# Two-State Lasing in Microdisk Laser Diodes with Quantum Dot Active Region
## 3 Results and Discussion
### Comparison of BA and Microdisk Lasers  
Returning to microdisk lasers, one can suggest the total loss in lasers with a diameter of 14 \(\upmu\)m is equal to \(\alpha_{GS}^{max}\). It is natural to assume that the internal losses in the lasers of stripe geometry and in the microdisks are of the same value. If so, then the dependence of total optical loss on the diameter of the microdisk lasers under study can be described by the following equation:  
\[\alpha_{n-disk}=\frac{A}{D}+\alpha_{in}, \tag{3}\]  
where \(A\) is a coefficient which describes the combined effect of sidewall roughness scattering and near-surface absorption. The value of the coefficient \(A=421\) cm\({}^{-1}\)\(\times\)\(\upmu\)m was determined, taking into account that the loss reaches its maximum value \(\alpha_{GS}^{max}\) when the diameter is equal to the critical one:  
\[A=(\alpha_{GS}^{max}-\alpha_{in})D_{\mathrm{ES1}}. \tag{4}\]  
In [28], it was found that the optical loss in microdisk lasers with a dense array of InGaAs QDs is inversely proportional to the diameter with the coefficient \(A\) of 2000 cm\({}^{-1}\)\(\times\)\(\upmu\)m. The modelling revealed that for those microdisk lasers, sidewall scattering is responsible for (16-390) cm\({}^{-1}\)\(\times\)\(\upmu\)m, while the main contribution to the value of \(A\) (\(\sim\)1700 cm\({}^{-1}\)\(\times\)\(\upmu\)m) is made by absorption by empty QDs in the near-surface region. The fact that the surface density of the InAs/InGaAs QDs in the microdisk lasers under study is approximately five times lower compared to that of [31] can explain a lower value of \(A\) in the former case. Using the parameter \(A\), as well as the value of the maximum optical loss \(\alpha_{\mathrm{ESI}}^{max}\), estimated from the stripe lasers, it can be assumed that in microlasers of an even smaller diameter (7 \(\upmu\)m or less), lasing will begin at the ES2 optical transition. It should be noted that the onset of two-state lasing is determined by the occupation of the QD states, which, in turn, depends not only on loss, but also on the saturated (maximum) modal gain of the active region. Thus, it is easier to achieve two-state lasing in a laser heterostructure with a lower saturated gain. Accordingly, the critical diameter will increase.  
It is interesting to compare the threshold current densities obtained for the microdisk and the stripe lasers. These data are presented in Figure 6. It is seen that the lowest values of the threshold current density among microdisk lasers of the same diameter are in good agreement with those of the BA lasers. This indicates that nonradiative recombination at the side walls of the microdisks is insignificant. Otherwise, surface recombination would lead to higher threshold current densities in all microdisks. A number of microdisk laser data points, for which the threshold current density values exceed those for stripe lasers, can be attributed to a non-reproducibility of the manufacturing process of microdisk lasers. For example, this can lead to increased light scattering on the side walls and, consequently, to higher optical losses compared to its nominal value.