Radial gradient refractive index from crystallized chalcogenide glass for infrared applications

Electro-Optic Materials

IR Optics Paper

Article shared under SPIE's Green Open Access Policy


The last twenty years have seen a dramatic improvement in the performance of infrared detectors, especially those with uncooled microbolometer arrays. These make new commercial applications possible, from the Internet of things to drones for crop monitoring. Such emerging markets are constantly pushing the requirements on the existing technology to improve cost, performance, weight and size. In this context, gradient index (GRIN) lenses can offer a new degree of freedom compared to their homogeneous counterparts. For example, recent papers have shown how GRIN lenses could help reduce the number of elements in a system, by helping correct lens chromatism and athermalization.

While the interest in using GRIN is obvious, mastering their fabrication with infrared materials remains highly challenging. Encouraging progress has been made in that direction, for instance by stacking different materials or by laser writing. Very recently, it has been demonstrated that partial crystallization of chalcogenide glass allows for tuning the refractive index.

In this paper, we introduce a new technique based on the controlled formation of nano-crystallites in chalcogenide glass to fabricate the first macroscopic radial GRIN in the infrared. We also propose a simple way to test the index gradient value by interferometry and demonstrate GRIN with index contrast of Δn ∼ 3⋅10-2 between the center and the edge of the disk. The process is easily repeated and opens the possibility for a rapid transfer to the industry.
Keywords: GRIN, infrared, chalcogenide, crystallization,


A Gradient Index (GRIN) lens is a lens where the refractive index is inhomogeneous and varies continuously. Similarly to aspheric surfaces, this offers an additional degree of freedom for the optical designer to compensate for aberrations, especially chromatic ones1,2. It has been understood since long that GRIN could help reducing the number of optical elements3, even in complex hyper-spectral systems4. Pushed by the need for performance, cost effectiveness and compacity, the interest in GRIN has been recently rekindled in the infrared (IR) wavebands.

However, the main challenge with GRIN lenses has been and remains fabrication. In the IR, concepts have been demonstrated already in the 80s in crystals. This comprised chemical vapor deposition (CVD) of mix of ZnS and ZnSe, as well as crystal pulling of Ge with Si doping5. Yet, these techniques were hardly transposable to large scale industry and remained at the stage of laboratory experiments.

More recently, work has been achieved in order to fabricate GRIN in chalcogenide glasses. These materials have indeed become ubiquitous in the LWIR industry thank to their very high infrared transmission, as well as their viscoelastic properties, which allow for shaping them by molding. By using thermal poling6, laser irradiation7 and electro-spray printing8, the refractive index has been tuned in chalcogenide compositions. However these examples have been limited to small scales. On larger samples, creation of longitudinal GRIN has been obtained by stacking different glass compositions9, as well as by controlling crystallization10. Nonetheless, the fabrication of radial GRIN remains a challenge, however useful they can be in lens design4. In this paper, we present a new technique to fabricate radial GRIN lenses in chalcogenide glass11. We also describe an interferometric set-up to directly measure the index profile.


In order to fabricate a GRIN, the first step is to determine a way to tune the refractive index. Since the index is somehow intrinsic to the material, changing the index means altering the material. This can be achieved in two ways. Either the composition can be changed, for example via mixing or doping, or the physical phase of the material can be changed, without modifying the composition. The last approach can be considered more simple since it can be done in situ, without any material flow. In chalcogenide glasses, a natural phase change is crystallization. Our first task is therefore to find a composition where crystallization can be controlled, and to verify that it has a significant impact on the refractive index. To this aim we have selected the chalcogenide glass 80 GeSe2 – 20 Ga2Se3, where crystallization has already be studied to produce glass-ceramics12.

The base glass for our experiment was synthetized with the vacuum-sealed melt-quenching method13. The high purity elements (5N-Ge, 5N-Se and 4N-Ga) were placed in a silica tube in vacuum (10-5 Pa) and consequently heated up to 900 °C in a rocking furnace, to improve the mixing. After 12 h, the temperature was lowered to 800 °C for 2 h and then the silica tube was plunged into water at room temperature to quench the glass. Finally, the sample has been annealed for 3 h at 360 °C (Tg - 20 °C) to release the internal strains. With this method, we obtained 10 mm-diameter glass rods, like the one displayed in in Figure 1(a). Because 80 GeSe2 – 20 Ga2Se3 glass can form two crystalline phases, Ga2Se3 and GeSe2, it is not obvious to predict the evolution of the refractive index with crystallization. Indeed, while the base glass has an index of 2.401 at a wavelength of 1.551 μm, the bulk crystals of Ga2Se3 and GeSe2 (shown in Figure 1(b) and (c)) display indices of respectively 2.579 and 2.368 at the same wavelength.

