# Research on Improving Optical Field Distribution of TOSA Based on 3D Defocusing Coupling
## 4 Verification of 3D Defocusing Coupling Model  
### Designing of Model  
The LD TO is 10 G DFB ML768K42T-91 from Mitsubishi, and the TO is welded onto a stainless body with energy storage welding. The adapter is an XMD (10 Gbit/s Miniature Device) -type receptacle with SMF-28e fiber. A single-stage free-space isolator is assembled in the receptacle. After coupling with the LD TO, the receptacle is welded onto the body through the stainless ring. Then, the TOSA is completed (see Table 2). The 2D and 3D beam quality of a set of LD TO is tested by a slit sweep beam quality analyzer, as shown in Figures 9 and 10. The test data are shown in Table 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Part** & **Parameter** & **Symbol** & **Specification** \\ \hline \multirow{3}{*}{LD} & Wavelength & \(\lambda\) & 1310 nm \\  & Far field divergence Angle & \(\theta_{\parallel}\) & 25\({}^{\circ}\) \\  & & \(\theta_{\perp}\) & 30\({}^{\circ}\) \\ \hline \multirow{3}{*}{Ball lens} & Refractive index & n & 1.5 \\  & Radius & R & 0.75 \\ \hline \multirow{2}{*}{Single Mode Fiber (SMF)} & Index of Core in SMF & n\({}_{\text{SMF}}\) & 1.468 \\  & Mode field radius of SMF & \(\omega_{\text{SMF}}\) & 4.6 \(\mu\)m \\ \hline \multirow{2}{*}{Isolator} & Clear aperture & CD & 0.5 mm \\ \hline \multirow{2}{*}{Working distance} & Distance of LD-lens & L1 & 1.13 mm \\  & Distance of fiber-lens & L2 & 3 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of TOSA. Figure 8: The optical field distribution of fiber moving up in \(Z\)-axis. (**a**) is the distribution of optical field when the end-face of fiber is at the focal point of the LD TO, \(Z=0\)\(\mu\)m. (**b**) is the distribution of optical field at the maximum power where the fiber moves up 60 \(\mu\)m along \(Z\)-axis, \(Z=60\)\(\mu\)m. (**c**) is the distribution of optical field at the maximum power where the fiber moves up 120 \(\mu\)m along \(Z\)-axis, \(Z=120\)\(\mu\)m.  
Figure 10: Beam quality of 3D. The 3D spatial power energy distribution of LD TO are tested by 3D beam analyzer. (**a**) is the beam quality of 3D shown in Figure 9a, and (**b**) is the beam quality of 3D shown in Figure 9b. \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Sample** & \begin{tabular}{l} **Beam Width** \\ **Limiting X (\(\upmu\)m)** \\ \end{tabular} & \begin{tabular}{l} **Beam Width** \\ **Limiting Y (\(\upmu\)m)** \\ \end{tabular} & \begin{tabular}{l} **Gaussian** \\ **Intensity X (\%)** \\ \end{tabular} & \begin{tabular}{l} **Gaussian** \\ **Intensity Y (\%)** \\ \end{tabular} & \
\begin{tabular}{l} **Gaussian** \\ **Diameter X (\(\upmu\)m)** \\ \end{tabular} &
\begin{tabular}{l} **Gaussian** \\ **Diameter Y (\(\upmu\)m)** \\ \end{tabular} \\ \hline
1 & 770.3 & 814.5 & 95.5 & 92.6 & 783.5 & 839.8 \\
2 & 774.1 & 817.9 & 95.7 & 92.4 & 781.9 & 839.7 \\
3 & 892.7 & 930.2 & 95.8 & 92.6 & 895.6 & 947.4 \\
4 & 894.8 & 930.9 & 95.8 & 92.7 & 894.6 & 944.7 \\
5 & 886.3 & 925.8 & 95.4 & 93.1 & 906.1 & 901.1 \\
6 & 890.2 & 925.2 & 95.7 & 92.7 & 906.9 & 900.2 \\
7 & 1019.1 & 1077.7 & 95.2 & 92.5 & 917.7 & 952.6 \\
8 & 1019.2 & 1074.2 & 95.3 & 92.6 & 914.8 & 949 \\
9 & 753.8 & 810.4 & 95.8 & 92.4 & 765.7 & 796.6 \\
10 & 755.2 & 810.1 & 95.8 & 93.1 & 766.3 & 797.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Data of beam quality. Figure 9: Beam quality of 2D. The horizontal axis and the vertical axis are the spatial coordinates of the 2D beam analyzer, and the (0,0) is the central point. The horizontal axis represents the direction of \(\theta_{\parallel}\), and the vertical axis represents the direction of \(\theta_{\perp}\). The color represents the energy. (**a**) is the beam quality of 2D with the central point offsetting (0,0) because the chip is bonded within the tolerance. (**b**) is the beam quality of 2D without the central point offsetting. From the beam quality data, the Gaussian diameter after converging through the lens is relatively large, mainly because of the large divergence angle of the LD and the large aberration caused by the ball lens.