# Simulation and Experimental Verification of the Thermal Behaviour of Self-Written Waveguides
## 2 Sample Design
Here, the required refractive index measurements were performed by using a refractive index profilometer, which is based on the refracted near-field method, as schematically shown in Figure 4 [29]. The near field approach allows the determination of the refractive index by measuring the change of the amplitude and deflection of the beam as given by the scalar wave function \(n_{x,y}^{2}\approx\frac{1}{k^{2}}\cdot\frac{\Lambda^{2}A}{A}\), with \(n_{x,y}\) as the two-dimensional refractive index profile, \(k\) the wave vector, and \(A\) as the field amplitude. The unknown refractive indices of the core and cladding will be approximated by using two references with defined refractive indices in the area of measurement, which is \(\approx\)500 \(\upmu\)m\(\times\)500 \(\upmu\)m. For this purpose, a reference glass block (i.e., BK7) is employed together with a specific immersion oil for which its refractive index is close to the expected one from the sample and the reference. Due to the measurement principle, it is not possible to determine the refractive index of the SWW if it is connected in between two fibers. Thus, for this measurement, a separate SWW was written perpendicular to the cover slit next to the reference glass as illustrated in Figure 4. In this configuration, the beam from the laser diode is focused on the upper surface of the cover slit, which is in contact with the sample. The focused beam is deflected by the different materials it propagates through, finally reaching the detector. Due to the determination of the TOC, we extended the measurement setup with a Peltier element to determine the refractive index of the sample at different temperatures. For this experiment, the immersion oil was exchanged by a thin coverslit which was characterized in detail beforehand. The results of measuring the refractive index distribution are shown in Figure 5.  
Figure 4: Scheme of the refractive index profilometer setup. A laser beam is focused on the sample surface. The main part of the beam exits the specimen through a layer of monomer (which is immersion oil in standard cases) on the backside of the reference glass, which is parallel to the entrance surface. Changes of the beam angle which exits the reference glass caused by a change of the refractive index in the beam path are detected by a large area CCD-Chip. The refractive index profilometer delivers a resolution of \(\approx\)10\({}^{-5}\) and a pixel-resolution of \(\approx\)100 nm at the employed wavelength of \(\lambda=638\) nm. The depiction in Figure 5 shows the higher refractive index of the SWW core and its gradient distribution. Due to the integration of a Peltier element as shown in Figure 4, the refractive index profilometer is enabled to measure the refractive index distribution at different temperatures in the range of 25-65 \({}^{\circ}\)C. The measurements taken with this device yields the required values for the refractive indices of the SWW core and cladding, which are required for the simulation. The somewhat irregular shape of the SWW shown in Figure 5 is due to the measurement setup. The depicted end facet is directly attached to the cover slit (see Figure 4), which results in reflections from the glass during the writing process, resulting in unwanted curing at the borders. A slight tilting can also not be excluded, which affects the measurement accuracy.