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Abstract
Third-order nonlinear optical properties of Ge10AsxTe90-x chalcogenide glasses were investigated utilizing the Z-scan method at the mid-infrared wavelengths of 2.5 and 3.0 µm. The compositional dependence of the third-order nonlinearity was analyzed, and their correlation with the refractive index and the optical bandgap was discussed. The results show that nonlinear refractive index n2 can be significantly enhanced by the addition of tellurium, and larger n2 values are observed at 3.0 µm rather than 2.5 µm due to the two-photon resonance effect, and the maximum of n2 is 4.96 × 10−13 cm2/W at the composition of Ge10As20Te70. In addition, the experimental results are in good agreement with the semi-empirical Miller’s rule whilst the variation of dispersive n2 values are in relatively good coincidence with the theoretical model by Sheik-Bahae et.al. for direct bandgap semiconductors.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Chalcogenide glasses, consisting of one or more chalcogen elements including S, Se, and Te that are covalently bonded with the other glass-forming elements like Ge, As, Sb etc., possess ultrahigh third-order optical nonlinearity χ(3) and broadband optical transmittance [1,2], thus are promising for various mid- & far-infrared photonic applications, such as environmental monitoring, biomedical sensing, energy research and supercontinuum generation [3–8]. For these applications, it is essential to investigate nonlinear optical properties of chalcogenide glasses for optimized compositions in the mid-infrared. This has been intensively performed in As-S-Se, Ag-As-Se, Ge-As-S(Se) and Ge-Sb-S(Se) [9–15], and several semi-empirical semiconductor models have been developed to predict the correlations of the optical nonlinearities with the other material properties such as optical bandgap energy Eg and linear refractive index n0. However, the transmission spectrum of S- and Se-based chalcogenide glasses is barriered at 12 µm and 15 µm, respectively [16,17], whilst extended long-wave transmission towards the far-infrared is sought by the emerging applications in environmental, biomedical, energy and astronomical sectors. By contrast, Te-based chalcogenide glasses are capable of exceptional long-wave transmission beyond 20 µm since Te is heavier element in contrast to S and Se, leading to lower lattice vibrational phonon energies [16,17]. Besides the outstanding long-wave transmission property, the advantages of Te-based chalcogenide glasses also include the highly linear refractive index for strong light confinement of photonic circuits, the significant nonlinear refractive index for all-optical signal processing [1,18] rapid reversible transition between crystalline and amorphous status for optical data storage [19] and so on. However, Te-based chalcogenide glasses have narrow glass-forming region, for example, GexTe1-x chalcogenide can only form bulk glasses in a range of 15 < x < 20 [20,21], thus the compositional tuneability for improved optical properties is restrained.
By adopting As into Ge-Te chalcogenide system, the glass-forming region of the ternary GexAsyTe1-x-y glass system is then extended so that the content of Ge can change from 0 to 15% and that of As is variable between 10% and 50%, so that screening the glass compositions for optimized nonlinear optical properties becomes possible in the ternary glass system. In this work, we set the Ge content as a constant value of 10 mol% and thus Ge10AsxTe90-x glasses with a varied As content from 15% to 55% were investigated for the correlations of As contents with the linear and nonlinear optical properties. The optical properties of the Ge10AsxTe90-x glasses like optical bandgap energy, refractive index and transmission spectra were investigated by using infrared spectroscopy and ellipsometer whilst the nonlinearities were characterized by using mid-infrared Z-scan method at the wavelengths of 2.5 µm and 3.0 µm. The dependence of nonlinear index on linear refractive index and the correlation of the dispersive nonlinearities with the optical bandgap energies were systemically analyzed following by the theorical predictions from the semi-empirical models.
2. Experiment
The bulk glasses were synthesized via the melt-quenching method from elemental Ge, As, and Te with 5N purity. The starting materials were weighted and then introduced into fused silica ampoules with an internal diameter of 10 mm. The ampoules were sealed under vacuum of 10−3 Pa, then placed into a rocking furnace homogenizing for no less than 12 h at 900 °C, and eventually quenched by cold water. In order to release the inner stress, the glass boules were subsequently annealed at 15°C below the glass transition temperature Tg for 5 h and then slowly cooled at a rate of 10°C/h to room temperature.
