## 4 EAM-VCSEL: Structure and Eigenmodes
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Section** & **Repetition** & **Thickness (nm)** & **Ref. Index** & **Loss (cm\({}^{-1}\))** \\ \hline Top & 1 & 50 & 3.642 & 25 \\ \hline \multirow{3}{*}{Top DBR} & 1 & 69.1 & 3.031 & 10 \\ \cline{2-5}  & 6 & 61.3 & 3.499 & 10 \\ \cline{2-5}  & 6 & 69.1 & 3.031 & 10 \\ \hline EAM clad. & 1 & \(t_{EAM}\) & 3.4939 & 0 \\ \hline EAM QW & 1 & 212.5 & 3.4939 & modulated \\ \hline EAM clad. & 1 & \(t_{EAM}\) & 3.4939 & 0 \\ \hline \multirow{3}{*}{Middle DBR} & 1 & 69.1 & 3.031 & 23 \\ \cline{2-5}  & 10 & 61.3 & 3.499 & 23 \\ \cline{2-5}  & 10 & 69.1 & 3.031 & 23 \\ \hline Contact & 1 & 201 & 3.499 & 57.5 \\ \hline \multirow{3}{*}{Middle DBR} & 12 & 69.1 & 3.031 & 23 \\ \cline{2-5}  & 12 & 61.3 & 3.499 & 23 \\ \hline \multirow{3}{*}{\(AlO_{x}\)} & 1 & 30 & 2.9975 & 23 \\ \cline{2-5}  & 1 & 55 & 3.031 & 23 \\ \hline \multirow{3}{*}{VCSEL cavity} & 1 & 90 & 3.263 & 0 \\ \cline{2-5}  & 1 & 22 & 3.379 & 0 \\ \cline{2-5}  & 1 & 25.5 & 3.642 & 0 \\ \cline{2-5}  & 1 & 22 & 3.379 & 0 \\ \cline{2-5}  & 1 & 90 & 3.263 & 0 \\ \hline \multirow{3}{*}{Bottom DBR} & 1 & 69.1 & 3.031 & 10 \\ \cline{2-5}  & 35 & 61.3 & 3.499 & 10 \\ \cline{1-1} \cline{2-5}  & 35 & 69.1 & 3.031 & 10 \\ \hline Substrate & 1 & \(\infty\) & 3.642 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Electro-absorption modulator vertical-cavity surface-emitting laser (EAM-VCSEL) structure. (decreased) confinement factor in the VCSEL (EAM) QWs similarly to [21]. Increasing the EAM absorption plays a similar role as increasing the detuning between the cavities (c.f. the similar optical power distribution for the detuned case without absorption in Figure 2b and the resonance case with large \(\alpha_{EAM}=5000\,\mathrm{cm}^{-1}\) in Figure 2c). The relevant quantities for the small-signal response Equation (14) are the derivatives \(da_{tot}/da_{EAM}\) and \(d\Gamma/da_{EAM}\). Repeating the eigenmode calculations when varying the absorption coefficient \(\alpha_{EAM}\) in the EAM QW layer, we obtain the dependence of the total absorption \(\alpha_{tot}\) of the EAM-VCSEL and the VCSEL cavity confinement factor \(\Gamma\) on the EAM absorption \(\alpha_{EAM}\) as shown in Figure 3. As can be seen from this figure, for the strongly and moderately coupled cases (blue and green curves) \(\alpha_{tot}\) and \(\Gamma\) and their derivatives are strongly nonlinear with \(\alpha_{EAM}\). Therefore, we draw the conclusion that the weak coupling case is best suited for loss modulation of the EAM-VCSEL as the device total absorption and VCSEL confinement factor are much less dependent on \(\alpha_{EAM}\). Figure 2: (color online) Optical power distributions along the EAM-VCSEL for the composed cavity mode situated primary in the VCSEL cavity and for strong—\(d_{EAM}=0.4972\,\upmu\)m (blue), moderate—\(d_{EAM}=0.5\,\upmu\)m (green) and weak—\(d_{EAM}=0.502\,\upmu\)m (red) coupling between the EAM and the VCSEL cavities. The top black line in (**a**) indicates the refractive index profile of the structure. The middle (**b**) and the bottom (**c**) panels are for absorption in the EAM QW regions of \(\alpha_{EAM}=0\,\mathrm{cm}^{-1}\) and \(\alpha_{EAM}=5000\,\mathrm{cm}^{-1}\), respectively.