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Abstract
Gradient refractive index (GRIN) materials utilize an internally tailored refractive index in combination with the designed curvature of the optical element surface, providing the optical designer with additional freedom for correcting chromatic and spherical aberrations. In this paper, new GRIN materials suitable for the second (3-5 µm) and third (8-12 µm) atmospheric windows were successfully developed by the thermal diffusion method based on Ge20As20Se60-xTex series high refractive index glasses, where the maximum refractive index difference (Δn) at 4 µm and 10.6 µm were 0.281 and 0.277, respectively. The diffusion characteristics and refractive index distribution of the GRIN glass were analyzed by Raman characterization. Furthermore, the performance of GRIN singlet and homogeneous singlet in the LWIR band (8 µm, 10.6 µm (primary wavelength), 12 µm) was compared, and the results showed that the GRIN singlet had better chromatic aberration correction and unique dispersion characteristics.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Over the past few decades, advanced technologies such as security surveillance, medical endoscopy, smartphones, micro cameras, and drones have evolved at breakneck speed, requiring iterations of their imaging systems with higher performance, lighter weight, and smaller size lenses [1]. As a result, smaller, lighter, and better-performing optical components are increasingly in demand, and the corresponding research on GRIN materials and optical design has received extensive attention. GRIN lenses feature short focal lengths and large numerical apertures, and can effectively correct chromatic aberration in the infrared broadband band and reduce the weight [2]. Chalcogenide glasses (ChGs) are now becoming the preferred choice for the preparation of IR GRIN materials [3]. Their refractive index gradient changes can be achieved by composition gradient changes, which undoubtedly provides excellent opportunities to prepare GRIN materials. In addition, the cost of preparing GRIN ChGs is lower than that of preparing GRIN crystallines such as Ge/Si and ZnSe/ZnS, and the refractive index and dispersion properties of ChGs have a wider adjustable range [4].
Recently, quite a lot of techniques such as ion exchange [5], electrospray printing [6], heat-induced crystallization [7,8], laser-induced vitrification [9], thermal diffusion [10] have been used for the development of chalcogenide GRIN materials. Such as Laurent Calvez team prepared low refractive index GRIN glasses with a maximum Δn of 0.045 by incorporating alkali halides (NaI) in a highly covalent GeSe2-Ga2Se3 matrix and through an ion exchange process between K+ and Na+ [5]. Thermally-induced crystallization is also a common method of producing compositional and refractive index changes within ChGs [11]. Changgui Lin et al. prepared GRIN chalcogenide glass-ceramic with a Δn of 0.04 by generating low refractive index CsCl nanocrystals in a high refractive index GeS2-Sb2S3 glass matrix [4]. Daniel Gibson et al. developed at least 24 sulfide fractions with similar thermal properties in an unpublished manner and prepared GRIN glasses with a Δn of 0.2 by multilayer stacking heat treatment, and the maximum refractive index of these glasses was only 2.78 at 3 µm wavelength [10]. Kang et al. used Ge-As-Se-Te glasses to prepare GRIN high refractive index glass with Δn = 0.12 by multilayer thermal diffusion method [12]. Compared with other technologies, thermal diffusion is the most effective method to prepare large-scale and large-diameter GRIN materials. The production of the multi-layer thermal diffusion method needs to pay attention to the limitation of the thickness of each layer of the sample, and it will be difficult to optimize the completely linear smooth refractive index distribution. Therefore, the double-layer thermal diffusion method is adopted in this paper. In addition, it is necessary to perform an effective optical design evaluation of GRIN materials to verify the dispersion characteristics [10]. In general, as a popular option for components of infrared broadband imaging systems, IR GRIN materials still have great research space and value in component design, preparation technology, optical design, etc.
In this paper, based on the fact that Te can effectively improve the refractive index, Ge20As20Se60-xTex series high refractive index glasses were prepared. The corresponding GRIN glass (Δn = 0.277 @ 10.6 µm and nmin > 2.74) was prepared by double-layer hot pressing diffusion method. Using Raman indirect characterization techniques, the diffusion characteristics of GRIN glass were analyzed and a smooth refractive index curve distribution was shown. Finally, the optical design of GRIN glass was carried out using the optical software ZEMAX, showing its ability to correct chromatic aberration and unique dispersion characteristics.
