Theoretical and experimental study of optical gain, refractive index change, and linewidth enhancement factor of p-doped quantum-dot lasers

A theoretical and experimental study of the optical gain, refractive index change, and linewidth enhancement factor (LEF) of a p-doped quantum-dot (QD) laser is reported. These parameters are measured by injecting an external pump, which induces cross-gain and cross-phase modulation. A comprehensive theoretical model for the optical gain and refractive index change of InAs QD lasers is introduced with the quasi-equilibrium approximation of carrier distribution. We use the Gaussian lineshape function for gain change and the confluent hypergeometric function of the first kind for refractive index change, which satisfies the Kramers-Kronig relation. We match the experimental data with the theoretical results when the thermal effect is isolated by an additional pulsed current measurement. We also calculate theoretically the optical gain, refractive index change, and LEF of an undoped QD laser of the same structure except the absence of p-type doping. We show that the differential gain and LEF of the p-doped QD laser are improved compared with those of the undoped QD laser due to the reduced transparency carrier density