Our first experiment was therefore to assess the effect of crystallization on the refractive index of the material. Rods of 80 GeSe2 – 20 Ga2Se3 glass were cut into discs and polished before being placed into a ventilated furnace at 390 °C. Then, each disc was removed from the furnace after a different duration, up to 72 h. In this way it was possible to monitor the progressive crystallization of the glass. This was achieved by X-ray diffraction (XRD). The refractive index was then characterized at 1.311 μm and 1.551 μm using the M-line technique (Metricon 2010/M Prism coupler). Experimental XRD data are displayed in figure 1(d), for different annealing times. Each curve has been shifted upwards proportionally to the annealing time, for easier reading. Based on the literature14,15, we can identify two families of peaks in the XRD curves. The peaks labelled “A” are attributed to the formation of Ga2Se3 crystallites, while the peaks identified with a “B” are attributed to GeSe2. We can observe that the lines associated to Ga2Se3 appear from the beginning and become more pronounced until approximately 32 h. Then, peaks associated to GeSe2 start building up. This behavior can be connected to the evolution of the refractive index, plotted in Figure 1(e). First, the index increases until around 32 h of crystallization, where we observe a maximal deviation of Δn ~ 0.032. Then the index gradually decreases until it seems to reach a plateau around Δn ~ 0.02 of its initial value. This is consistent with the fact that the index of Ga2Se3 is higher than the one of the base glass, while the index of GeSe2 is lower than the one of the base glass. In the beginning of the experiment, a crystalline phase of Ga2Se3 is forming, which leads to an increase of the index. Then, in a less favorable reaction, GeSe2 eventually crystallizes, which drives the index down. We can conclude that controlling the crystallization in 80 GeSe2 – 20 Ga2Se3 is a direct way to tune the refractive index.

Figure 1 - Crystallization of 80 GeSe2-20 Ga2Se3 under a fixed temperature. (a) Bulk glass sample of 80 GeSe2 – 20 Ga2Se3 synthesized by the vacuum-sealed melt-quenching method. (b) Ga2Se3 and (c) GeSe2 in a crystallized phase. (d) Evolution of X-ray diffraction patterns as function of the dwell time at 390°C. Peaks labelled with A and B are respectively attributed to Ga2Se3 and GeSe2 crystallites. The curves are shifted vertically according to the dwell time in the oven (e) Corresponding value of the refractive index measured at wavelengths of 1.551 μm and 1.311 μm. Dashed lines are a guide for the eyes.


3.1 Principle

We have demonstrated that the index of the partially crystallized glass differs from the index of the base glass. In order to achieve the spatial change of refractive index required in a GRIN lens, it is necessary to crystallize heterogeneously the material. Two parameters have an impact on crystallization, which is a thermally activated reaction: the duration of the reaction and the temperature at which it occurs. While in the previous experiment, it was easier to maintain the temperature and increase the dwell time in the oven, it is hardly feasible to obtain a spatially resolved crystallization in this way. Rather, it is much easier to play with the temperature profile in a sample to achieve various crystallization rates. This can notably be helped by the relatively low thermal conductivity chalcogenides generally display, around 0.3 W/(mK)16. By heating the glass in only given locations, temperature gradients will establish in the sample that should convert to crystallization gradients.


3.2 Description of the process

These considerations together with the goal to fabricate a GRIN with a radial symmetry have led to the experimental set-up schematized in Figure 2(a). A 80 GeSe2 – 20 Ga2Se3 glass cylinder of 10 mm in diameter and 80 mm in length is translated at a constant speed of 0.6 mm/min through an annular furnace. To avoid oxidation of the glass surface, the rod was maintained in a constant helium gas flow. In these conditions, the elevated temperature of 430 °C in the annular furnace results in an elevation in the temperature at the surface of the glass rod, like illustrated in Figure 2(b). Because of the low heat diffusion in the sample, compared to the speed at which the rod is translated, we can expect to observe a radial temperature gradient within the glass, from the hot circumference to the cooler center. This should in turn lead to a gradient of crystallization, and hence of refractive index, that we propose to characterize in the next section.

Figure 2 - Radial crystallization in an annular oven. (a) Schematic of the experiment. The 80GeSe2-20Ga2Se3 rod is moved through an annular oven at a constant speed. (b) Schematic view of the temperature profile within the glass rod. At higher temperature, the sample crystallizes faster, leading to a decreased glass fraction and a higher index of refraction.