The transmission spectra of the glasses were characterized by utilizing a spectrometer (Lambda 950, PerkinElmer) in visible and near infrared region and a Fourier transform infrared spectrometer (Nicolet 380, Thermo Scientific) in a spectral range between 2.5 and 25 µm. The refractive index was measured by using an infrared variable angle spectroscopic ellipsometer (IR-VASE, J. A. Woollam, Lincoln, NE) ellipsometry in the range between 1.7-20 µm and was processed by using Cauchy model that had widely used for chalcogenide glasses.
For preparing the Z-scan samples, the glass boules were sectioned to flat disks of 1.0 mm thickness and then polished to optical quality. The Z-scan pump light was ∼170 fs pulses generated from an optical parametric amplifier (Orpheus-HP, Light Conversion, Lithuania) pumped by an Yb: KGW laser at a repetition rate of 100 kHz. To inhibit the scattering noise due to the laser instability, the pump light was split into two beams, so as one of the beams was monitored by a HgCdTe detector (S180C, Thorlabs, USA) as the reference light, and the other one was focused into gaussian beam by a 30 cm focal length optical lens as the pump light that was detected by another HgCdTe detector.
Z-scan technique was implemented to characterize both the nonlinear index and two-photon absorption of the Te-based chalcogenide glasses. The close aperture measurement acquires the nonlinear phase change information whilst the open aperture experiment is in regard to the two-photon nonlinear absorption. Because the two-photon absorptions of GexAsyTe1-x-y glasses were not negligible, we had to adopt the Z-scan fitting equations so that the influence of two-photon absorption was contemplated for the close aperture experimental results [22,23],
Figures 1(a)-(b) show the close aperture measurement on composition of Ge10As20Te70 glass at 2.5 and 3.0 µm respectively. These signals of all Ge10AsxTe90-x glass samples show similarities to each other: the pre-focal valley followed by a post-focal peak indicates a positive n2 due to self-focusing effect, whilst the gaps between valley and peak represent the value of the nonlinear phase change induced by the pulsed laser in the samples that is used to determine the nonlinear refractive index of the materials. Figure 1(c) is the open aperture measurement for varied As content compositions at 3.0 µm. The relation of the nonlinear absorption Ln(1-TOA) versus peak irradiance Ln(I0) is demonstrated in Fig. 1(d) in which a linear fitting with slope of 1.07 indicates that the dominant nonlinear absorption at the investigated wavelength is two-photon absorption [24].
Fig. 1. Closed-aperture Z-scans measurement and fittings for Ge10As20Te70 at 2.5 µm (a) and at 3.0 µm (b). (c) The open aperture measurement and the fitting for four compositions. (d) The linear fitting of Ln(1-TOA) vs peak irradiance Ln(I0). The slope of the fitting line determines the two-photon absorption.
3. Results and discussion
Figure 2 shows the transmission spectrum and linear refractive index for a Te-based chalcogenide glass with composition of Ge10As20Te70. The other compositions of this series of glasses show similar transmittances except the shifts on the short transmission edges due to the variation of optical bandgap energies. The values of linear index of Te-based chalcogenide are as high as >3.6 in mid-infrared leading to significant light confinement and manipulation capabilities. Such values are also in agreement with the reported values in Ref. [25].
Fig. 2. Optical transmittance spectrum and linear of refractive index dispersion for Ge10As20Te70 glass.
The optical band gap (Eg) was derived from the Tauc plots [26] using ultrathin glass samples with a thickness of 10-50 µm prepared by the hot-pressing method [27]. All the results were summarized in Table 1. The increase of Te content coincides with the decrease in Eg that is consistent with previous reports in Ge-Se-Te [18] and Ge-Se-Sb-Te [28] glasses. In chalcogenide glasses, usually the valence bands are dominated by the lone-pair electrons whilst the conduction bands are related to the antibonding orbitals [29]. Consequently, Eg decreases with the Te content because of the increase of Te-induced lone-pair electrons in the valence band so as rising of the highest occupied molecular orbital states [30].
