# Two-State Lasing in Microdisk Laser Diodes with Quantum Dot Active Region
## 3 Results and Discussion
### Broad Area Lasers  
Estimation of loss from the spectral width of the lasing line faces difficulties caused by the uncertainty of the Henry factor, the effect of gain in the active region, and the influence of the spectral resolution of the optical measurement system. Since there is no simple formula for evaluating loss in a microdisk, it is useful to compare the microdisk characteristics with those of stripe lasers made of the same QD epitaxial wafer. Similar two-state lasing behavior has been observed for edge-emitting lasers when the stripe length shortens [33]. The critical point corresponds to the maximum optical loss, \(\alpha_{GS}^{max}\), at which GS lasing is still possible. In its turn, the value of \(\alpha_{GS}^{max}\) is close to the saturated (maximum) optical gain, which can be achieved on the GS optical transition.  
The measured lasing wavelength, threshold current density, and differential quantum efficiency of the broad-area lasers are presented in Figure 5a against the cavity length. It was found that the critical cavity length, \(L_{\text{ES1}}\), at which lasing begins at the ES1 optical transition and GS lasing disappears, is approximately 0.4 mm. It falls within the interval from 425 to 375 \(\upmu\)m, where the lasing wavelength \(\uplambda\) drops from 1259 nm (GS) to 1172 nm (ESI), respectively. For even shorter laser cavities, one more jump in the lasing wavelength down to 1099 nm is observed. This wavelength corresponds to the ES2 optical transition, and the critical cavity length, \(L_{\text{ES2}}\), falls in the range from 250 to 200 \(\upmu\)m.  
The differential quantum efficiency data for the cavity lengths of GS lasing can be fitted well by the equation:  
\[\frac{1}{\eta_{D}}=\frac{1}{\eta_{in}}\left(1+\frac{\alpha_{in}}{\frac{1}{L} \ln(1/R)}\right), \tag{1}\]  
where \(\eta_{in}=0.6\) is the internal efficiency of laser emission, \(\alpha_{in}=3.1\) cm\({}^{-1}\) is the internal optical loss, and \(R\) is the facet reflectivity, which is assumed to be 0.3. Using the obtained  
Figure 5: Threshold current density (circles), lasing emission wavelength (squares) and reciprocal differential quantum efficiency (triangles) as function of stripe laser length (**a**). Lasing spectra (not to scale) taken at different currents for 425-\(\upmu\)m-long sample (**b**).  
value of the internal loss, and taking into account that the output loss for stripe laser is \(L^{-1}\ln(1/R)\), the maximum optical loss of GS lasing can be estimated as:  
\[\alpha_{GS}^{max}=\frac{1}{L_{\mathrm{ESI}}}\ln(1/R)+\alpha_{in}. \tag{2}\]  
The calculation gives 33 \(\pm\) 2 cm\({}^{-1}\). Using Equation (2) with the critical length \(L_{\mathrm{ES2}}\) instead of \(L_{\mathrm{ESI}}\), the maximum optical loss \(\alpha_{\mathrm{ESI}}^{max}\) of ES1 lasing can be found, which is 57 \(\pm\) 6 cm\({}^{-1}\). It should be noted that the real value may be somewhat higher due to an increase in the internal loss in short laser cavities.  
It is also worth mentioning that the two-state (GS-ES1) lasing effect is pronounced in the edge-emitting lasers with the cavity lengths close to the critical one, \(L_{\mathrm{ESI}}\) or \(L_{\mathrm{ES2}}\). As an example, Figure 5b demonstrates emission spectra measured at different injections for the 425 \(\upmu\)m long laser. The ES1 emission appears already at a current of 1.15 A (2.71 kA/cm\({}^{2}\)), i.e., very close to the GS lasing threshold, which is 0.85 A (2 kA/cm\({}^{2}\)).