef]

Novak, D.

A. J. Lowery, D. Novak, “Performance comparison of gain-coupled and index-coupled DFB semiconductor lasers,” IEEE J. Quantum Electron. 30, 2051–2063 (1994).
[CrossRef]

Olesen, H.

B. Jonsson, A. Lowery, H. Olesen, B. Tromborg, “Instabilities and nonlinear L-I characteristics in complex-coupled DFB lasers with antiphase gain and index grating,” IEEE J. Quantum Electron. 32, 839–850 (1996).
[CrossRef]

Randone, F.

F. Randone, I. Montrosset, “Analysis and simulation of gain-coupled distributed feedback lasers,” IEEE J. Quantum Electron. 31, 1964–1973 (1995).
[CrossRef]

Scifres, D. R.

W. Streifer, R. D. Burnham, D. R. Scifres, “Effect of external reflectors on longitudinal modes of distributed feedback lasers,” IEEE J. Quantum Electron. QE-11, 154–161 (1975).
[CrossRef]

Shank, C. V.

H. Kogelnik, C. V. Shank, “Coupled wave theory of distributed-feedback lasers,” J. Appl. Phys. 43, 2327–2335 (1972).
[CrossRef]

Soda, H.

H. Soda, Y. Kotaki, H. Sudo, H. Ishikawa, S. Yamakoshi, H. Imai, “Stability in single longitudinal mode operation in GaInAsP/InP phase adjusted lasers,” IEEE J. Quantum Electron. QE-23, 804–814 (1987).
[CrossRef]

Streifer, W.

W. Streifer, R. D. Burnham, D. R. Scifres, “Effect of external reflectors on longitudinal modes of distributed feedback lasers,” IEEE J. Quantum Electron. QE-11, 154–161 (1975).
[CrossRef]

Sudo, H.

H. Soda, Y. Kotaki, H. Sudo, H. Ishikawa, S. Yamakoshi, H. Imai, “Stability in single longitudinal mode operation in GaInAsP/InP phase adjusted lasers,” IEEE J. Quantum Electron. QE-23, 804–814 (1987).
[CrossRef]

Suzuki, A.

A. Suzuki, K. Tada, “Theory and experiment on distributed-feedback lasers with chirped grating,” in Guided-Wave Optical and Surface Acoustic Wave Devices, Systems and Applications, C. S. Tsai, ed., Proc. SPIE239, 10–18 (1980).
[CrossRef]

Tada, K.

Y. Luo, Y. Nakano, K. Tada, T. Inoue, H. Hosomatsu, H. Iwaoka, “Purely gain coupled distributed feedback lasers,” Appl. Phys. Lett. 56, 1620–1622 (1990).
[CrossRef]

A. Suzuki, K. Tada, “Theory and experiment on distributed-feedback lasers with chirped grating,” in Guided-Wave Optical and Surface Acoustic Wave Devices, Systems and Applications, C. S. Tsai, ed., Proc. SPIE239, 10–18 (1980).
[CrossRef]

Thompson, G. H. B.

J. E. A. Whiteway, B. Garrett, G. H. B. Thompson, A. J. Collar, C. J. Armistead, M. J. Fice, “The static and dynamic characteristics of single and multiple phase-shifted DFB laser structures,” IEEE J. Quantum Electron. 28, 1277–1293 (1992).
[CrossRef]

Tromborg, B.

B. Jonsson, A. Lowery, H. Olesen, B. Tromborg, “Instabilities and nonlinear L-I characteristics in complex-coupled DFB lasers with antiphase gain and index grating,” IEEE J. Quantum Electron. 32, 839–850 (1996).
[CrossRef]

Vankwikelberge, P.

K. David, D. Morthier, P. Vankwikelberge, R. Baets, T. Wolf, B. Borchert, “Gain-coupled DFB lasers versus index-coupled and phase-shifted DFB lasers: a comparison based on spatial hole burning corrected yield,” IEEE J. Quantum Electron. 27, 1714–1722 (1991).
[CrossRef]

G. Morthier, P. Vankwikelberge, K. David, R. Baets, “Improved performance of AR-coated DFB lasers by the introduction of gain coupling,” IEEE Photon. Technol. Lett. 2, 170–172 (1990).
[CrossRef]

P. Vankwikelberge, G. Morthier, R. Baets, “CLADISS-A longitudinal model for the analysis of the static, dynamic, and stochastic behavior of diode lasers with distributed feedback,” IEEE J. Quantum Electron. 26, 1728–1741 (1990).
[CrossRef]

G. Morthier, P. Vankwikelberge, Handbook of Distributed Feedback Laser Diodes (Artech House, Norwood, Mass., 1997), Chap. 3.

Whiteway, J. E. A.

