# 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
In order to measure the room temperature's optical transmission of the samples over a wide spectral band, we used two spectrophotometers: an Agilent Cary 5000 (\(\Delta\lambda\in[0.2\,;3.3]\)\(\upmu\)m) and a Bruker Equinox 55 (\(\Delta\lambda\in[2\,;20]\)\(\upmu\)m). Thanks to the results presented in Figure 2 of the phase variation as a function of laser energy, we were able to implement a phase change in \(\pi\) rad in our materials. We chose this \(\pi\) rad variation because it is a phase shift particularly used to design Fresnel lenses, binary ring phase masks, etc. Figure 2: Phase variation implemented by the FLDW technique as a function of laser energy. The writing speed of these irradiations is fixed at 1 mm/s (corresponding to about 120 pulses/\(\upmu\)m). Inset: an example of a quantitative phase map measured by the Quantitative Phase Microscopy technique has been added for each material. Laser parameters: 1030 nm, 800 fs, 100 kHz, and 0.6 NA. We can observe in Figure 3 a rather important difference in transmission between the chalcogenides, transmitting up to 10-12 \(\upmu\)m, and the heavy oxides transmitting only up to 4-5 \(\upmu\)m. Then we notice in particular that the difference in transmission before and after femtosecond laser texturing remains quite negligible for a photo-induced phase variation of \(\pi\) rad. Although it is likely that implementing a larger phase variation would imply additional optical losses in these materials, the results in Figure 3 are encouraging and bode well for a small change in the optical transmission of these glasses despite a useful magnitude of the observed changes in the refractive index. We have seen that we are able to implement a strong phase variation in these glasses and more particularly in GeS\({}_{2}\) because of its binding energy, which is much lower than those of the heavy oxide glasses. The formation energy of GeS\({}_{2}\) is about \(-0.66\) eV/atom, whereas the formation energy of PbO (a key constituent of SF10) is about \(-1.47\) eV/atom and \(-2.07\) eV/atom for GeO\({}_{2}\) and \(-3.41\) eV/atom for Al\({}_{2}\)O\({}_{3}\). These data are extracted from The Material Project website and calculated based on Ref [28]. For many applications, it would be necessary to convert phase variation (\(\varphi\) in rad) into refractive index changes written by the femtosecond laser. In this view, it is sufficient to measure the thickness of the laser-modified region d to have:  
\[\Delta n=\frac{\lambda}{2\pi d}\varphi, \tag{3}\]  
where \(\lambda\) is the probe wavelength used for the quantitative phase measurement (here \(\lambda=550\) nm). This value of \(\Delta n\) is only an approximation. Indeed, it is assumed that the FLDW technique implements a constant index variation over a cylinder in the thickness of the material. In fact, the real shape of the trace depends first of all on the focusing optics, on the index, and on the non-linear index of the material. There is then a competition between the Kerr effect focusing the rays and the defocusing due to the plasma created by the fs-laser [29]. Nevertheless, we aim to use the FLDW technique to fabricate gradient index optics and geometric phase optics for infrared imaging systems. Thus, for the fabrication of graded index optics, we need to know the index variation implemented by the laser. One of the current development axes of the direct femtosecond laser writing technique is to find the materials and the laser parameters allowing one to obtain the highest possible refractive index variations. Indeed, the greater the range of index variation available, the more freedom the optical designer will have to create the optical component needed for their system. We have therefore reviewed in Figure 4 the different ranges of index variation obtained in the literature (data collected from Refs. [5; 9; 18; 29; 30; 31]). Several glass families  
Figure 3: Optical transmission of the studied glasses before and after a \(\pi\) rad phase variation was implemented using FLDW.