2. Experiment
2.1 Base and GRIN glasses preparation
The Ge-As-Se60-xTex (Tex, x = 20, 24,28, 32, 36, and 40) series glasses were made using the sealed-ampoule melt-quenching method. Ge (5N), As (5N), Se (5N), and Te (5N) were weighed and placed into clean quartz ampoules, which were subsequently pumped with a vacuum pump until the internal air pressure reached about 10−4 Pa and then sealed with an acetylene torch. The sealed ampoules were placed in a swinging furnace at 850°C for 24 hours to ensure adequate reaction of the raw materials, followed by quenching and annealing. The glasses (Φ = 10 mm) were then cut using an internal circular cutter, one part (h = 2 mm) for testing the properties of the glass and the other (h = 6 mm) for diffusion experiments. In order to ensure a close contact between the two glasses, the glasses need to be polished to optical quality while strictly controlling the parallelism between their upper and lower faces. Then the polished samples were put into the ultrasonic cleaner to avoid the influence of impurities. The dried two glasses were tightly stacked in the mold and quickly bonded within 10 minutes at a heating temperature of 280 °C, an axial pressure of 30 Mpa, and a vacuum of 10−4 Pa. The bonded glasses were then thermally diffused at higher temperatures (280-360 °C) and a small axial pressure (0-2 Mpa).
2.2 Characterization
The infrared transmission spectra from 2.5 to 20 µm were tested with an FTIR spectrometer (Nicolet 380, USA). The refractive index of the glasses from 2 to 20 µm was measured using an infrared spectroscopic ellipsometer (J.A. Woollam IR-Vase II, USA). The transition temperature of the glasses was measured at a heating rate of 10°C per minute using a differential scanning calorimetry (DSC, TA Q2000, USA). Based on the Archimedes principle, the density of the glasses was measured in absolute ethanol at room temperature. The Raman spectra of the glasses were measured by a micro-confocal Raman spectrometer (Renishaw inVia, UK), and the resolution of the instrument is about 1 cm−1. The variation curves of elemental concentrations in the axial direction of GRIN glass were obtained by electron microscopy (Tescan VEGA 3 SBH, Czech Republic) and energy dispersive spectrometer (Oxford EDS Inca Energy Coater) using the 25 µm per point method.
3. Results and discussion
3.1 Characterization of base glasses properties
The IR transmission spectra of six base glasses were shown in Fig. 1(a). With the increase of Te content, the refractive index and transmittance of this series of glass increase and decrease [13], respectively. This phenomenon is consistent with the theoretical relationship between transmittance (T) and refractive index (n): T = 2n/(1 + n2) [14]. In addition, the absorption peaks in Fig. 1(a) can be understood as H2O(2.86 µm and 6.31 µm), Se-H(4.57 µm), Ge-H(4.95 µm), and hetero-oxygen(12.9 µm nearby) peaks, respectively [15]. Figure 1(b) shows the refractive index of glasses with different Te content as a function of wavelength. It is clear that the refractive index of glass increases with the increase of Te content. Te atoms have high ionic polarizability and high relative atomic mass compared to Se atoms, so glass with high Te content has a large refractive index [16,17]. Furthermore, the refractive index of the base glasses at wavelengths of 8, 10.6, and 12 µm was given in Table 1.
Fig. 1. (a) The transmittance spectra of Ge-As-Se60-xTex glasses at 2.5-20µm (the sample thickness is 3 mm); (b) the relationship between refractive index and wavelength of Ge-As-Se60-xTex glasses; (c) differential scanning calorimetry (DSC) curves of Ge-As-Se60-xTex glasses; (d) density and the average atomic weight of the Ge-As-Se60-xTex glasses.
