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 g1mod (first subband transition, solid curves) and g2mod (second subband transition, broken curves) versus N for various well widths Lz (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 Lz = 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
PDF ArticleMore Like This
Jijo P. Ulahannan, Manu P. John, and V. M. Nandakumaran
JWC43 Frontiers in Optics (FiO) 2007
R. Müller
PTh084 International Quantum Electronics Conference (IQEC) 1992
M. A. NEWKIRK, KERRY J. VAHALA, T. R. CHEN, and AMNON YARIV
WG1 Conference on Lasers and Electro-Optics (CLEO:S&I) 1989