## 4 Fabrication and Characterization of a Fresnel GRIN Plate  
As described in the present section, an initial prototype of the Fresnel lens was written by femtosecond laser. We wanted to verify the ability of the FLDW technique to quickly write Fresnel lenses. The key laser parameters were fixed as follows: a pulse duration of 800 fs, a central wavelength of 1030 nm, a repetition rate of 100 kHz and a scanning speed of 1 mm/s. The laser beam was focused inside the sample at 500 \(\upmu\)m below its front face using a microscope objective with a numerical aperture of 0.6. There are two different ways to manufacture what we call fs-laser-written GRIN lenses. The first is described herein as the gradient thickness lens. It consists of creating a single value of refractive index variation \(\Delta\)n and superimposing layers of uniform index changes to create a lens in the bulk of the material. Most previous papers on femtosecond laser graded index lens fabrication have dealt with this method [16]. The second is really a gradient index lens, meaning that the refractive index is varied spatially in the lens by changing the laser power during the writing process i.e., during the trajectory. Figure 9  
Figure 8: Spectral transmission in Vis–IR range before and after writing a 1.5 mm diameter homogenous disk with a fixed phase variation of \(\uppi\) rad in the 75(GeS2) \(-\)15(In2S3) \(-\)10(CsCl) glass material. _Parameters: 1030 nm, 800 fs, 100 kHz, 0.6 NA, 1 mm/s, 0.05 \(\upmu\)_]._  
describes the differences between these two manufacturing methods. It shows the gradient thickness lens written to index \(n_{1}=n_{0}+\Delta n\) folded into the \(n_{0}\) refractive index of the background material. In contrast, the gradient index lens showed a radial variation of the refractive index i.e., \(n(r)=n_{0}+\Delta n(r)\). These two lenses are optically equivalent in the basic phase profile but are manufactured differently. The thickness gradient lens is simpler to manufacture because only one value of laser energy is needed to obtain a specific variation of index \(\Delta n\). The shape of the lens can then be created with constant energy. However, the gradient index lens allows manufacturing optics much more quickly since it can be achieved in a single layer. Indeed, once the curve (Figure 7) giving the variation of phase according to the laser energy is known, we only need to radially vary the energy to create the desired phase shift. Instead of a superposition of N discrete layers, which needs a lot of time, one layer with N energies is sufficient, or even a continuous (but controlled) change of the energy along the writing trajectory. The gradient index lens method was used as it the fastest inscription process. We designed this Fresnel lens with the same characteristics as the GRIN Fresnel lens presented above (Figure 5), except that we chose a central wavelength of 550 nm due to the lack of available IR equipment and in order to simply measure the different focal lengths of the lens with a classical visible microscope (Olympus BX51) and some spectral filters. In addition, the diameter of the lens was reduced to only 500 \(\upmu\)m (for a focal length of 2 mm) in order to write the Fresnel lens more quickly. The curve of phase variation as a function of laser energy (Figure 7) allowed us to write a first-order Fresnel lens in the GeS\({}_{2}\) glass, as presented in Figure 10.  
Figure 9: (**a**) The phase profile of a GRIN lens. (**b**) The corresponding thickness profile of a gradient thickness lens and its discretization. (**c**) The corresponding refractive index profile of a gradient index lens and its discretization. The color variation represents the radial refractive index variation. (**a–c**) The solid line represent the blazed profile and the dashed-line represent the discretized profile. These preliminary results were easily transposable from a Vis to an infrared system to build the final demonstration of our multispectral camera.