# Simulation and Experimental Verification of the Thermal Behaviour of Self-Written Waveguides
## 5 Conclusions  
In this work, we investigated the unusual behaviour of self-written waveguides as a function of temperature and different curing times applied during the waveguide production. The observations support the assumption that the behaviour is due to a change of the material parameters during the external curing phase. Therefore, the TOCs for the core and cladding became different, which finally increases the numerical aperture \(\mathrm{NA}=\sqrt{n_{core}^{2}-n_{cladding}^{2}}\) during the heating process. We also noticed a difference in the change of the transmitted intensity during the heating process between the simulation and the experimental results, see Figures 7 and 11 (for the gap size of 500 \(\mathrm{\SIUnitSymbolMicro m}\) ). This is due to the missing material parameters which are required for the simulation but are not available, i.e., the complex refractive index parameter \(k\), mechanical parameters as the linear expansion coefficient, or the material density for different curing times. Therefore approximations were necessary, or values from similar materials were taken, respectively. The achieved temperature sensitivity of \(\approx\)0.4% K\({}^{-1}\) is relatively small. However, the fact that the change of the signal is opposite to the one induced by other environmental influences such as, i.e., drift of the intensity of the light source, degradation of the waveguides, or change of the coupling conditions is an interesting property. Generally, the structure is integratable in more complex photonic networks and could be used as sensing element therein. Possible further steps for increasing the performance of this structure to be employed as a temperature sensor are, e.g., the use of materials with more favorable thermal behaviour or the exchange of the cladding material by removing the liquid resin after the SWW writing. Therefore, more detailed simulations are required to evaluate which material combinations are usable to increase the temperature sensitivity of the structure. Another point of interest is the optimal combination of the waveguides core size. Due to the fact that increasing temperature changes the \(\mathrm{NA}\) and, thus, the optical transmission of the structure, a combination of different core diameters for input and output fibers can achieve a change in the optical transmission in the same manner, which can even be larger than the observed effect so far. The unique thermal response of the structure opens a promising new field of applications. In this work, we characterized a single external parameter in detail, which affects the performance of the SWW. Future work will focus on the investigation of the influence of humidity and axial strain on the SWW transmission. These studies might enable the reliable detection of multiple parameters simultaneously. Conceptualization, A.G.; methodology, A.G. and M.B. ; investigation, M.B. and A.G.; resources, B.R. ; data curation, A.G.; writing--original draft preparation, A.G.; writing--review and editing, A.G., M.B., B.R. and W.K. ; supervision, B.R. and W.K. ; project administration, A.G. and B.R. All authors have read and agreed to the published version of the manuscript. Figure 11: Thermal response of the SWWs for different gap sizes of 250 \(\mathrm{\SIUnitSymbolMicro m}\) (brown line), 500 \(\mathrm{\SIUnitSymbolMicro m}\) (dashed magenta line), and 750 \(\mathrm{\SIUnitSymbolMicro m}\) (dotted red line). The measurements were performed with the diode laser at \(\lambda=850\) nm. The two lines for each color corresponds to the heating and cooling cycle, respectively. **Funding:** This research was funded by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy within the Cluster of Excellence PhoenixXD (EXC 2122, Project ID 390833453). **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** Data available on request due to restriction of privacy.