After the dynamic annealing, the rod has been sliced to obtain flat discs, like illustrated in Figure 3(a). The first characterization is to verify that the sample is crystallized, with a radially increasing crystal fraction. Therefore, one of the disc was studied by Scanning Electronic Microscopy (SEM). The SEM pictures at different locations are reproduced in Figure 3(b-d). While the center (b) remains homogeneous and glassy, the edge of the sample (d) displays a high granularity, which is associated to the formation of crystallites. This is further confirmed by the X-ray diffraction characterization of the same sample in Figure 3(e). While in the center of the sample the pattern is the one of an amorphous material, three crystalline peaks are visible in the edge of the disk. These lines, which are indicated with arrows, can be attributed to the formation of a Ga2Se3 crystalline phase. Another point is that the transmission of the sample, plotted Figure 3(f), remains high. This is important since the ultimate goal is to produce lenses. What can be observed is that at short wavelength, there is a lower transmission in the edge of the sample. This can be attributed to diffusion by the crystallites. Nonetheless, this does not impede significantly the transmission in the mid-wave IR and long-wave IR bands.

Figure 3 - Characterization of the radially crystallized sample. (a) Picture of the sample. 1, 2, 3 designate respectively the center, the zone in-between center and edge and the edge of the sample. (b), (c) and (d) are SEM images of the sample taken in the areas labelled in (a), respectively 1, 2 and 3. (e) X-ray diffraction pattern of the sample in the center and the edge. The peaks pointed with arrows are signature of Ga2Se3 crystallites. (f) Transmission of the sample in the infrared region, at locations 1, 2 and 3 of picture (a).

A radial gradient of crystallization has been effectively created in the sample. Now the question is to know whether this corresponds, like expected, to a radial gradient of refractive index. To this aim, we have built the interferometric set-up described in Figure 4(a). A collimated laser beam at 10.6 μm emitted by a CO2 laser goes through the radially crystallized disc. The discs have been polished by single point diamond turning (SPDT) to obtain flat parallel surfaces (curvature radius R=3400 mm, and roughness Ra < 7 nm). Because of this, any spatial variation in phase delay created by the sample can only be attributed to the refractive index. After the sample, a “4-f” setup is used to replicate the wavefront at the output of the disc directly onto the wavefront analyzer, a quadriwave lateral shearing interferometer from Phasics®. The measured wavefront is plotted in Figure 4(b). The whiter regions correspond to a phase advance compared to the black regions. Under the assumption that the sample is thin before the index change, the relation Δφ = (2π/λ)Δnt applies, with Δφ being the phase delay, λ the wavelength and t the thickness of the sample. Therefore, we can conclude that the sample does present a radial GRIN. In order to quantify more the index profile, a line-cut was taken in the phase of Figure 4(b) (blue dashed line) and plotted in Figure 4(c), revealing an index difference of Δn ~ 0.03 at 10.6 μm. This value is comparable to the maximal difference observed between the homogeneously crystallized samples of Figure 1 and must translate into noticeable optical power. To observe the latter, a simple imaging set-up was built and is schematized in Figure 4(d). A hot plate, which emits light in the long wave infrared region, serves to illuminate a grid. The grid is imaged by a thermal camera through a sample. When a homogeneous glass disc (Figure 4(e)) is used, the only effect is a drop of transmission due to Fresnel losses. However, with the GRIN disc (Figure 4(f)), the grid is visibly deformed due to the optical power. On top of this, and similar to what was observed in Figure 3(f), the transmission remains very good. We can confirm that the dynamic radial annealing technique presented in this work allows for fabricating chalcogenide GRIN lenses.

Figure 4 - Optical characterization. (a) Schematic of the interferometric setup used to measure the phase delay induced by the GRIN. (b) Phase delay induced on a collimated laser beam at λ = 10.6 μm by the radially crystallized 80GeSe2-20Ga2Se3 sample. (c) Refractive index difference Δn retrieved from the line-cut (blue dashed line) in (b). (d) Schematic of a simple setup used to observe the optical power of the GRIN lens. (e) Image of the grid through a homogeneous 80GeSe2-20Ga2Se3 glass sample and (f) the same grid imaged through the GRIN 80 GeSe2-20 Ga2Se3 sample. The optical power is clearly noticeable.


While GRIN are promising for lens design, their fabrication remain complex. Here we have introduced a new technique to fabricate index gradients, by spatially controlling crystallization in chalcogenide glasses. This is achieved by creating temperature gradients above the glass transition temperature within samples. In our experiment, a radial gradient was obtained by using an annular furnace, but virtually any shape could be done in a sample if the temperature profile is controlled.
Another challenge in manufacturing GRIN elements is to dispose of a fast and non-destructive method of measurement. We presented here a simple interferometric set-up to check within seconds the GRIN profile, and measured an amplitude of the GRIN of Δn ~ 0.03 at 10.6 μm.
As a final note, the method is not limited to the 80 GeSe2 – 20 Ga2Se3 composition chosen here. Different chalcogenide glasses could be used in order to tune the index difference Δn and match requirements of optical designs



This work was funded by the DGA project ANR-18-ASTR-0014.



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