Effect of excited-state transitions on the threshold characteristics of a quantum dot laser

The general relationship between the gain and spontaneous emission spectra of a quantum dot (QD) laser is shown to hold for an arbitrary number of rad iative transitions and an arbitrary QD-size distribution, The effect of mic roscopic parameters (the degeneracy factor and the overlap integral for a t ransition) on the gain is discussed. We calculate the threshold current den sity and lasing wavelength as a function of losses. The conditions for a sm ooth or step-like change in the lasing wavelength are described. We have si mulated the threshold characteristics of a laser based on self-assembled py ramidal InAs QDs in the GaAs matrix and obtained a small overlap integral f or transitions in the QDs and a large spontaneous radiative lifetime. These are shown to be a possible reason for the low single-layer modal gain, whi ch limits lasing via the ground-state transition for short (several hundred s of micrometers) cavity lengths.