Table 1. Bandgap energy (Eg), refractive index (n0), nonlinear refractive index (n2), two-photon absorption coefficient (β) and FOM = n2/βλ at 2.5 and 3.0 µm, respectively, for Ge10AsxTe90-x glasses.
In Table 1, the overall n2 values are above 10−13 cm2/W with a maximum value of 4.96 ×10−13 cm2/W at 3.0 µm. In comparison, As2S3, Ge11.5As24Se65.5 and AMTIR-1 chalcogenide glasses are reported of n2 values between 3.02×10−14 cm2/W and 8.31×10−14 cm2/W at 1.55 µm whilst their n2 values further decrease with increasing wavelengths [10–12,27,31]. So the maximum of n2 value for Ge10AsxTe90-x glasses at 3.0 µm is 5 to 15 times higher than those in the other chalcogenide glasses such as As2S3, Ge11.5As24Se65.5 and AMTIR-1, even taking their n2 value at 1.55 µm Meanwhile, significant enhancement of n2 is observed when the pump wavelength varies from 2.5 µm to 3.0 µm that is the evidence of two-photon resonance effect at the photon energies approaching the half of the bandgap energies.
Figures 3(a)-(c) show linear refractive index n0, nonlinear refractive index n2 and two-photon absorption coefficient β of Ge10AsxTe90-x glasses as functions of As content, respectively. According to Raman scattering [32,33] and x-ray photoelectron spectroscopy analysis [34], with increasing As content x in Ge10AsxTe90-x glasses, the numbers of Te-Te-Te trimmers and Te-Te-As(Ge) structural units decrease and finally disappear, while the perfect AsTe3/2 pyramidal and GeTe4/2 tetrahedral structure in Te-rich samples gradually transferred to defect structures including As-As and Ge-Ge homopolar bonds at x = 50. Therefore, the maximum and minimum values of n0 at x = 30 and 50 as shown in Fig. 3(a), appear to correspond to the chemical stoichiometric structure of Ge10As28Se62 ({GeTe2}0.1-{As2Te3}0.14) and the appearance of homopolar defective Ge-Ge bonds, respectively.
Fig. 3. (a) Linear refractive index, (b) nonlinear refractive index and (c) two-photon absorption coefficient as a function of As content in mol% at 2.5 µm (blue) and 3.0 µm (red).
In Fig. 3(b), the evolution of n2 does not exhibit clear threshold behaviors, probably due to the relatively larger error in the measurement of the nonlinearity on one hand. On the other hand, n2 might be more relevant to Eg since the ratio of 3.0 µm wavelength photon energy hv over Eg steps from 0.53 to 0.50 at x = 30 and 35 which is located at the peak and the sharp declining tail respectively of the two-photon resonance effect (as shown in Fig. 5(a) below). By contrast, the hv/Eg ratios of 2.5 µm wavelength range between 0.58-0.7 where n2 slowly change along the ratios so as the n2 keep almost still at 2.5 µm. Therefore, n2 exhibits a sharp decrease in the glass with As content from x = 30 to 35 at 3.0 µm as shown in Fig. 3(b).
In Fig. 3(c) the two-photon coefficient β generally exhibits larger values at Te-rich region whilst it becomes smaller in Te-poor glasses for both 2.5 and 3.0 µm. Nevertheless, an exceptional minimum β value is observed in Ge10As35Se55 ({GeTe2}0.1-{AsTe}0.35) near chemically stoichiometric composition, implying that the less number of defective bonds near the stoichiometric compositions is favorite to achieve lower nonlinear absorption in the glasses, although the difference of the β values is not so much.
The semi-empirical Miller’s rule demonstrates the relation between the linear and nonlinear susceptibility χ(3) written as [35],
Fig. 4. Variation of the nonlinear susceptibility versus (n02-1)/4π. Dashed lines are the theoretical fitting based on Eq. (5) at (a) 2.5 µm, and (b) 3.0 µm. The inset is the dependence of experimental n2 on n0.
