# Photosensitivity of Infrared Glasses under Femtosecond Laser Direct Writing for mid-IR Applications
## 3 Results and Discussion
### Determination of the optical modifications landscape in the energy-speed domain
The maximum temperature is given by [25]:  
\[\mathrm{T}_{\mathrm{max}}=\frac{\mathrm{AE}_{\mathrm{P}}}{\pi^{3/2}\rho\mathrm{ C}_{\mathrm{P}}\mathrm{w}_{0}^{2}\mathrm{w}_{\mathrm{z}}} \tag{2}\]  
where \(\mathrm{AE}_{\mathrm{P}}\) is the energy absorbed per unit volume, \(\rho\) is the glass density, \(\mathrm{C}_{\mathrm{P}}\) is the heat capacity, \(\mathrm{w}_{0}\) is the beam waist radius, and \(\mathrm{w}_{\mathrm{z}}\) is the longitudinal laser beam size (depending on the NA, pulse duration, and non-linear effects). Thus, the increase in energy \(\mathrm{E}_{\mathrm{P}}\) induces an increase in temperature \(\mathrm{T}_{\mathrm{max}}\) and thus a spatial enlargement (beyond the light affected zone) of the imprinted laser track. This corresponds to the volume within which the temperature is higher than a threshold temperature (i.e., a transformation temperature), leading to glass structural relaxation and thus permanent index changes. Figure 1: On the top, processing windows in the Corning 9754. In the middle, processing windows in the Schott SF10. On the bottom, processing windows in the GeS\({}_{2}\) glass. In the blue areas, images of a spatial broadening regime profiles (criterion: a 20% increase in laser track width compared to the beam waist). In the red areas, images of Type I profiles. Laser parameters: 1030 nm, 800 fs, 100 kHz, 0.6 NA, and linear polarization along X. From that point, one could explain the decrease in the spatial broadening threshold when the writing speed decrease, which is a general trend observed in all three samples. Here, one explanation could be based on the accumulation of point defects (also called color centers) from pulse to pulse. This results in an increase in the absorption coefficient A, with A = \(\sigma_{\mathrm{k}}\).I\({}^{\mathrm{k}}\), either through an increase in the multiphoton absorption cross-section \(\alpha_{\mathrm{k}}\) or even a reduction in the multiphoton process order k by passing through a relay state (i.e., an electronic absorption level attributed to a point defect). Then, the resulting increase in energy absorbed per unit of volume (AE\({}_{\mathrm{p}}\)) leads to a reduction in the spatial broadening threshold when reducing the writing speed. _Quantification of the photo-induced refractive index changes:_ In addition to microscopic observations, we performed a quantitative measurement of the phase variation implemented by fs-laser direct writing [26]. Using Quantitative Phase Microscopy (QPM, Iatia), we were able to measure a mapping of the localized phase (expressed in rad) compared to the pristine background. To study the photo-induced phase variations, a constant writing speed was set at 1 mm/s. This speed was chosen as a compromise in order to achieve fast laser writing while maintaining a high and constant index profile all along the spiral trajectory. Figure 2 plots the phase variation implemented in each material as a function of laser pulse energy. We notice that a strong phase variation appears at a very low energy in the GeS\({}_{2}\) (about 2\(\pi\) rad at 0.125 \(\upmu\)J). We also note that SF10 remains on a nearly constant phase variation above 0.7 \(\upmu\)J (\(\sim\) 1.9 rad). On the other hand, the 9754 glass exhibits a monotonous growing over a wide range of energies and allows reaching relatively strong phase variations (around 4\(\pi\) rad at 1.7 \(\upmu\)J). All these glasses are of interest for the fabrication of 3D geometric phase optics [7]. Variations of \(\pi\) rad with a precise phase distribution are sufficient to create most of the complex optics. The FLDW technique locally changes the glass density of the glasses but also creates some point defects, which in turn affect its optical transmission [27]. Therefore, we measured the optical transmission as a function of wavelength for all samples before and after laser irradiation.