Table 1. The compositions, density, Tg, and refractive index (n) of Ge-As-Se60−xTex glasses
Figure 1(c) shows the DSC curves of the base glasses. Since the Te element in the ChGs replaces the Se element, the bonding energy between Te and other elements is smaller than that between Se and other elements, resulting in a decrease in Tg [18]. The maximum Tg difference is within 20 °C, as shown in Table 1. In addition, these glasses have no crystallization peak before 350 °C, showing good thermal stability [19]. These properties are precisely the requirements for the preparation of GRIN glass by thermal diffusion. The average atomic mass and density of each homogeneous glass are shown in Fig. 1(d). Since the relative atomic mass of Te (127.6 g/cm3) is greater than that of Se (78.96 g/cm3), the average atomic mass of ChGs with high Te content is greater. Moreover, the density obtained from practical tests based on Archimedes’ principle is positively correlated with the relative atomic mass.
Figure 2 shows the Raman spectra of Ge-As-Se60-xTex series glasses, which are consistent with the similar Ge-As-Se-Te system reported by Pumlianmunga et al. [20]. According to the principle of the chemical bond method (CBA) [21,22], the approximate proportion of different bonds in the glass in the Ge-As-Se-Te system can be known in advance [23]. Starting from Te > 32 mol%, the [GeTe4] tetrahedral structure gives rise to a weak peak near 125 cm−1 [15]. In addition, a Raman peak is also formed near 145 cm−1 as the Te content increases. The peak at 166 cm−1 is due to the antisymmetric bending vibration of AsTe3 [24]. The broad shoulder at 198 cm−1 should be attributed to the symmetric stretching of the GeSe4/2 tetrahedra with shared angles, and the peak intensity increases significantly with increasing Se elements [25,26]. It is known that the Ge-Se bond energy is the strongest in this glass system, and more Ge will preferentially bond with Se. The weak Raman peak near 240 cm−1 is mainly due to the influence of two vibrational modes of As-Se [26]. The inset of Fig. 2 shows the Raman spectrum of Ge-As-Se60. By comparison with the Raman spectra of Ge-As-Se60-xTex glasses, it can be seen that the Ge-As-Se60 glass does not have any significant Raman peaks before 170 cm−1. Therefore, it can be considered that the Raman peak before 170 cm−1 of Ge-As-Se60-xTex is mainly related to Te. Then we normalized Raman peak intensity at 166 cm−1 to allow for easy visualization of the changes in the Ge-Se dominant peak intensity at 198 cm−1 [27,28]. This change rule can effectively reflect the change of Se element content and refractive index distribution in axial GRIN glass, as shown below.
Fig. 2. The Raman spectra of Ge-As-Se60-xTex glasses, the inset shows the Raman spectrum of Ge-As-Se60 glass.
3.2 Characterization of glasses after diffusion
Regarding the unsteady-state diffusion of GRIN glasses, Fick's second law of diffusion is suitable for studying the diffusion process of elements between two glass interfaces [29]. The formula of Fick's second law of diffusion is shown as the following [30,31]:
Fig. 3. (a) The relationship between Raman intensity and diffusion depth of Te20-Te40 GRIN samples at different temperatures and times. (b) Comparison of Normalized Raman data and EDS Data for the characterization of GRIN samples. (c) Diffusion coefficients with different diffusing processes. (d) The transmittance spectra of GRIN sample (360°C 72 h) (The inset shows its IR photos).
