# Simulation and Experimental Verification of the Thermal Behaviour of Self-Written Waveguides
## 1 Introduction  
Photonic structures and components have become extremely important during the last decades. Due to higher data transmission and electromagnetic compatibility, they can supersede their electronic counterparts for special applications, i.e., in a biomedical context or in high voltage environment [1, 2]. In particular, polymer-based optical components and systems have become more attractive due to the lower production costs compared to their semiconductors or glass-based counterparts [3]. Next to pricing, polymers offer multiple characteristics which make them suitable for, e.g., optical sensing and short-distance transmission. Additional important aspects for photonic structures are optical interconnects to overcome gaps between optical waveguides or for connecting them with light sources or detector elements. A relatively new concept in this topic include self-written waveguides (SWWs), which have been intensively studied during the last decade [4, 5, 6]. Moreover, a connection between optical components, which are misaligned with respect to one another, is possible within limitations [7]. An advantage of such types of interconnection is the integrability into a variety of waveguide fabrication processes including hot embossing [8, 9, 10, 11, 12, 13], photolithography [14, 15], or direct laser ablation [16]. It offers the possibility to connect components that have been manufactured with different techniques, resulting in slightly different waveguide shapes [17]. Another technology that is able to create free form optics and thus can be used to connect different types of optical components is direct laser writing [18, 19]. This technology is much more precise and flexible compared to the SWW-writing process, which on the other sidedoes not need expensive equipment or optical access to the position where the connection is to be established. Thus, SWWs are able to connect buried waveguides located inside a photonic integrated circuit, which cannot be easily achieved by other techniques [20; 21].  
An additional characteristic of adding an SWW in between waveguides or fibers that consist of other materials is the different optical response after changing external physical parameters, which is due to varying material characteristics. Concerning the thermo-optical coefficient (TOC), there are large differences between the optical materials. Thus, polymers show a large negative TOC, which can be 10-40 times higher than for conventional optical components such as glass [22]. This large value results in drift of the operating conditions when increasing or decreasing temperature. The change of the refractive index with respect to the temperature depends mostly on the change in density of the polymer due to the positive thermal expansion coefficient. Even small thermally-induced variations of the refractive index can significantly alter the intensity distribution within waveguides, especially in coupled systems [23]. Due to the material characteristics, polymers are thermally less robust than Si-based components. Depending on their respective glass transitions temperatures (\(T_{G}\)), polymers can be heated up to 60-250 \({}^{\circ}\)C (i.e., \(T_{G}(PMMA)\approx 100\)\({}^{\circ}\)C) and glass up to 400-700 \({}^{\circ}\)C (i.e., \(T_{G}(BK7)\approx 570\)\({}^{\circ}\)C), respectively [24; 25; 26].  
In this work, we focus on the investigation of the thermal response of the SWW and whether this characteristic can be used as a sensing element. Therefore, detailed optical FEM-based and numerical simulation has been performed with different tools, and the results were compared with experimental measurements. We investigated theoretically and experimentally the variation of the refractive indices of an SWW by changing the thermal conditions and explain the underlying effects.