# Simulation and Experimental Verification of the Thermal Behaviour of Self-Written Waveguides
## 2 Sample Design  
The focus of our work is the investigation of the thermal behaviour of an SWW which connects two silica fibers (OM2) with a core diameter of 50 \(\upmu\)m. A scheme of the writing procedure of an SWW is shown in Figure 1.  
As indicated in Figure 1, a monomer drop is applied between two silica fibers which are aligned with respect to one another along their common optical axis. One of the fibers, which is connected to a laser diode, emits light at \(\lambda=406\) nm, which starts the polymerization process at the end of the fiber. This process step is illustrated in Figure 2.  
Figure 1: Scheme of the writing process of an SWW created between two silica fibers. Due to the curing of the monomer, the refractive index increases locally at the point where the beam enters the monomer, which further traps the light and results in the development of a straight waveguide, as shown in Figures 1 and 2. For processing, it is advantageous to use multi-mode fibers. If a smaller fiber core size is chosen, it is more difficult to point the laser light to the opposite fiber end. Additionally, a smaller core size results in a smaller SWW diameter which subsequently reduces the adhesion strength and, thus, the robustness between the fibers and the SWW. In a last step the surrounding resin is cured by UV flood exposure. This enables a rigid connection between the two fibers. Here, it is important to realize that the final external curing yields two important characteristics. Due to the high material absorption of the UV light on the surface of the drop, the intensity for the curing inside the drop decreases significantly, which results in a refractive index distribution with a lower value inside the drop compared to its surface. This expected refractive index distribution is indicated in Figure 3.  
The model of the refractive index distribution shown in Figure 3 is based on previous measurements where an approach based on Syntholux as matrix monomer was used [4]. The simulations and measurements presented in this work are based on NOA68, which is an optical adhesive from Norland Products. Due to the change of the material and the information needed for the simulation, the refractive index and the TOC have to be determined. The temperature-caused change of the refractive index is directly correlated to a change of the density and temperature itself. The whole correlation was determined as follows [27]:  
\[\frac{dn}{dT}=(\frac{\delta n}{\delta\rho})\tau(\frac{\delta\rho}{\delta T})+( \frac{\delta n}{\delta T})_{\rho}=-\alpha\cdot(\frac{\rho\delta n}{\delta\rho })\tau+(\frac{\delta n}{\delta T})_{\rho} \tag{1}\]  
Figure 3: Cross section of a cured SWW with surrounding resin and gradually refractive index distribution. A darker color represents a higher refractive index. Figure 2: Image (**a**) is illustrating the creation of a SWW by a self-trapped laser beam with a wavelength of \(\lambda=405\) nm between two OM2-fibers with a core size of \(50\,\mathrm{\SIUnitSymbolMicro m}\) and a cladding diameter of \(125\,\mathrm{\SIUnitSymbolMicro m}\), respectively. The red bars in the lower image (**b**) represents the measuring point for determining the thickness and length of the SWW. The fact that the width of the SWW decreases in the middle between the fibers is studied systematically as a function of the relevant process parameters in the next steps. where \(n\) is the refractive index, \(\rho\) is the density, \(\alpha\) is the volume coefficient of thermal expansion of a polymer, \(dn/dT\) is the temperature-caused refractive index change, \((\delta n/\delta T)_{\rho}\) is the refractive index change for constant density, and \((\rho\delta n/\delta\rho)_{T}\) is a constant for a given polymer. Measuring all these parameters is very inconvenient and uncomfortable. The expected changes of the refractive indices are negative, which is common for polymers, and will be in the range of \(\approx\)(\(-100\)--\(500\)) \(\times\)\(10^{-6}\) K\({}^{-1}\), necessitating a very sensitive measuring device [28].