# Impact of Device Topology on the Performance of High-Speed 1550 nm Wafer-Fused VCSELs
## 3 Results and Discussion
### Small-Signal Modulation  
To analyze the electrical reflection (\(S_{11}\) parameter) and small-signal modulation response (\(S_{21}\) parameter), a Rohde & Schwarz ZVA 40 network analyzer and a 25 GHz New Focus 1434 photodetector were used. The VCSELs emission was coupled to a single-mode fiber (SMF) and detected by a Newport 1414-50 photodetector with a 25 GHz bandwidth. A 65 GHz Anritsu V255 bias tee and 40 GHz Picoprobe 40A-GSG-125-P RF probe were used to modulate the VCSELs current. A three-pole transfer function characterizing the laser response to sinusoidal modulation of the drive current at a given frequency \(f\): \(H(f)\propto f_{\mathrm{R}}{}^{2}/(f_{\mathrm{R}}{}^{2}-f^{2}+j\gamma(f/2\pi))(1+ j(f/f_{\mathrm{P}}))\), where \(f_{\mathrm{R}}\) is the relaxation resonance frequency, \(\gamma\) is the intrinsic damping factor, and \(f_{\mathrm{P}}\) is the parasitic cutoff frequency, was used to extract the key intrinsic parameters of the VCSEL. To minimize the error in recovering the laser intrinsic parameters from the \(S_{21}\) data, the cutoff frequency was independently determined from the VCSEL equivalent electrical circuit, and the parameters were extracted from the \(S_{11}\) data. Carrier injection through intracavity contacts forces to use an equivalent circuit with distributed parameters, which in turn makes the inverse problem nontrivial (convergence to different local minima). A slight increase in the number of lumped elements in the VCSEL equivalent circuit can potentially improve the quality of the experimental data fit [17]. Figure 5 depicts the results of the small-signal frequency analysis and the intrinsic modulation parameters determined from the measured \(S_{21}(f)\) for lasers of \(L\)-type topology at 20 \({}^{\circ}\)C.  
The \(-3\) dB modulation bandwidth \(f_{-3\mathrm{dB}}\) is 6 GHz at a drive current of 4.5 mA and saturates at \(\sim\)8 GHz (see Figure 5c). The modulation current efficiency, calculated by MCEF =\(f_{-3\mathrm{dB}}/(I-I_{\mathrm{th}})^{15}\), is 3.6 GHz/mA [5]. These results compare well with data for 1550 nm WF VCSELs based on thick InAlGaAs QWs and an In(Al)GaAs TJ [34]. If one increases the drive current above 6 mA, the \(f_{\mathrm{R}}\) value then exceeds the modulation bandwidth and yields around 12 GHz. The \(D\)-factor, determined as \(D=f_{\mathrm{R}}/(I-I_{\mathrm{th}})^{0.5}\), is 3.2 GHz/(mA) [5]. Figure 5: The 1550 nm InGaAs QW-based WF VCSEL with 6 \(\upmu\)m BTJ diameter and \(L\)-type device topology: (**a**) measured (points) and fitted (solid lines) \(S_{21}\) versus frequency dependencies for different drive currents; (**b**) parasitic cutoff frequency as function of drive currents extracted from microwave reflection \(S_{11}\); (**c**)\(f_{\mathrm{R}}\) and modulation bandwidth as function of the square root of the drive current above threshold; (**d**) damping versus \(f_{\mathrm{R}}{}^{2}\) value. The temperature is fixed at 20 \({}^{\circ}\)C.  
Figure 5d shows the dependence of the intrinsic damping factor \(\gamma\) on the square of the relaxation resonance frequency \(f_{\mathrm{R}}\)\({}^{2}\). Because the contribution of spontaneous emission to the lasing mode beyond the laser threshold and the effects of self-heating and gain saturation at large drive currents can be neglected at moderate photon densities, one can characterize the \(\gamma\)(\(f_{\mathrm{R}}\)\({}^{2}\)) dependences by linear fit: \(\gamma=Kf_{\mathrm{R}}\)\({}^{2}+\gamma_{0}\), where \(\gamma_{0}\) is the damping offset. As a result, the \(K\)-factor is determined to be 0.46 ns, which exceeds the \(K\) value for 1550 nm VCSELs based on thick InAlGaAs QWs and an InAlGaAs TJ [34] and 1550 nm WF VCSELs based on InGaAs QWs and an InAlGaAs TJ [36], showing similar differential efficiencies.