Abstract

This paper deals theoretically with light emission from GRIN-SCH single-quantum-well diode lasers where the optical transitions between the first subbands (n=1) as well as between the second ones (n=2) are taken into account, see Fig.1. The mathematical model consists of three rate equations describing the time evolution of the carrier concentration N and the photon densities P₁, P₂ at the frequencies γ₁ = E₁/h and γ₂ = E₂/h, Moreover, nonlinear gain suppression depending on P₁ and P₂ and noise terms are considered too. In addition, algebraic equations are used giving the gain at the two frequencies of interest in dependence on the time-varying electron and heavy-hole concentration via the Fermi-Dirac distribution functions. Since the nonlinear gain flattening effect /1/ is larger for γ₁ than for γ₂ the gain at γ₂ will succeed that at γ₁ for sufficiently large values of N. Hence it depends on the threshold value of N (or on the laser losses respectively) if stationary laser action is reached at frequency γ₁ or γ₂. Fig. 2 shows the static maximum modal gain g_1mod (first subband transition, solid curves) and g_2mod (second subband transition, broken curves) versus N for various well widths L_z (10, 15, and 20 nm). Some loss levels are indicated by broken horizontal lines (a,…,d) crossing both the gain curves for each well width. For a constant injection current these crossing points relate to stationary stable or unstable solutions. For example, the points marked C₁ and D₂ belong to stable stationary solutions for P₁ (loss level c) and P₂ (level d) at L_z = 20 nm, respectively, while C₂ and D₁ relate to unstable solutions for P₂ and P₁. Relaxation oscillations to stable stationary states and the behavior of the light output in case of sinusoidal modulation of the applied current have been investigated by numerical calculations.

© 1991 Optical Society of America