J. E. A. Whiteway, B. Garrett, G. H. B. Thompson, A. J. Collar, C. J. Armistead, M. J. Fice, “The static and dynamic characteristics of single and multiple phase-shifted DFB laser structures,” IEEE J. Quantum Electron. 28, 1277–1293 (1992).
[CrossRef]

Wolf, T.

K. David, D. Morthier, P. Vankwikelberge, R. Baets, T. Wolf, B. Borchert, “Gain-coupled DFB lasers versus index-coupled and phase-shifted DFB lasers: a comparison based on spatial hole burning corrected yield,” IEEE J. Quantum Electron. 27, 1714–1722 (1991).
[CrossRef]

Yamakoshi, S.

H. Soda, Y. Kotaki, H. Sudo, H. Ishikawa, S. Yamakoshi, H. Imai, “Stability in single longitudinal mode operation in GaInAsP/InP phase adjusted lasers,” IEEE J. Quantum Electron. QE-23, 804–814 (1987).
[CrossRef]

Zhou, P.

P. Zhou, G. S. Lee, “Phase-shifted distributed-feedback laser with linearly chirped grating for narrow linewidth and high-power operation,” Appl. Phys. Lett. 58, 331–333 (1991).
[CrossRef]

P. Zhou, G. S. Lee, “Mode selection and spatial hole burning suppression of a chirped grating distributed feedback laser,” Appl. Phys. Lett. 56, 1400–1402 (1990).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

Y. Luo, Y. Nakano, K. Tada, T. Inoue, H. Hosomatsu, H. Iwaoka, “Purely gain coupled distributed feedback lasers,” Appl. Phys. Lett. 56, 1620–1622 (1990).
[CrossRef]

P. Zhou, G. S. Lee, “Phase-shifted distributed-feedback laser with linearly chirped grating for narrow linewidth and high-power operation,” Appl. Phys. Lett. 58, 331–333 (1991).
[CrossRef]

P. Zhou, G. S. Lee, “Mode selection and spatial hole burning suppression of a chirped grating distributed feedback laser,” Appl. Phys. Lett. 56, 1400–1402 (1990).
[CrossRef]

IEEE J. Quantum Electron. (12)

J. Chen, A. Champagne, R. Maciejko, T. Makino, “Improvement of single-mode gain margin in gain-coupled DFB lasers,” IEEE J. Quantum Electron. 33, 33–40 (1997).
[CrossRef]

K. Kwon, “Effect of grating phase difference on single-mode yield in complex-coupled DFB lasers with gain and index grating,” IEEE J. Quantum Electron. 32, 1937–1949 (1996).
[CrossRef]

P. Vankwikelberge, G. Morthier, R. Baets, “CLADISS-A longitudinal model for the analysis of the static, dynamic, and stochastic behavior of diode lasers with distributed feedback,” IEEE J. Quantum Electron. 26, 1728–1741 (1990).
[CrossRef]

A. J. Lowery, D. Novak, “Performance comparison of gain-coupled and index-coupled DFB semiconductor lasers,” IEEE J. Quantum Electron. 30, 2051–2063 (1994).
[CrossRef]

K. B. Kahen, “Analysis of distributed-feedback lasers using a recursive Green’s functional approach,” IEEE J. Quantum Electron. 29, 368–373 (1993).
[CrossRef]

S. R. Chinn, “Effect of mirror reflectivity in a distributed-feedback laser,” IEEE J. Quantum Electron. QE-9, 570–574 (1973).

W. Streifer, R. D. Burnham, D. R. Scifres, “Effect of external reflectors on longitudinal modes of distributed feedback lasers,” IEEE J. Quantum Electron. QE-11, 154–161 (1975).
[CrossRef]

H. Soda, Y. Kotaki, H. Sudo, H. Ishikawa, S. Yamakoshi, H. Imai, “Stability in single longitudinal mode operation in GaInAsP/InP phase adjusted lasers,” IEEE J. Quantum Electron. QE-23, 804–814 (1987).
[CrossRef]

J. E. A. Whiteway, B. Garrett, G. H. B. Thompson, A. J. Collar, C. J. Armistead, M. J. Fice, “The static and dynamic characteristics of single and multiple phase-shifted DFB laser structures,” IEEE J. Quantum Electron. 28, 1277–1293 (1992).
[CrossRef]

K. David, D. Morthier, P. Vankwikelberge, R. Baets, T. Wolf, B. Borchert, “Gain-coupled DFB lasers versus index-coupled and phase-shifted DFB lasers: a comparison based on spatial hole burning corrected yield,” IEEE J. Quantum Electron. 27, 1714–1722 (1991).
[CrossRef]

F. Randone, I. Montrosset, “Analysis and simulation of gain-coupled distributed feedback lasers,” IEEE J. Quantum Electron. 31, 1964–1973 (1995).
[CrossRef]

B. Jonsson, A. Lowery, H. Olesen, B. Tromborg, “Instabilities and nonlinear L-I characteristics in complex-coupled DFB lasers with antiphase gain and index grating,” IEEE J. Quantum Electron. 32, 839–850 (1996).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

