RETRACTED ARTICLE: Mode-competition phenomena among longitudinal modes in semiconductor lasers under the effect of external optical feedback

Abstract

Comprehensive theoretical investigation of the influence of external optical feedback on the dynamics of semiconductor lasers are introduced. The analyses are based on numerical simulation of the multimode rate equations superposed by Langevin noise sources that are generated in such a way as to keep the correlation of the modal photon number with the injected electron number. The gain saturation effect which causes mode-competition phenomena among longitudinal modes are considered in our multimode rate equation model. The dynamics of modes and the characteristics of the output spectrum are investigated for strong external optical feedback strength. Numerically simulated results show that the mode-competition phenomena induce quasi-periodic hopping among several longitudinal modes which reveals multimode-like output spectra in lasers. This mode-hopping phenomena is described in terms of asymmetric gain saturation effect.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3

References

  1. 1.

    M. Yamada, K. Hayano, H. Ishiguro, Y. Suematsu, An approximate analysis of gain suppression in injection lasers for band-to-band and band-to-impurity-level transitions. Jpn. J. Appl. Phys. 18, 1531–1541 (1979)

    ADS  Article  Google Scholar 

  2. 2.

    M. Yamada, H. Nagato, Analysis of longitudinal mode behavior around the threshold level in undoped injection lasers. Trans. Inst. Electron. Commun. Eng. Japan E64, 770–777 (1981)

    Google Scholar 

  3. 3.

    M. Yamada, Transverse and longitudinal mode control in semiconductor injection lasers. IEEE J. Quantum Electron. QE-19, 1365–1380 (1983)

    ADS  Article  Google Scholar 

  4. 4.

    M. Nakamura, K. Aiki, N. Chinone, R. Ito, J. Umeda, Longitudinal-mode behaviors of mode-stabilized Al Ga As injection lasers. J. Appl. Phys. 49, 4644–4648 (1978)

    ADS  Article  Google Scholar 

  5. 5.

    M. Yamada, Y. Suematsu, A condition of single longitudinal mode operation in injection lasers with index-guiding structure. IEEE J. Quantum Electron. QE-15, 743–749 (1979)

    ADS  Article  Google Scholar 

  6. 6.

    M. Yamada, Y. Suematsu, Analysis of gain suppression in undoped injection lasers. J. Appl. Phys. 52, 2653–2664 (1981)

    ADS  Article  Google Scholar 

  7. 7.

    J. Buus, Single Frequency Semiconductor Lasers (SPIE, Bellingham, WA, 1991)

    Google Scholar 

  8. 8.

    T.P. Lee, C.A. Burrus, J.A. Copeland, A.G. Dentai, D. Marcuse, Short-cavity InGaAsP injection lasers: Dependence of mode-spectra and single-longitudinal mode power on cavity length. IEEE J. Quantum Electron. QE-18, 1101–1113 (1982)

    ADS  Google Scholar 

  9. 9.

    I. Mito, M. Kitamura, K. Kaede, Y. Odagiri, M. Seki, M. Sugimoto, K. Kobayashi, InGaAsP planar heterostructure laser diode (PBH-LD) with very low threshold current. Electron. Lett. 18, 2–3 (1982)

    ADS  Article  Google Scholar 

  10. 10.

    S. Ogita, A.J. Lowery, R.S. Tucker, Influence of asymmetric nonlinear gain on the transient of longitudinal modes in long wavelength Fabry–Perot laser diodes. IEEE J. Quantum Electron. 33, 198–210 (1997)

    ADS  Article  Google Scholar 

  11. 11.

    M. Ahmed, M. Yamada, Influence of instantaneous mode competition on the dynamics of semiconductor lasers. IEEE J. Quantum Electron. 38, 682–693 (2002)

    ADS  Article  Google Scholar 

  12. 12.

    M. Yamada, W. Ishimori, H. Sakaguchi, M. Ahmed, Time-dependent measurement of the mode-competition phenomena among longitudinal modes in long-wavelength lasers. IEEE J. Quantum Electron. 39(12), 1548–1554 (2003)

    ADS  Article  Google Scholar 

  13. 13.

