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.
Similar content being viewed by others
References
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)
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)
M. Yamada, Transverse and longitudinal mode control in semiconductor injection lasers. IEEE J. Quantum Electron. QE-19, 1365–1380 (1983)
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)
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)
M. Yamada, Y. Suematsu, Analysis of gain suppression in undoped injection lasers. J. Appl. Phys. 52, 2653–2664 (1981)
J. Buus, Single Frequency Semiconductor Lasers (SPIE, Bellingham, WA, 1991)
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)
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)
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)
M. Ahmed, M. Yamada, Influence of instantaneous mode competition on the dynamics of semiconductor lasers. IEEE J. Quantum Electron. 38, 682–693 (2002)
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)
M. Yamada, Theory of mode competition noise in semiconductor lasers. IEEE J. Quantum Electron. QE-22, 1052–1059 (1986)
G. Gray, R. Roy, Noise in nearly-single-mode semiconductor lasers. Phys. Rev. A 40, 2453–2461 (1989)
M. Alalusi, R.B. Darling, Effect of nonlinear gain on mode-hopping in semiconductor laser diodes. IEEE J. Quantum Electron. 31, 1181–1192 (1995)
G.P. Agrawal, Effect of gain nonlinearites on periodic doubling and chaos in directly modulated semiconductor lasers. Appl. Phys. Lett. 49, 1013–1015 (1986)
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)
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)
G.R. Gray, D. Haung, G.P. Agrawal, Chaotic dynamics of semiconductor lasers with phase-conjugate feedback. Phys. Rev. A 47, 2096–2105 (1994)
M. Yamada, Computer simulation of feedback induced noise in semiconductor lasers operating with self-sustained pulsation. IEICE Trans. E81-C, 768–780 (1998)
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)
R. Lang, K. Kobayashi, External optical feedback effects on semiconductor injection laser properties. IEEE J. Quantum Electron. QE-16(3), 347–355 (1980)
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)
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)
N. Schunk, K. Petermann, Noise analysis of injection-locked semiconductor injection lasers. IEEE J. Quantum Electron. QE-22, 642–650 (1986)
D. Lenstra, M. Yousefi, Rate-equation model for multi-mode semiconductor lasers with spatial hole burning. Optics Express, 22(7), 8143–8149 (2014)
Author information
Authors and Affiliations
Corresponding author
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
About this article
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
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00340-018-7088-5