Refractive index to gain derivative ratio in GaAs/GaAIAs semiconductor injection lasers

A linear dependence of refractive index n¿ and gain coefficient g on carrier density N has been widely used by many authors in the investigation of the dynamic behaviour of semiconductor injection lasers. In the paper, it is proposed that the variation of real refractive index with carrier density should be linear, while the variation of gain coefficient with carrier density should be logarithmic. This gives an expression for the gain to refractive index derivative ratio ¿ that is proportional to N, with a constant of proportionality A. Quantitative estimates are made of the variations of real refractive index and gain with carrier density in the GaAs/GaAIAs double-heterostructure laser, with active layer p-doping equal to 4 × 1017 cm¿3, operating at 297 K. It is found that the value of ¿n¿ should lie anywhere between ¿0.01 and ¿0.05, and the value of ¿n¿/¿N should lie between ¿1.2 × 10¿20 cm3 and ¿1.6 × 10¿20 cm3. Here, ¿n¿ is the change in the real part of the complex refractive index from the `background¿ effective refractive index, and ¿n¿/¿N is the variation of the real refractive index with carrier density. The value of A does not depend critically on the wave number, but on the ratio N0/¿ where N0 (cm¿3) is the carrier density for transparency at the wavelength concerned and ¿ (cm¿1) is the gain constant. The graph of A against N0/¿ is plotted, from which the value of A may be determined for a given value of N0/¿