The third-order nonlinear optical properties of GeS2-Sb2S3-CdS chalcogenide glasses were investigated utilizing the Z-scan and femtosecond time-resolved optical Kerr effect (OKE) methods at the wavelength of 800nm, respectively. The compositional dependences were analyzed and the influencing factors including the linear refractive index, the concentration of lone electron pairs, the optical bandgap and the amount of weak covalent/ homopolar bonds were discussed. A glass, i.e. 76GeS2·19Sb2S3·5CdS, with large nonlinear refrative index (n 2 = 5.63 × 10−14 cm2/W), low nonlinear absorption coefficient (β = 0.88 cm/GW) and minimum figure of merit was finally prepared. The electronic contribution in weak heterpolar covalent and homopolar bonds are responsible for large n 2 in chalcogenide glass, and the Sheik-Bahae rule combining the Moss rule are proved to be an effective guidance for estimating the third-order nonlinearities and further optimizing the compositions in chalcogenide glasses.
©2010 Optical Society of America
The rapid development of optical communication requires the novel materials with large and ultrafast nonlinear optical responses in the femtosecond or picosecond domain for fabricating the compact and low-threshold all-optical switching and processing devices. Among the developing materials, chalcogenide glasses are of particular interest due to their ultrafast (~100fs) and large nonlinearities which are generally several hundred times as large as that of silica, especially for the As and Se-contained ones [1–4]. Some all-optical switching applications have been demonstrated using the single-mode As2S3-based glass fiber [5,6], proving the great potential of chalcogenide glasses in all-optical network (AON).
One problem being faced at present is that the main contribution to large nonlinear refractive index n 2 in chalcogenide glass has not been cognized clearly therefore making confusion in glass composition’s design. In previous reports, some works related the value of nonlinear refractive index n 2 in chalcogenide glass with the concentration of lone electron pair . Some ascribed it to the two (or three, fore…)-photon resonant enhancement associated with red shift in the absorption edge [8,9]. Multiple covalent bonds with different polarity were also considered responsible for the n 2 variation following the compositional change . But the researches are limited and evidences are still not sufficient. On the other hand, much effort is required in the aspect of theoretical rules for estimating the third-order nonlinearities and further optimizing the compositions in chalcogenide glasses, considering the fact that the semiempirical Miller rule does not apply in many cases [11,12].
In this paper, we prepared the homogeneous GeS2-Sb2S3-CdS chalcogenide glasses. Compared with As and Se-based glasses, these glasses have advantages such as environmentally friendship, wider transparency in the visible region allowing lower two photon absorption and higher glass transition temperature permitting better resistance to thermal shock [13,14]. Their third-order nonlinearities’ dependences on composition were analyzed and the influencing factors were discussed. The comparison of theoretical results with the experimental ones is also processed. Our work was aimed at the elucidation of the influencing factors following the glass composition’s variation on the third-order nonlinearities, the affirmance of an effective theoretical guidance for estimating the third-order nonlinearities and further optimizing the compositions in chalcogenide glasses, and a search of new material for application in future all-optical switching devices.
2. Experimental procedure
The investigated samples were prepared by the melt-quenching technique from the high purity Ge, Sb and S (5N-purity) and spectral-grade CdS (4N-purity). Sample compositions (typically 8g) were sealed under vacuum (7 × 10−4 Pa) in quartz ampoules (10mm inner diameter) and heated gradually up to 970°C. After heated for12 hours, the melt was quenched in cold water and then annealed near the glass transition temperature for 2 hours. Samples were obtained after the glass rods were cut and polished to mirror smoothness. These samples have fine performances such as stria-free, the parallelism with 3 minutes of arc.
All optical and spectroscopic measurements were carried out at room temperature. The UV-Vis-NIR transmission spectra of the samples were recorded using the Shimadzu UV-3101PC spectrophotometer between 400 to 1100nm wavelength. Refractive indices were measured by using a Spectro-Ellipsometer (W-VASE32TM, J.A.Woollam, USA) between 400 to 1300nm wavelength. The third-order nonlinearities were measured using the Z-scan and femtosecond time-resolved optical Kerr effect (OKE) methods, respectively. The schematic pictures are shown in Fig. 1 .
