Spectral hole-burning and nonlinear-gain decrease in a band-to-level transition semiconductor laser

Frequency characteristics of a nonlinear lasing gain under the condition that a laser oscillation exists at a fixed frequency are theoretically obtained on the basis of a band-to-level transition model (without the
k
- selection rule) of semiconductor lasers. This nonlinear gain exhibits a spectral hole-burning in the vicinity of oscillation frequency as well as a decrease from the corresponding linear gain over the entire spectral region. The analysis uses a semiclassical density-matrix formalism and a perturbation method. The lasing transitions are assumed to occur between a conduction-band Bloch state and a localized acceptor level. The above-defined nonlinear gain is obtained from a third-order perturbation calculation. In the neighborhood of a lasing frequency, a narrow spectral region where the gain is burned is theoretically found (hole-burning effect). The width of this "hole" increases with the relaxation rate at acceptor states, and is almost independent of excitation level. The gain decrease over the entire spectral region results from the absence of the
k
-selection rule, and corresponds to the saturation of spontaneous emission after the onset of lasing. Rapid relaxations in the conduction band and lower acceptor concentrations make more significant gain decreases at a frequency sufficiently apart from the lasing frequency. This effect makes possible a single axial-mode operation in some cases.