## 1 Introduction  
The SWAP problem (Size, Weight and Power) is an important challenge in infrared imaging applications today. In embedded optics, reducing the size, mass and power of systems while maintaining their quality is essential for their integration into ever-smaller carriers (optronic balls, micro-drones, etc.). In order to simplify the optical system before the sensor and to maintain a high image quality, optical designers have to find new degrees of freedom in their designs. Several avenues have been thus explored, such as freeform optics [1], GRIN (gradient index) optics [2] and metasurfaces [3]. GRIN optics involve creating a spatial variation of the refractive index in the material. In its primary use, this index variation can correct some optical aberrations such as spherical aberration [4] and chromatic aberrations [5; 6; 7], or can encode optical power inside the lens (not simply at the surface) [8; 9]. One of the main limitations of GRIN optics is their manufacturing [10]. Most fabrication techniques can create typical index profiles such as axial or radial [11]. However, freeform or even aspheric index profiles are much more challenging to implement [10]. Alternative solutions exist, such as using materials transparent to the visible range and coated with thin films [12]. However, this method is restricted in terms of material choice [10]. In this work, we focused on femtosecond laser direct writing (FLDW), which is, to date,the most flexible technique with respect to both inscribed shape and refractive index modulation amplitude and profile. More specifically, FLDW is a technique for locally modifying the physicochemical properties of amorphous and crystalline transparent materials. It consists of focusing a femtosecond laser beam at, or under, the surface of a material, typically from a few \(\upmu\)m up to a few cm [13]. The focused laser light can thus reach intensities higher than tens of TW/cm\({}^{2}\) inside the material. At these intensities, nonlinear light absorption phenomena become preponderant, including multiphoton photoionization and tunneling effects. This ultimately yields to local and permanent modifications of the glass, strongly confined in the focal volume on a few \(\upmu\)m\({}^{3}\) around the laser focal point. Because of its flexibility in terms of both accessible materials and writing possibilities [14], it is a very attractive technique for the fabrication of complex 3D photonic components in a single step. It has been particularly studied for imprinting gratings and optical waveguides [15]. However, FLDW also has attracted the attention of researchers in other photonics applications such as diffractive [16] and polarization [17] optics, gradient index optics [18] and 3D geometric phase optics [19]. FLDW has been extensively studied over the last two decades in silica glass [20], which offers excellent optical properties in the visible and near-infrared range, and more recently in silicon [17]. However, investigations in other materials remain quite limited, especially those to be used in the Mid-Wavelength InfraRed (MWIR 3-5 \(\upmu\)m) and Long-Wavelength InfraRed (LWIR 8-14 \(\upmu\)m) ranges. It would be of practical importance for applications including, but not limited to, home automation, smartphones and even automotive applications. The few studies of infrared glasses mainly dealt with the fabrication of waveguides [13; 21; 22] and did not address the fabrication of free space optics or micro-optics for imaging applications. In order to reach these longer wavelengths in the IR range, nonsilicate glasses such as chalcogenide [23], fluoride [24] or heavy oxide [25] glasses must be used. All these glass families have a wider transmission band than the ubiquitous silicate glasses up to the mid-IR range. More specifically, chalcogenide materials have the advantage of exhibiting a very wide transmission band which can, for some specific compositions, span the visible and LWIR windows.