J. Hong, T. Makino, H. Lu, G. P. Li, “Effect of in-phase and antiphase gain coupling on high-speed properties of MQW DFB lasers,” IEEE Photon. Technol. Lett. 7, 956–958 (1995).
[CrossRef]

G. Morthier, P. Vankwikelberge, K. David, R. Baets, “Improved performance of AR-coated DFB lasers by the introduction of gain coupling,” IEEE Photon. Technol. Lett. 2, 170–172 (1990).
[CrossRef]

J. Appl. Phys. (1)

H. Kogelnik, C. V. Shank, “Coupled wave theory of distributed-feedback lasers,” J. Appl. Phys. 43, 2327–2335 (1972).
[CrossRef]

Other (2)

G. Morthier, P. Vankwikelberge, Handbook of Distributed Feedback Laser Diodes (Artech House, Norwood, Mass., 1997), Chap. 3.

A. Suzuki, K. Tada, “Theory and experiment on distributed-feedback lasers with chirped grating,” in Guided-Wave Optical and Surface Acoustic Wave Devices, Systems and Applications, C. S. Tsai, ed., Proc. SPIE239, 10–18 (1980).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (15)

Fig. 1
Fig. 1

Schematic of a dephased complex-coupled DFB laser.

Fig. 2
Fig. 2

Plot of δl as a function of dephasing of an AR-coated complex-coupled DFB laser for three coupling strengths.

Fig. 3
Fig. 3

Normalized gain margin as a function of dephasing in an AR-coated complex-coupled DFB laser for three coupling strengths.

Fig. 4
Fig. 4

Plot of δl as a function of dephasing for several facet reflectivities.

Fig. 5
Fig. 5

Gain margin versus dephasing for several facet reflectivities.

Fig. 6
Fig. 6

Plot of δl as a function of the ratio |κ g |/|κ n | for three coupling coefficients for AR-coated facets.

Fig. 7
Fig. 7

Gain margin as a function of the ratio |κ g |/|κ n | for three coupling coefficients for AR-coated facets.

Fig. 8
Fig. 8

Plot of δl as a function of the ratio |κ g |/|κ n | for several coupling coefficients for cleaved facets. r 1 and r 2 were taken as 0.1, and φ1 and φ2 were set as zero.

Fig. 9
Fig. 9

Gain margin as a function of the ratio |κ g |/|κ n | for several coupling coefficients for cleaved facets. r 1 and r 2 were taken as 0.1, and φ1 and φ2 were set as zero.

Fig. 10
Fig. 10

Variation of δl as a function of the phase of facet reflectivity r 1. The magnitude of r 1 is 0.1, and the values of r 2 are as shown. The phase of r 2 is 0.

Fig. 11
Fig. 11

Gain margin as a function of facet reflectivity r 1. The magnitude of r 1 is 0.1, and the values of r 2 are as shown. The phase of r 2 is 0.

Fig. 12
Fig. 12

Variation of δl as a function of the magnitude of facet reflectivity r 1. The phase of r 1 and r 2 is zero.

Fig. 13
Fig. 13

Gain margin as a function of the magnitude of facet reflectivity r 1. The phase of r 1 and r 2 is zero.

Fig. 14
Fig. 14

CF number of an AR-coated complex-coupled DFB laser versus (a) dephasing |κ g |l = 0.5 and |κ n |l = 1.0 and (b) ratio |κ g |/|κ n |, |κ|l = 1.0.

Fig. 15
Fig. 15

Normalized threshold gains g th l versus δl of a CG DFB laser for four chirping factors.

Equations (17)

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

dAzdz=iΔβAz+iκabBz,
dBzdz=-iΔβBz+iκbaAz,
κab=κg+iκn,
κba=κg*+iκn*,
d2Azdz2=-pAz,
d2Bzdz2=-pBz,
k kk-1akzk-2=-p k akzk.
ak=-pak-2kk-1  k=2, 3,.
Az=α1k akzk+α2k bkzk,
ak, bk=-p ak-2, bk-2kk-1  k=2, 3,.
Bz=1iκabα1k kakzk-1-iΔβ k akzk+α2k kbkzk-1-iΔβ k bkzk.
iκab+r1Δβa0-r1b1k kaklk-1-iΔβ+κabr2k aklkk kbklk-1-iΔβ+κabr2k bklkα1α2=0.
ia0κab+r1Δβk kbklk-1-iΔβ+κabr2k bklk+r1b1k kaklk-1-iΔβ+κabr2k aklk=0.
Λz=Λ0+Λ1z,
βz=πΛzβ01-Λ1Λ0 z,
dAzdz=iΔβ+2 Λ1Λ0 β0zAz+iκabBz
dBzdz=-iΔβ+2 Λ1Λ0 β0zBz+iκbaAz.

Metrics