An infinite order perturbation approach to gain calculation in injection semiconductor lasers

Nonlinear gain in injection semiconductor lasers is analyzed by applying an infinite order perturbation treatment to the density matrix analysis and taking in account the electron relaxation processes in single-mode operation. The infinitely expanded gain can be applied to future laser developments having much lower threshold current. Formulas for linear and higher orders of the expanded density matrix element and for their corresponding orders of the gain coefficient are investigated. The infinitely expanded gain is obtained in closed form which, in general, cannot be handled analytically. This closed form is simplified in the simple case of plane-wave fields and is approximated to the previously reported gain formulas within limits of perfectly homogeneous and inhomogeneous gain broadening. Numerical examples are given for the case of GaAs lasers having a specified intraband relaxation time. Based on these numerical results, simplified expressions are presented for linear and higher orders of the gain coefficient in terms of the injected carrier number. Furthermore, numerical criteria to truncate the infinite gain expansion for different higher orders are investigated based on the values of the lasing power. In the case of conventional semiconductor lasers, where the injection current is up to three times its threshold value, the third-order gain expansion corresponds to the infinitely expanded gain. However, the fifth-order expansion gives a more accurate description at higher current up to ten times the threshold. More exact gain analysis at higher ranges of the injection current requires higher orders in the gain expansion. (C) 1998 American Institute of Physics..