In the Z-scan measurement, a laser pulse with 120fs pulse duration at 800nm was regenerated from a Ti: sapphire laser (UF-T2S, Spectra-Physics, USA). For avoiding the influence of laser radiation parameters’ instability, the input beam of the laser was divided into two parts. One beam was detected by Energy Probe D1 (Rjp735, Laser Probe Inc. USA) as reference light; the other acting as detecting one was focused on the prepared sample by a lens with 30 cm focal length and the transmitted light was detected by Energy Probe D2 (Rjp736, Laser Probe Inc. USA). The ratio of D2/D1 was given by a Dual Channel Energy Meter (Rjp7620, Laser Probe Inc. USA). An aperture was put in front of D2 during the close aperture Z-scan experiment’s performance and removed when the close aperture Z-scan experiment was carried out. The movement of sample with respect to the focal plane was performed by a stepper motor controlled by computer. On the other hand, in the OKE measurement, the input beam of the laser was split into two parts; one beam was used as the pump beam, the other as the probe beam. The pump pulses induce transient birefringence in the nonlinear sample and cause the polarization change of the probe light. The intensity of the probe pulses is kept small compared to the pump pulses (ratio; 1:10). The sample was positioned between a polarizer and an analyzer in a cross Nicole polarizer configuration. The polarization of the probe beam was rotated 45° with respect to the linear polarization of the pump beam. The OKE signals were detected by photomultiplier tube. The data were displayed and recorded by a computer that was also used to control the time delay between the pump and probe pulses by a stepping motor. Liquid carbon bisulfide (CS2) in a quartz cell with a thickness of 1.0mm was used as reference in the Z-scan and OKE measurements.
3.1 Transmission spectrum and Refractive index
The glass samples are all 0.94mm in thickness, presenting colors changing from yellow to red. Figure 2 shows the UV-Vis-NIR optical transmission spectrum of the 63GeS2·27Sb2S3·10CdS glass as an example. The largest transmittance for this sample is 65% and no absorption is found at the laser wavelength as 800nm as well. The transmission spectra of all samples are very similar to each other except for some shifts of the absorption edge, λ vis, which is defined as the wavelength for which the linear absorption coefficient is 10cm−1 and corresponds to respective optical bandgap, E g. The values of E g are listed in Table 1 .
In the GeS2-Sb2S3-CdS glasses, a monotonic decrease in E g with increasing Sb2S3 content is observed and expected in view of the loose electronic shell of Sb3+ ion and 5S2 outer-most electron. Whereas E g shows an inverse dependence on the CdS content, this mainly ascribes to the decrease of original metallic homo-bonds, i.e. Ge-Ge, Ge-Sb and Sb-Sb in glasses .
The refractive index of the 63GeS2·27Sb2S3·10CdS glass collected as a function of wavelength from 300~1300nm is also shown in Fig. 2. It follows as typical dispersion curves of chalcogenide glasses. The data of the refractive indices of investigated glasses at laser wavelengths 800 nm are summarized in Table 1, which are used for calculating third-order nonlinear susceptibility, and etc.. The refractive indices of these glasses are relatively high, which may induces large optical nonlinearities, therefore be rather beneficial for promising applications in all-optical devices. Furthermore, with the addition of Sb2S3, the refractive index increases monotonously, which is due to the larger polarizability of Sb3+ ions in comparison with Ge4+ ones’.
3.2 Z-Scan measurement result
Figure 3 shows the Z-scan signals of the 63GeS2·27Sb2S3·10CdS glass in the conditions of close and open apertures measurements, respectively. For elimination the calculation error due to nonlinear absorption, the close aperture measurement result in Fig. 3(a) has been normalized through the original result be divided by the open aperture measurement result.
Based on the fitting curves, the transmittance changes, and , are obtained from the relations and, in which S is the closed aperture parameter. The nonlinear refractive index n 2, the nonlinear absorption coefficient β and the third-order nonlinear susceptibility χ (3) are then determined using the following formulas 
The Z-scan measurement results of the examined glasses in the GeS2-Sb2S3-CdS system at 800 nm are presented in Table 1. Three serial glasses are included, i.e. Series I: (100-x)GeS2·xSb2S3 with x = 10,20,30,40; Series II: (100-x)(0.7GeS2·0.3Sb2S3)·xCdS with x = 0,10,20,30; Series III: Series 60GeS2·(40-x)Sb2S3·xCdS with x = 0,5,10,15. The compositional effects of Sb2S3 and CdS on the third-order nonlinearity are aimed to be investigated. The measurement result of the reference CS2 is also presented in Table 1, and the obtained value for n 2, i.e. 3.36 × 10−14 cm2/W is in good agreement with most of the published measurements .