To understand the effect of temperature and time on the diffusion characteristics between the two glass interfaces, the depth of glass diffusion at different times and temperatures explored in this study is shown in Fig. 3(a). The diffusion depth increases from 1.9 mm to 3.3 mm by appropriately extending the diffusion time at the same temperature. This phenomenon is consistent with the principle of Fick's second law. In the diffusion process, the concentration of any point will change with time, and the concentration change affects the diffusion flux, thus the diffusion distance changes. In addition, by increasing the diffusion temperature while maintaining the same diffusion time, the diffusion depth was increased by about 3 mm. Improving temperature increases the kinetic energy of atoms, thus increasing the diffusion efficiency. Figure 3(b) shows the comparison of Raman spectroscopy and EDS test results for the same sample, and it can be seen that the test results of the two methods are in good agreement, which verifies the accuracy of characterizing the diffusion performance of GRIN glass by Raman method. After analyzing the absolute error of both methods, the maximum value of absolute value error is close to 1 mol%. We also found that the Ge and As content do not undergo any change in diffusion, which is because there is no concentration difference in the double-layer glass. In addition, the diffusion coefficients of different diffusion processes were calculated according to Boltzmann-Matano method [32], as shown in Fig. 3(c). It can be found that the change in temperature and time will affect the change in diffusion coefficient. It is well known that the diffusion coefficient can change the refractive index distribution by the migration ability of atoms or molecules in the material. In the actual preparation process, in order to obtain the expected concentration (refractive index) profile, we can create a semi-infinite diffusion model, and the diffusion distance is less than the thickness of the sample. The diffusion coefficient and Eq. (1) are used to calculate the concentration at different positions, and then the expected results are achieved according to the corresponding temperature and time. Figure 4(d) shows the transmission of the GRIN sample, and there are some obvious absorption peaks without purification treatment.
Fig. 4. The refractive index (n@10.6 µm) as a function of normalized Raman intensity at 198 cm−1 (the dotted line is the result of function fitting).
The U.S. Naval Laboratory has demonstrated that the Raman peak intensity can be used as an indicator of element concentration in GRIN samples, and this Raman peak intensity is also related to the spatial variation of the refractive index [28,33]. Given this relationship, based on the known refractive index data (Fig. 1(b)) and Raman data (Fig. 2), the variation relationship of the refractive index (n @ 10.6µm) of the Ge-As-Se60-xTex series of glasses versus the normalized Raman intensity at 198 cm−1 of the glass is shown in Fig. 4. This variation relationship we can express in the equation as:
where A1 = 3.14205, A2= 2.73497, B = 0.3646, and C = 0.05295; Ri is denoted as the normalized Raman intensity. Figure 5(a) shows the refractive index and Raman intensity variations with axial depth, and note here that the refractive index is calculated from Raman data and Eq. (2). The region of refractive index and normalized Raman intensity variation is indicated between the two black dashed lines, and it can be seen that the refractive index difference at 10.6 µm wavelength is 0.277 at an axial variation depth of 5 mm. In addition, the GRIN glass sample was sliced at 0.7 mm intervals, and the refractive index of each glass sheet was measured using an ellipsometer, as shown in Fig. 5(b). The blue sphere in Fig. 5(a) is the refractive index data at 10.6 µm wavelength from Fig. 5(b), which is in basic agreement with the fitted refractive index variation curve. The absolute error of the two refractive indexes is 0.014. This confirms the reliability of characterizing the refractive index distribution with Raman intensity variations.Fig. 5. (a) The variation of refractive index (at 10.6 µm) and Raman intensity with axial depth (The refractive index was calculated from Raman intensity and Eq. (2)); the blue dots are the refractive index data measured by the ellipsometer at 10.6 µm. (b) The gradient refractive index was measured at 0.7 mm intervals along the axial direction.
