Analysis of gain suppression in undoped injection lasers

This paper gives an analysis and discussion of gain suppression in injection lasers which have an undoped active region and an index guiding structure. In previous papers, we used a semiclassical density-matrix analysis to show that an injection laser with an updoped active region has a nearly, but not perfectly, homogeneous (or uniform) gain property under operating conditions due to the mode coupling effects by phase synchronization of electrons to the lasing field. The gain of adjacent modes is well suppressed by the oscillating mode, and single-longitudinal-mode operation is obtained in undoped injection lasers. However, such suppression depends closely on the spacial distribution of the resonating field and injected carrier density. In this paper, the suppression effect is examined theoretically considering electronic intraband relaxation, effects from the standing wave of the lasing field, spatial diffusion of carriers, etc. When the relaxation time is larger than 3×10^-13 sec, the gain shows ''hole burning,'' namely, strong nonuniformity across the spectral or energy distributions, and, at the same time, the gain of some resonating modes is increased. Single-longitudinal-mode operation is not obtained in such a strongly inhomogeneous laser. When the relaxation time is smaller than 2×10^-13 sec, the gain can be seen to be nearly homogeneous, and the gain of nonoscillating modes is sufficiently suppressed, that is, lower than that at threshold, because of the strong-mode-coupling effect. The relaxation time of GaAs is expected to be approximately 1×10^-13 sec, implying 0.1% of excess suppression. The spatial distribution of the resonating field and induced ''spatial hole burning'' of carriers tends to increase the gain of higher transverse modes, but only weakly affects the fundamental transverse modes when the oscillating mode is the fundamental mode. It is then necessary to design the laser so that such higher transverse modes are cut off. The results of this analysis explain the experimental data of well-designed lasers which have an undoped active region and an index guiding structure. Such a gain suppression effect is crucial for the operation of injection lasers in a single-longitudinal mode.