From the results in Series I, it can be seen that with the increasing of Sb2S3, the n 2 increases obviously but the β increases drastically. The figure of merit FOM described as , which is considered to be a criterion to analyze the suitability of a glass for all optical switches, therefore decreases first and then increases. A best one, i.e. a minimum value of FOM = 2.76 is obtained when x = 20. From the results in Series II and III, it can be seen that with the increasing of CdS, the n 2 decreases but the β decreases simultaneously. It should be noticed that when x changes from 0 to 5 in Series II and when x changes from 0 to 10 in Series III, a drastic decrease of β is induced, resulting in a relatively satisfactory FOM in each series, respectively.
Based on the above results, another new glass composition, i.e. 76GeS2·19Sb2S3·5CdS is designed, which is come from 5mol% CdS addition into the composition of x = 20 in Series I: (100-x)GeS2·xSb2S3. Its fundamental optical parameters and third-order nonlinearities are also shown in Table 1. Its n 2 is calculated to be 5.63 × 10−14 cm2/W, which is about 200 times as large as that of silica. The β is estimated to be 0.88 cm/GW and the FOM is then determined to be 2.51.
For a glass material be expected to be used in all optical switches, FOM<1 is needed. Although the values of FOM for GeS2-Sb2S3-CdS chalcogenide glasses at 800 nm are higher than 1, early studies have indicated that the value of FOM depends on the wavelength of light mainly because of the variation of nonlinear absorption. For example, in Quemard’s study , the value of FOM for As40Se60 glass is higher than 1 at 1064nm but less than 1 at 1430nm. Therefore, FOMs<1 are expected for GeS2-Sb2S3-CdS chalcogenide glasses at 1330nm and 1550nm telecommunication wavelengths.
3.3 OKE measurement result
Figure 4(a) shows the optical Kerr signal of the reference CS2 at the wavelength of 800nm. The CS2 has an asymmetrical decay tail with over 1ps response originating from the molecular reorientation relaxation processes, i.e., the nuclear response. Under the same experimental conditions, the glassy samples were substituted for CS2 and some of the typical experimental results are shown in Fig. 4(b). The temporal profiles of the optical Kerr signals in these samples are symmetrical (Gaussian shape) with the full width at half maximum of 180fs, indicating an ultrafast third-order nonlinear response time ~100fs.
Using the standard procedure of reference measurement, the value of third-order optical nonlinear susceptibility, χ (3), of the sample can be calculated by the following equation :Table 1.
Comparing the values of χ (3) obtained from OKE measurement with those from Z-scan measurement indicates that the variation trends of χ (3) with the additions of Sb2S3 and CdS are accordant. But it is easy to be found that the values of χ (3) obtained from OKE measurement are generally higher than those from Z-scan measurement. The differences are approximately 5~20%, which probably come from the complex estimated error derived from respective ones in two measurements.
For the glass materials, the ultrafast third-order nonlinear optical responses originate from the distortion of electron cloud or the motion of nuclei. The former has a response time less than 10fs and the latter has a relaxation time lying between 100fs and 10ps. In our experiment, the pulse duration is 120fs; therefore the nuclear optical nonlinear contributions cannot be resolved. However, the nuclear optical nonlinear contribution is much smaller than the electronic part . Therefore, it can be deduced that the third-order nonlinear responses of the GeS2-Sb2S3-CdS chalcogenide glasses are produced dominantly by the electronic contribution.
For the composition dependence of third-order nonlinearity in chalcogenide glasses, several factors were put forward to explain it, and some fundamental properties such as linear refractive index, n 0, or optical bandgap, E g are considered to be related. In the following text, they will be detailedly discussed and verified.
Firstly, Semiempirical Miller rule  suggests a simple way to estimate the third-order nonlinear susceptibility, χ (3), of a material from the linear refractive index, n 0,
In Fig. 5 , the evolutions of experimental χ (3) obtained from Z-scan and OKE measurements as a function of n 0 are presented and the theoretical fitting curve basing on the Eq. (7) are also exhibited. It should be noticed that because there is a large difference between the original theoretical value from Eq. (7) and experimental one, a correction factor 1/A (A≈4) is deduced for the right side of the Eq. (7).