    M. Yamada, Theory of mode competition noise in semiconductor lasers. IEEE J. Quantum Electron. QE-22, 1052–1059 (1986)

    ADS  Article  Google Scholar 

  14. 14.

    G. Gray, R. Roy, Noise in nearly-single-mode semiconductor lasers. Phys. Rev. A 40, 2453–2461 (1989)

    ADS  Article  Google Scholar 

  15. 15.

    M. Alalusi, R.B. Darling, Effect of nonlinear gain on mode-hopping in semiconductor laser diodes. IEEE J. Quantum Electron. 31, 1181–1192 (1995)

    ADS  Article  Google Scholar 

  16. 16.

    G.P. Agrawal, Effect of gain nonlinearites on periodic doubling and chaos in directly modulated semiconductor lasers. Appl. Phys. Lett. 49, 1013–1015 (1986)

    ADS  Article  Google Scholar 

  17. 17.

    M. Yamada, N. Nakaya, M. Funaki, Characteristics of mode-hopping noise and its suppression with the help of electric negative feedback in semiconductor lasers. IEEE J. Quantum Electron. QE-23, 1297–1302 (1987)

    ADS  Article  Google Scholar 

  18. 18.

    G.P. Agrawal, G.R. Gray, Effect of phase-conjugate feedback on the noise characteristics of semiconductor lasers. Phys. Rev. A 46, 5890–5898 (1992)

    ADS  Article  Google Scholar 

  19. 19.

    G.R. Gray, D. Haung, G.P. Agrawal, Chaotic dynamics of semiconductor lasers with phase-conjugate feedback. Phys. Rev. A 47, 2096–2105 (1994)

    ADS  Article  Google Scholar 

  20. 20.

    M. Yamada, Computer simulation of feedback induced noise in semiconductor lasers operating with self-sustained pulsation. IEICE Trans. E81-C, 768–780 (1998)

    Google Scholar 

  21. 21.

    M. Ahmed, M. Yamada, S. Abdulrhmann, A multimode simulation model of mode-competition low-frequency noise in semiconductor lasers. Fluct. Noise Lett. 1, L163–L170 (2001)

    Article  Google Scholar 

  22. 22.

    R. Lang, K. Kobayashi, External optical feedback effects on semiconductor injection laser properties. IEEE J. Quantum Electron. QE-16(3), 347–355 (1980)

    ADS  Article  Google Scholar 

  23. 23.

    S.M.S. Imran, Numerical analysis of optical feedback noise and its reduction in semiconductor lasers, Doctoral Dissertation, Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa, Japan (2013)

  24. 24.

    M. Yamada, Theoretical analysis of nonlinear optical phenomena taking into account the beating vibration of the electron density in semiconductor lasers. J. Appl. Phys. 66(1), 81–89 (1989)

    ADS  Article  Google Scholar 

  25. 25.

    N. Schunk, K. Petermann, Noise analysis of injection-locked semiconductor injection lasers. IEEE J. Quantum Electron. QE-22, 642–650 (1986)

    ADS  Article  Google Scholar 

  26. 26.

    D. Lenstra, M. Yousefi, Rate-equation model for multi-mode semiconductor lasers with spatial hole burning. Optics Express, 22(7), 8143–8149 (2014)

    ADS  Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Sazzad M. S. Imran.

Additional information

The authors have retracted this article [1] because the article shows significant overlap with a previously published article by Ahmed and Yamada [2]. All authors agree to this retraction.

[1] Imran, S.M.S., Hassan, N., Rahman, S., Meshuk, MB. Mode-competition phenomena among longitudinal modes in semiconductor lasers under the effect of external optical feedback. Appl. Phys. B 124: 220 (2018) https://doi.org/10.1007/s00340-018-7088-5

[2] Ahmed, M., Yamada, M. Influence of instantaneous mode competition on the dynamics of semiconductor lasers. IEEE J Quantum Electron. 38, 682-693 (2002) https://doi.org/10.1109/JQE.2002.1005419

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Imran, S.M.S., Hassan, N., Rahman, S. et al. RETRACTED ARTICLE: Mode-competition phenomena among longitudinal modes in semiconductor lasers under the effect of external optical feedback. Appl. Phys. B 124, 220 (2018). https://doi.org/10.1007/s00340-018-7088-5

Download citation