# 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
Laser parameters: 1030 nm, 800 fs, 100 kHz, 1 mm/s, 0.6 NA. are considered, in particular mid-IR glasses: fluorides, chalcogenides, and heavy oxides, including Barium Gallo-Germanate (BGG). The phase profile and the picture illustrated in Figure 4 show a distribution of the refractive index variation inside the GeS\({}_{2}\) material that can be roughly seen as two parts of thickness, \(d_{1}\) and \(d_{2}\). The upper part contributes twice as much as the lower part (\(\varphi_{1}=2\varphi_{2}\), which can be deduced from the cross-section phase profile shown in the inset of Figure 4), where \(\varphi_{1}\) and \(\varphi_{2}\), respectively, represent the phase variations in the first part and the second part of the material. Therefore, the total phase variation is \(\varphi=\varphi_{1}+\varphi_{2}=\frac{3}{2}\varphi_{1}\). Thus, for a disc written in a single pass at high energy, we obtain two index variation sections along the z-axis, with a total thickness \(d_{1}+d_{2}=80\)\(\mu\)m:  
\[\varphi=\varphi_{1}+\varphi_{2}=\frac{3}{2}\varphi_{1}=\frac{3\pi}{\lambda}d_ {1}\Delta n_{1} \tag{4}\]  
with \(d_{1}=d_{2}=40\)\(\mu\)m (estimated from phase profile, see inset of Figure 4). Consequently, with a total phase variation of \(\varphi=37.8\) rad inside the GeS\({}_{2}\) material (Figure 2), we obtained:  
\[\Delta n_{1}=\frac{\lambda\varphi}{3\pi d_{1}}\,\sim\,\,0.0551 \tag{5}\]  
The results presented in Figure 4 confirm the good photosensitivity (i.e., \(\Delta n\) at \"saturation\") of chalcogenide glasses to fs-laser writing. Indeed, refractive index changes \(\Delta n\) up to \(5.5\times 10^{-2}\) in GeS\({}_{2}\) were successfully implemented. In contrast, the two heavy oxide glasses studied achieved quite large index variations for their class and in particular \(2.08\times 10^{-2}\) in the Corning 9754 glass and \(6.8\times 10^{-3}\) in the SF10 glass. _Implementation of a GRIN lens phase profile using FLDW:_ We are now well aware of the phase variation implemented in these materials as a function of laser energy (see Figure 2), and we can now fabricate optical components embedded in the substrate by the fs-laser writing method. Two types of gradients, described in Figure 5, are possible in order to create the phase profile of a lens by the FLDW technique. We will call the first type a thickness gradient. For this thickness gradient, only one value of refractive index variation is chosen. The phase variation is then created by the superposition of layers of the uniform index but different diameters. It is therefore a classical lens of constant refractive index \(n_{1}\) immersed in a material of constant index \(n_{0}\): \(n_{1}=n_{0}+\Delta n\). The second type of gradient is the refractive  
Figure 4: Range of refractive index variation induced by fs-laser vs. refractive index (typ. Measured at 550 nm) for different glasses. Our materials: GeS\({}_{2}\) in red, Corning 9754 in blue, and Schott SF10 in pink. Inset: a false color image of a textured disc profile showing the two sections of the phase and the associated phase profile along the cross-section. index gradient. Here, the thickness of the texturing is constant, and it is the refractive index that varies spatially. The index modified by the laser power variation during the writing process is then defined by \(n(r)=n_{0}+\Delta n(r)\). The phase profiles of these two types of gradients are identical but are fabricated in different ways. It will be simpler to manufacture a thickness gradient lens in that only a specific value of index variation is required. It is therefore sufficient to know the laser energy required for a single-phase variation. However, many layers are needed to manufacture a gradient thickness lens, while only one layer may be sufficient for a gradient index lens. The gradient index lens will therefore be written more quickly. For example, Figure 6 shows a 100 \(\mu\)m diameter gradient index lens written on eight layers.