# Research on Improving Optical Field Distribution of TOSA Based on 3D Defocusing Coupling
## 2 Analysis of the Influence of Optical Field Distribution in TOSA
### Effect of Existing Coupling Model on the Distribution of Optical Field  
A TOSA is composed of a LD TO (Transistor-Outline) -can, metal body, isolator and receptacle. The TO-can includes a tube cap with a lens, as shown in Figure 2. If the optical power of the TOSA is required to be relatively high, a tube cap with an aspherical lens is necessary [27; 28; 29; 30]. The function of the lens is to transform the light emitted by the LD into convergent light, so that it can be more easily coupled into the fiber, as shown in Figure 1. In order to improve the optical return loss and reduce the influence of the optical reflection from the end-face of fiber to the LD, the end-face is usually processed into slop, and the angle of the slop is usually 2-8\({}^{\circ}\). The angle is decided by the requirement of coupling efficiency and optical return loss. At present, the coupling process of TOSAs in the industry is mainly 2D and 3D coupling. As shown in Figure 3, optical power is the only monitored criterion. Figure 3a is the schematic diagram of the 2D coupling model of the TOSA, and the receptacle is linked directly to the tube body, so the coupling process is very easy. The end-face of the receptacle is located on the focal plane of the LD TO, and the receptacle is moved up on the X/Y plane. The optical power changes by changing the relative position of the receptacle on the X/Y plane. At first, the receptacle is moved up to attain the highest optical power (Pmax). If the Pmax is within specification, the receptacle is stopped from moving. Conversely, if the Pmax is out of specification, the receptacle is moved up to reduce the optical power until the optical power is within specification. Finally, the receptacle and tube body are welded together using laser welding. Figure 3b is the schematic diagram of the 3D coupling model, it has one more ring than the 2D model. The receptacle can be inserted into the ring smoothly, and the ring lays on the tube body. During coupling, the receptacle is moved up and the ring is driven to move on the X/Y plane, and the receptacle can be moved up along the Z-axis, but the ring still lays on the tube body. Figure 3: Coupling model of TOSA. (a) 2D coupling model; (b) 3D coupling model. Figure 2: Structure of TOSA. In order to further illustrate the optical field distribution in 2D coupling, a simulation model is established based on the optical model in Figure 1. The optical field distribution in the core and cladding of the fiber after changing the relative position of the fiber and optical axis is shown. Figure 4 is the distribution of the optical field in the fiber at the focal point of the LD TO. The X (\(\upmu\)m) and \(Y\) (\(\upmu\)m) represent the diameter of cladding, and (0,0) is the central point of the fiber core. The color represents the energy density. The optical field is mainly concentrated in the core and around the core, but the distribution is not uniform. This is because the end-face of fiber is not perpendicular to the central axis, which can cause the beam to segregate [27]. As shown in Figure 5, \(\upalpha\) is the inclination angle of the end-face, which is between the normal of the incident surface and the central axis; i represents the angle of incidence, i\({}^{\prime}\) represents the angle of refraction into the core, and \(\upbeta\) represents the angle of segregation. Assuming that there is no off-axis and angular deflection for the fiber, the optical field distribution in the fiber can be shown as [28]:  
\[\psi_{f}=\sqrt{\frac{2}{\pi}}\frac{1}{\omega_{f}}exp\left[-\left(\frac{x^{2}+ y^{2}}{\omega_{f}}\right)\right]exp[ikx\tan\alpha(n_{1}-1)] \tag{8}\]  
The segregation angle is calculated according to the geometric-optical relationship of the optical total reflection in the fiber. \[n_{1}\sin\alpha=n_{0}\sin(\alpha+\beta) \tag{9}\]  
Figure 4: Optical field distribution in fiber with 8\({}^{\circ}\) end-face at the focal position (0,0,0). Figure 5: Schematic diagram of the end-face with 8\({}^{\circ}\) of fiber.