Usually, Abbe number and partial dispersion represent the optical dispersion properties of glass materials. Optical designers can select the materials by selecting the appropriate Abbe number and partial dispersion. The Abbe number is defined as [34]:
And the partial dispersion is defined as [35]:
where nmid, nshort, and nlong represent the refractive index at the center, short, and long wavelengths, respectively. Similarly, the Abbe number of GRIN glass materials can be defined as:And the partial dispersion is defined as :
Fig. 6. (a) The refractive index difference between Ge-As-Se40Te20 and Ge-As-Se20Te40 glass. (b) Abbe number and (c) Partial Dispersion as functions of center wavelength for Ge-As-Se60-xTex (it is simplified as Tex in the d diagram) and the Te20-Te40 GRIN in LWIR spectral bands. (d) The glass diagram of Abbe number and partial dispersion of common infrared materials in LWIR band (containing relevant material from this paper)
3.3 GRIN glass design study
The main advantage of IR-GRIN material applied to LWIR imaging is that it can partially correct chromatic aberration and improve imaging quality [39]. Therefore, in this part, a Te20-Te40 GRIN singlet with F = 30 mm, f/3 was designed on the ZEMAX commercial optical software. GRIN singlet adopted GRIN material (360°C 72 h) in this work, and the refractive index distribution of GRIN singlet is shown in Fig. 5(a). Then the wavelength of the GRIN singlet was chosen to 8 µm, 10.6 µm, and 12 µm, and the field of view was set to on-axis and 1° off-axis, respectively. Some parameters of the singlet were optimized by Zemax to improve the focusing characteristics and correct the chromatic aberration. In the optimization process, the change of operand control parameters was used. The maximum refractive index and minimum refractive index at both ends of the lens are controlled by ZPLM, OPGT, and OPLT in order to prevent the system from continuously local optimization and the physical data from being inconsistent with the actual data of the material. ETGT and CTGT were used to control the center and edge thickness of the lens. In addition, CVVA, XDVA, and DIFF operands can be used to control the relationship between the GRIN profile and the front surface profile. EFFL operand was used to control the effective focal length. Each of the above operands selected different weight values to achieve the best singlet performance optimization. A 30 mm focal length, f/3 homogeneous Ge-As-Se20Te40 singlet was designed for comparison with the GRIN singlet. In addition, The diameter of these two singlets was set to 10 mm and the length is 5 mm.
As shown in the transverse ray fan diagram on the right side of Fig. 7, whether the field of view is 0° or 1°, the slopes of the meridian and the sagittal are approximately equal, and the directions are the same, indicating that the astigmatism is small. The three wavelengths have independent longitudinal focus, and the maximum separation is at the edge of the spectrum, indicating that there is a certain lateral color aberration. In addition, the RMS wavefront performance at 10.6 µm wavelength is 0.0362 wvs at 1 ° field of view.
Fig. 7. On the left is a schematic of a homogeneous Ge-As-Se20Te40 singlet (Rf = 29.5 mm, Rb = 51 mm). On the right is the transverse ray fan Plot with a scale of 100 µm. The upper right is a 1° field of view, and the lower right is a 0° field of view. The black, red, and blue curves refer to 8 µm, 10.6 µm, and 12 µm, respectively.
As shown on the left of Fig. 8, the right transverse ray fan diagram shows that the GRIN material significantly improves the performance, reducing the spot size and RMS wavefront performance (RMS wavefront performance is 0.0152 wvs at 10.6 µm) by a factor of about two. It is evident that GRIN material plays a role in correcting chromatic aberration and improving imaging quality. However, the separation of the spectral edges still exists, which indicates that there is still a certain axial color aberration. Therefore, GRIN and other suitable materials are required to form doublets or multiplets to optimize their optical performance further.
Fig. 8. On the left is a schematic of a GRIN Te20-Te40 singlet (Rf = 25.9 mm, Rb = 34.5 mm). On the right is the transverse ray fan Plot with a scale of 50 µm. The upper right is a 1° field of view, and the lower right is a 0° field of view. The black, red, and blue curves refer to 8 µm, 10.6 µm, and 12 µm, respectively.
4. Conclusion
In summary, a series of Ge20As20Se60-xTex high refractive index glasses with high refractive index difference, good thermal stability and similar Tg were prepared by replacing Se with Te. The GRIN glass was successfully prepared by thermal diffusion method. The gradient diffusion properties of GRIN glass in the axial direction were effectively demonstrated by Raman and EDS spectroscopy, respectively. By comparing with a homogeneous singlet, the results show that the GRIN singlet has significantly improved the performance, reducing the spot size and RMS wavefront performance by about half. In general, The GRIN glass in this work provides a new component selection for infrared optical designers and has broad application prospects in the future infrared broadband imaging optical system.
Funding
National Natural Science Foundation of China (61975086, 62375147); Key Research and Development Program of Zhejiang Province (2021C01025); Major Program of Natural Science Foundation of Zhejiang Province (LDT23F05012F05); Fundamental Research Funds for the Provincial Universities of Zhejiang (SJLY2022004); K. C. Wong Magna Fund at Ningbo University.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper may be available from the corresponding author upon reasonable request.
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