Sheik-Bahae et.al. [36] have derived universal model to anticipate the dispersion of n2 for direct-gap semiconductors. Meanwhile, a different model was suggested by Dinu et.al. [37] for indirect-gap semiconductors. Figure 5(a) shows that the theoretical prediction of n2 from the Sheik-Bahae’s model (solid line) is in satisfactory agreement to the Z-scan results with the maximum n2 located at hv/Eg ≈0.54 due to the enhancement of two-photon resonance effect. Meanwhile, the two-photon absorption β is shown in Fig. 5(b), where the experimental result somehow resembles that predicted by Sheik-Bahae’s model although there is a relatively big mismatch. This is mainly due to the fact that, it is much easier to produce more defective bonds in Te-based glasses [28], and these defective bonds tend to form intermediate states in the bandgap of Ge10AsxTe90-x, leading to additional nonlinear absorption so that β does not vanish at half bandgap energy but remains significant. This also cause poor figure of merit (FOM) as listed in Table 1 that is impedible for nonlinear integrated photonic applications. Nevertheless, our experimental results seem to deviate from the Dinu’s model.
Fig. 5. (a). The behavior of normalized n2 as a function of hv/Eg. (b) The behavior of normalized two photon absorption as a function of hv/Eg. The squares are the experimental data, the solid line are the fitting curves based on Sheik-Bahae’s model and the dashed lines are Dinu’s model.
4. Summary
In summary, we found that, the nonlinear optical index n2 of Ge10AsxTe90-x measured at 3.0 µm is larger than that at 2.5 µm because of the two-photon resonance effect, and a maximum nonlinear index is 4.96 × 10−13 cm2/W at composition of Ge10As20Te70. We also analyzed the evolution of n0, n2 and β as a function of As content. It is found that, both maximum n0 and minimum β are in the glasses close to the stoichiometric composition, whilst n2 is more relevant to the variation of bandgap energies. While the data set of the n2 can be well fitted by the direct-gap semiconductor model provided by Sheik-Bahae, the evolution of β also follow variation trend described by Sheik-Bahae’s model, but do not extend far enough to confirm the consistency although the overall trend indicates a reasonable correlation exists. The inconsistency of β might be due to the absorption from the intermediate states formed by the large amount of defective bonds existed in the Te-based glasses. Nevertheless, large optical nonlinearity around 10−13 cm2/W, which is one/two order larger than that in S- and Se-based chalcogenide glasses, makes it promising for mid- and far-infrared nonlinear processing such as supercontinuum and comb generation. Meanwhile the large linear refractive index of Ge10AsxTe90-x glasses (3.60∼3.72) promises strengthened light confining and manipulating capabilities that are crucial for long wave light operation. Less defective glasses need to be sought around chemically stoichiometric compositions of Te-based glasses with aims to lower two-photon and intermediate state absorptions and thus improve FOM of integrated photonic devices.
Funding
National Natural Science Foundation of China (61575086, 61775109); 3315 Innovation Team in Ningbo City; the K. C. Wong Magna Fund in Ningbo University; Research Grants Council, University Grants Committee (8770006, 9048150); State Key Lab of Terahertz and Millimeter Waves (9360130, 9448001, 9605002); City University of Hong Kong Internal Grants (7005064, 7200572, 9610453).
Acknowledgements
This work is supported by the Natural Science Foundation of China (Grant No. 61775109, 61575086); 3315 Innovation Team in Ningbo City, Zhejiang Province, China; the K. C. Wong Magna Fund in Ningbo University, China; Research Council of Hong Kong (Grant No. 9048150, 8770006); State Key Lab of Terahertz and Millimeter Waves, City University of Hong Kong, Hong Kong SAR, China (Grant No. 9360130, 9605002, 9448001); City University of Hong Kong Internal Grants (Grant No. 9610453, 7005064, 7200572).
Disclosures
The authors declare no conflicts of interest.
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