Secondly, according to the lone electron pair theory, large amount of lone electron pairs has positive effect on the n 2 of glass . In our experiment, the numbers of lone electron pair in related elements Ge, Sb, Cd, S are 0, 1, 0 and 2, respectively. From the composition and the density of the glass, the electronic lone pairs concentration in each glass can be calculated. The results indicate that the lone pairs concentration increases linearly with the amount of Sb2S3 increases (in Series I) in the glass, whereas decreases with the addition of CdS (in Series II and III). Figure 6 presents the variation of n 2 as a function of the lone pairs concentration in the examined GeS2-Sb2S3-CdS glasses. It can be seen that in each series, the n 2 increases with the increasing lone pairs concentration. It proves that the lone pairs concentration has positive effect on n 2. However, the disordered variation of n 2 in whole glass system after comparison indicates that the effect of parameters on n 2 are still complex. The amount of lone electron pairs cannot be a criterion for estimating the value of n 2.
Thirdly, for the n 2 and β optical nonlinearities in direct-gap semiconductors with E g, Sheik-Bahae et al.  have derived a universal rule, that is,
Figure 7 shows the evolutions of n 2 and β as a function of Eg in the examined GeS2-Sb2S3-CdS glasses. The squares are the experimental data and the solid lines are the fitting curves basing on the Sheik-Bahae’s rule, respectively. The spectral functions G and F, are obtained to be 0.2125 and 0.005 according to the fitting curves.
It can be seen that for n 2, the theoretical results basically have a same variation trend with the experimental ones, but still exhibit some marked deviations. For β, the theoretical results show satisfactory agreement with the experimental ones. This indicates that the Sheik-Bahae’s rule can be used for rough estimate in the glass’s optical nonlinearities.
Finally, some researchers have figured out that covalent, homopolar bonds have contribution to large n 2 in chalcogenide glasses [10,22]. In the GeS2-Sb2S3-CdS glasses, the bonds can be divided into three categories, i.e. the Ge-S and Sb-S covalent bonds, the Cd-S ionic bond and the Ge-Ge, Sb-Sb, Ge-Sb and S-S homopolar bonds deriving from compositional fluctuation. According to the experimental data of n 2 in Serial I (see Table 1), the Sb-S bonds are found to have larger contribution to n 2 in comparison with the Ge-S ones. This should be resulted from that the electronegativity of Sb is larger than Ge, and therefore the bond polarity of Sb-S is smaller than Ge-S, inducing a larger electron cloud’s distortion degree under laser pulse. On the other hand, in Serial II and III, the addition of CdS diminishes the amount of the Ge-S, Sb-S covalent bonds because of the corresponding decrease of GeS2 and Sb2S3 compositions in glass. Besides, the Ge-Ge, Sb-Sb and Ge-Sb metal- homopolar bonds are also dissolved because of the CdS’s disrupting role . Considering the fact that the n 2 decreases obviously in Serial II and III, negative effect of ionic bond to n 2 in chalcogenide glasses is therefore concluded. Similar variation trends of n 2 in previous reports [11,12] were also found, in the cases of other compounds’ addition such as PbI2 and KX(X = Cl, Br, I), proving the correct of above conclusion.
Although the addition of CdS has negative effect to n 2, its regulating role to E g should not be ignored. It is helpful to decrease the nonlinear absorption degree and therefore satisfactory FOM can be obtained after compositions’ optimization.
The third-order nonlinear susceptibilities, χ (3), obtained from Z-scan and OKE measurements almost coincided within the range of experimental errors. A glass with large nonlinear refractive index, n 2, low absorption, β, and minimum figure of merit can be obtained in GeS2-Sb2S3-CdS system by optimizing the amounts of Sb2S3 and CdS, resulting from their respective effect to n 2 and β. The third-order nonlinear responses of the glasses are produced dominantly by the electronic contribution in the weak covalent and homopolar bonds. The modified semiempirical Miller rule just roughly estimate the nonlinearities but the Sheik-Bahae rule combining the Moss rule are proved to have relatively good coincidence with the experimental results. It is an effective guidance for estimating the third-order nonlinearities and further optimizing the compositions in chalcogenide glasses. Although figure of merit FOM of GeS2-Sb2S3-CdS glasses tested at 800nm does not satisfy a standard criterion (FOM<1), it could be expected to decrease at 1330nm and 1550nm telecommunication wavelengths and therefore makes them potential candidates for applications in future all-optical switching devices.
This work was financially supported by the National Natural Science Foundation of China (NSFC, No. 60807034, 10874239 and 60907039), the Opening Research Fund of State Key Laboratory of Transient Optics and Photonics, and the “Hundreds of Talents Programs” from the Chinese Academy of Sciences.
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