7 July 1998 Theoretical study of the perturbation-expanded higher-order nonlinear gain coefficients in injection semiconductor lasers
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In the recent established theories of semiconductor lasers, the gain is analyzed basing on a third order perturbation theory in which the gain suppression is approximated by the third order. The limitation of applying such theories stands on the limited range of the applied injection current. To extend the application to higher ranges of the injection current, we go beyond the third order towards an infinite gain expansion, presenting full analysis and discussion of the gain suppression basing on a two-mode model. Formulas for general terms of the density matrix and gain are reported. A general formula for the gain of a non- oscillating mode is presented and is shown to reduce to the previously reported formulas in cases of homogeneous and inhomogeneous broadening in a single mode operation. Numerical discussion of the unsuppressed, linear, and suppressed gain as well as the contribution of the higher order gain terms is presented. Furthermore, simplified and convenient expressions of the different orders of the gain expansion are investigated basing on the numerical results. A criterion to truncate the expansion is then investigated basing on the magnitude of the applied range of the injection current. The gain can be represented only by a third order expansion in the conventional range of the injection current up to about 7 of its threshold value Ith within accuracy less than 0.1%, while the 5-th order expansion gives accurate description at higher current values up to about 25 Ith. The higher order terms have to be included in the gain expansion at the higher ranges of the injection current to get more exact gain analysis.
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Moustafa Ahmed, Moustafa Ahmed, Minoru Yamada, Minoru Yamada, } "Theoretical study of the perturbation-expanded higher-order nonlinear gain coefficients in injection semiconductor lasers", Proc. SPIE 3283, Physics and Simulation of Optoelectronic Devices VI, (7 July 1998); doi: 10.1117/12.316699; https://doi.org/10.1117/12.316699


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