Effect of an excited-state optical transition on the linewidth enhancement factor of quantum dot lasers

An analytical expression is derived for the linewidth enhancement factor of a quantum-dot laser, which makes it possible to describe its dependence on optical loss and photon density in an explicit form. The model accounts for refractive index variations at the ground-state optical transition due to gain/absorption variations upon the first excited-state transition in quantum dots. It is shown that a decrease in optical loss, an increase in saturated gain, and an increase in the energy separation between the excited-state and ground-state transitions results in a decrease in the $\alpha$ factor both at and above the lasing threshold.